Experimental charge density of organic nanocrystals revealed by 3D electron diffraction

Experimental charge density of organic nanocrystals revealed by 3D electron diffraction | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Experimental charge density of organic nanocrystals revealed by 3D electron diffraction Paulina Dominiak, Anil Kumar, Ashwin Suresh, Arianna Lanza, Jakub Wojciechowski, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7433721/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Charge density analysis is a cornerstone of quantum crystallography, offering deep insights into electron densities and chemical bonding in crystals, traditionally relying on high-resolution X-ray diffraction (XRD). Three-dimensional electron diffraction (3D ED) emerges as a powerful alternative, uniquely suited for micro- and nanocrystals and accurate hydrogen atoms localization due to a strong electron-matter interaction. This study presents a comprehensive experimental charge density analysis of L-alanine, urea, and L-tyrosine crystals using 3D ED. Incorporating dynamical scattering into multipole refinement allowed to model accurately electron density and simultaneously to reliably refine hydrogen positions and anisotropic displacements−beyond XRD limitations. Results align well with DFT and experimental XRD data, validating the approach. These findings establish 3D ED as a powerful and viable method for full charge density analysis for organic crystals, particularly in cases where conventional XRD is limited by small crystal size, difficulty in resolving hydrogen atoms, or reduced sensitivity to subtle electron density features. Physical sciences/Chemistry/Physical chemistry Physical sciences/Chemistry/Theoretical chemistry/Quantum chemistry Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Introduction Experimental charge density analysis has become an important tool in modern crystallography for elucidating the underlying electronic structure of materials 1 – 3 . By mapping the detailed electron density distribution within molecules and crystals, this approach offers critical insights into interatomic interactions that govern chemical bonding and molecular assembly. Several fundamental properties of interactions can be analyzed using this approach. For example, the spatial distribution of electrons in molecules and crystals can be visualized, allowing for direct observation of both radial and angular deformations in electron charge 4 – 9 . Additionally, the evaluation of topological features of the electron density and its associated Laplacian yields quantitative measures of bond strength and character, whether covalent, ionic, or intermediate 10 – 12 . Moreover, visualizing and quantifying electrostatic potential distributions allows for evaluating the effects of local charge variations on inter- and intramolecular interactions clarifying the balance between attractive and repulsive forces and facilitates investigation of evolving electrostatic interactions with precise energetic measurements 13 – 15 . Collectively, these fundamental electronic properties are intrinsically linked to the macroscopic behaviour and overall properties of materials. The kappa formalism 16 improves upon the independent atom model (IAM), wherein crystals are treated as collections of non-interacting, neutral atoms. While retaining spherical symmetry, in the kappa formalism two additional parameters are refined against experimental data: the valence electron populations ( P val ) and valence electron density expansion-contraction parameter ( κ ). This allows to describe charge transfer between atoms and estimate molecular dipole moments for example, overcoming the primary limitation of the IAM. One of the most widely adopted approaches for experimental charge density analysis is the multipolar model proposed by Hansen and Coppens 17 . In the Hansen-Coppens multipole formalism, the atomic electron density is modelled as aspherical and decomposed into three terms, as outlined below. $$\:{\rho\:}_{at}\left(\varvec{r}\right)=\:{\rho\:}_{core}\left(r\right)+{P}_{val}{\kappa\:}^{3}{\rho\:}_{val}\left(\kappa\:r\right)+\:\sum\:_{l=0}^{{l}_{max}}{\kappa\:}^{{\prime\:}3}{R}_{l}\left({\kappa\:}^{{\prime\:}}r\right)\sum\:_{m=0}^{+l}{P}_{lm}{d}_{lm\pm\:}(\theta\:,\phi\:)$$ The first term represents core electrons, assumed to remain unperturbed and non-interacting. The second term captures partial charge transfer via valence electron population ( P val ) and valence electron density expansion/contraction ( κ ) coefficients, constituting the kappa formalism. The third term models valence electron asphericity using a radial function R l ( κ'r ) and spherical harmonics d lm± (θ,φ) , together with their expansion/contraction ( κ' ), and population ( P lm ) coefficients. Charge density analysis based on the multipole formalism applied to high-resolution XRD data is well established and plays a crucial role in crystal engineering and pharmaceutical sciences by enhancing our understanding of non-covalent interactions and drug-receptor complex interactions 18 – 24 . Despite its significant contributions, this approach has notable limitations. First, high-resolution XRD requires relatively large crystals of high quality –a major challenge when working with small organic molecules and macromolecules. Second, the time consuming data collection time poses further difficulties, although the use of synchrotron radiation can mitigate this issue to some extent 25 . Moreover, a critical drawback of XRD data is that it is hardly possible to perform free refinement of hydrogen atom positions and atomic displacement parameters simultaneously with multipole model parameters 26 . Three-dimensional electron diffraction (3D ED), also known as MicroED, is a recent addition to the structural science toolbox that effectively addresses challenges associated with analyzing micro- and nanocrystals 27 and the accurate localization of hydrogen atoms 28 . Initially introduced by Kolb et al. 29 and subsequently adapted into several variants 30 – 36 . 3D ED has advanced significantly over the past decade, driven by ultrafast data acquisition from nanocrystals. The technique is particularly well suited for studying micro- and nanocrystals because electrons, as charged particles, interact with matter approximately 10 4 times more strongly than X-rays. Electrons are scattered by the electrostatic (Coulombic) potential of the sample, which arises from both atomic nuclei and electron clouds. Since the positive potential of nuclei is largely cancelled by the negative potential of electrons, 3D ED in fact probes the difference between these two contributions. Consequently, hydrogen atom localization is facilitated, as protons are largely de-shielded due to the absence of core electrons and the high polarization of their valence electrons towards covalent partners. Moreover, electron charge transfer between atoms leads to significant changes in their electrostatic potential and thus their scattering power, particularly at low scattering angles 32 , 37 , 38 . This effect is only weakly dependent on the atomic number and may remain still relatively large for heavier elements 39 . Thus, 3D ED data may allow for the free refinement of hydrogen atom positions and anisotropic atomic displacement parameters (ADPs) along with electron density-deformation parameters. Moreover, valence electron charge transfer as well as radial and angular deformations of the valence electron charge density distribution should be easier to capture by multipole model refinement, even for atoms dominated by the core electron density. One reason why 3D ED is not yet widely used for charge density studies is that it is significantly impacted by dynamical diffraction. When this effect is neglected, and only the kinematic approximation is used, the resulting fit to the experimental data is poor, the refinement results in poor refinement statistics, the structural models may suffer from large inaccuracies and extracting detailed structure information becomes exceedingly difficult, making kinematical refinement unsuitable for charge density studies 40 . Pioneering experimental charge density studies using electron diffraction data for inorganic crystals 41 , 42 were initially performed as full multipole model refinement under the kinematical approximation or dynamically corrected CBED data combined with XRD data. A possibility to study chemical bonding in organic crystal using 3D ED data by refinemenent of spherical charge density model involving a mid-bond charge-clouds complemented with dynamical diffraction theory was shown for the first time by Wu and Spence 43 . Recently, advanced computational methods based on Bloch wave calculations have enabled the dynamical refinement of 3D ED data, routinely yielding improved structural models 44 , 45 and making dynamical kappa refinement on inorganic crystals possible 46 . Combined with the current ability to collect high-resolution, high-quality 3D ED data with limited beam damage 40 , these developments now open the possibility of performing full multipole model refinements also on organic crystals using the dynamical refinement approach, thereby extending charge density analysis to nanocrystalline samples. In this study, we performed the experimental charge density analysis using 3D ED data on three organic crystals. High-resolution 3D ED data for L-alanine, urea and L-tyrosine were collected and subjected to full multipole refinement using the dynamical diffraction approach. We compare our results with multipole refinement results obtained from simulated electron diffraction data based on DFT calculations as well as high-resolution experimental XRD data, thereby validating the obtained models and elucidating the differences and similarities between 3D ED and XRD. Results Experimental charge density analysis requires good-quality high-resolution diffraction data. We have selected L-alanine, urea and L-tyrosine molecules for the experimental charge density analysis on 3D ED data primarily because their crystals are relatively stable under the electron beam, i.e., they are less prone to radiation damage. Moreover, the experimental charge density analyses for L-alanine and urea from XRD data are well documented in the literature 47 , 48 , constituting excellent reference data as well as proving that good quality crystals can be grown for these compounds. Surprisingly, there was no experimental charge density analysis for L-tyrosine molecules from XRD data available in the literature. Therefore, for this work, we additionally collected high-quality high-resolution XRD data for L-tyrosine and performed the experimental charge density analysis for reference. Excellent quality single crystals of the compounds L-alanine, urea and L-tyrosine ( Fig. S1 ) were selected for the 3D ED data collection in the continuous rotation mode at a temperature of 100 K. The data were extracted up to the resolution of 0.44 Å, 0.53 Å, and 0.59 Å, respectively (Table 1 ). At these resolutions, relatively high completeness was achieved for all three compounds (around 90%). The R int values of all three data sets, in the range of 12.5–16.7%, are quite low for electron diffraction data, and indicate a high data quality, although it should be noted that the R int has only a limited predictive power in the presence of strong dynamical effects. The kinematical IAM refinements were performed on the 3D ED data for crystals of all three compounds and yielded figures of merit ( R 1 -factors) in the range of 15.2–18.4% ( Table S1 ) and structure models of quality not satisfactory to perform the charge density analysis. In all subsequent steps, the dynamical effects were taken into account, and both dynamical IAM and, subsequently, dynamical multipole model refinements were performed using the dynamical refinement approach. During the dynamical refinements, the thickness, shape and mosaicity of the crystal were taken into account. The multipole refinements were initiated from the results of a Transferable Aspherical Atom Model (TAAM) refinements, utilizing multipole parameters taken from the MATTS data bank (see Materials and SI for further details). These parameters provided a physically meaningful and chemically realistic starting point for the dynamical multipole model refinements. This initial step is essential because multipole model refinements involve optimizing a large number of correlated parameters on top of the, already computationally expensive, dynamical refinement. Starting from MATTS-derived parameters speeds up the convergence and improves the likelihood of converging to a physically reasonable and global or near-global minimum, rather than trapping the refinement in nonphysical local minima. The quality of the multipole model refinements on experimental 3D ED data was evaluated by analyzing the residual Fourier maps and merged R-factors 44 (MR-factors, calculated by performing symmetry-averaging of intensities) to judge the quality of the model fit to the data, and by analyzing the physical correctness of the refined multipole models. For the latter, we focused on atomic charges computed from P val ( q = N va l – P val , where N val is the number of valence electrons in a neutral atom), κ and κ' values, deformation electron density, electrostatic potential and electron density topology. The results were compared with the properties computed from the multipole models refined against theoretical electron static structure factors obtained from periodic DFT calculation and experimental high-resolution XRD data. The details of the qualitative and quantitative charge density analyses for each compound are discussed in the following subsections. From now on, the multipole model refinements against experimental 3D ED data, against theoretical electron static structure factors, and against experimental XRD data will be referred to as eMM exp , eMM theo and xMM exp , respectively. Similarly, the dynamical IAM refinements against 3D ED data are denoted eIAM exp . L-alanine IAM refinement In the eIAM exp refinement of L-alanine, the coordinates and anisotropic ADPs of all the atoms, including hydrogen, were refined freely, i.e. no restraints or constraints were used during the refinement. After eIAM exp refinement, the ADPs of all the atoms were positive definite (Fig. 1 a ) . The M R 1 (obs) was 6.15%, and the residual electrostatic potential maximum and minimum values were 0.274/-0.313 e Å −1 (Table 1 ). The 3D Fourier map of the residual electrostatic potential showed that despite the relatively good model and model-to-data fit, some unmodelled information was still present in the data (Fig. 1 b), justifying the usage of more sophisticated multipole model. Multipole model refinement For L-alanine, the refinement of multipole parameters associated with the oxygen atoms required special handling due to convergence issues and parameter correlations. Initially, the spherical harmonic coefficients P lm for oxygen were constrained to their values from the MATTS data bank to stabilize the refinement. Following the convergence of all other parameters, the P lm values for oxygen along with their associated valence population ( P val ), and expansion/contraction parameters ( κ and κ′ ) were released and refined. Subsequently, the remaining parameters were refined again with the updated P lm values of oxygen atoms fixed, ensuring internal consistency and stability in the final model. The eMM exp refinement resulted in improvements in the refinement statistics (Table 1 ) and better structural model (Fig. 1 c-d). The Fourier residual electrostatic potential maps (Fig. 1 e) clearly indicated the better fit of the eMM exp model to the data compared to eIAM exp (Fig. 1 b). The X–H bond lengths (Fig. 1 c) obtained from the eMM exp were systematically shorter compared to eIAM exp , by 0.04 Å ( Table S2 ), and more similar to the reference bond lengths from eMM theo (RMSD of 0.01 Å) and from xMM exp (RMSD by 0.01 Å). It is worth noticing that in the eMM theo , model the X–H bond lengths resulted from the DFT geometry optimization, and in the xMM exp model the mean values from neutron 49 diffraction were used as constraints. The anisotropic ADPs of H-atoms were improved after the multipole refinement (Fig. 1 d ) , though some still resulted in ellipsoids having their orientation and shape at the border of being physically correct. The resulting U eq of the H-atoms of eMM exp falls in between the U eq values from neutron diffraction data 50 collected at 60 K and 295 K, and much closer to the 60 K (Fig. S2 ), indicating that overall magnitudes of hydrogen atom displacements were physically correct. U eq for non-hydrogen atoms of eMM exp also had an appropriate magnitude compared to neutron diffraction data and were very similar to U eq from xMM exp . The chemically plausible atomic charges confirmed the accuracy of the eMM exp model. The majority of the atoms followed the same trend as seen in the reference eMM theo and xMM exp models, except N1 and C2 atoms (Fig. 1 f). The root mean square differences in atomic charges between eMM exp and any of the reference models (0.14 e and 0.10 e for eMM theo and xMM exp , respectively, except the N1 and C2, ( Table S2 ) were not larger than the RMSD between the two reference models (0.14 e), and only slightly larger than the mean e.s.d. for P val parameters from eMM exp . Moreover, the κ and κ' values from eMM exp were in the physically acceptable range (oscillating around 1.0) (Fig. 1 g-h) and the agreement with the eMM theo and xMM exp (RMSDs of 0.07 and 0.10 for κ and κ' , respectively) is comparable with the agreement between the two reference models (RMSD of 0.06 and 0.09 for κ and κ' , respectively). Deformation electron density, electrostatic potential and QTAIM topology properties (dup: abstract ?) The deformation of electron density maps of L-alanine computed from eMM exp highlighted the accurate features of covalent bond densities, locations, and orientations of the lone electron pairs (Fig. 2 a) and regions of depletion of electron densities around the molecule ( Fig. S3a ), which is confirmed by qualitative agreement with the reference eMM theo and xMM exp (Fig. 2 b-c, Fig. S3b-c ). The molecular electrostatic potential of L-alanine calculated from the eMM exp and plotted on the molecular surface allowed to identify the electropositive, neutral, and electronegative regions in the molecule, helping to understand the nature of the intermolecular interactions (Fig. 2 d ) . The oxygen atoms of the carboxyl group and hydrogen atoms of the ammonium group had electronegative and electropositive surfaces, respectively, whereas the methyl group had a neutral potential surface, which agreed with the reference eMM theo and xMM exp models (Fig. 2 d-e). Quantitatively, the surface potential maxima and minima from eMM exp and eMM theo agreed very well ( Table S3 ), while xMM exp potentials were slightly shifted towards negative values. The small differences may be the result of the different sensitivity of X-ray radiation to the charge distribution as well as the usage of fixed averaged neutron-diffraction H positions and estimated ADPs. The QTAIM 51 topological analysis of electron density calculated from the eMM exp of L-alanine crystal showed to be useful to further characterize the nature of covalent and intermolecular interactions. Bonding paths (BP) for all expected covalent bonds were identified, and all hydrogen bonding interactions were found (Fig. 3 a ) as observed in the reference models ( Fig. S4a-b ). The maps of ▽ 2 ρ bcp showed all characteristic features of covalent bonds, electron pairs and hydrogen bonding interactions (Fig. 3 b, Fig. S5a-e ). The topological values at bond critical points (BCPs) ( ρ bcp , ▽ 2 ρ bcp and R ij ) obtained from eMM exp were comparable with the reference values from eMM theo and xMM exp (Fig. 3 c-f, Fig. S6 , Table S4-S5 ). They clearly indicated, especially by the sign of ▽ 2 ρ bcp at the BCP, which interactions were covalent (▽ 2 ρ bcp 0). For covalent bonds, the differences between topological values from eMM exp and the reference eMM theo and xMM exp were not much larger than the difference between the eMM theo and xMM exp themselves (0.2 e Å −3 vs. 0.1 e Å −3 for ρ bcp , and 6–8 e Å −5 vs. 4 e Å −5 for ▽ 2 ρ bcp , Table S2 ). In the case of hydrogen bonding, the topological values of eMM exp for the H···Acceptor interactions were on average slightly closer to the reference eMM theo (0.03e Å −3 for ρ bcp and 0.3 e Å −5 for ▽ 2 ρ bcp ) than the xMM exp was to eMM theo (by 0.04 e Å −3 for ρ bcp and 0.4 e Å −5 for ▽ 2 ρ bcp ). This proves that the refinement of hydrogen atomic positions and anisotropic ADPs leads not only to improved geometry but also improved electron density properties. Table 1 Crystal data and refinement parameters against 3D ED data for dynamical IAM and multipole refinement Parameters L-alanine Urea L-tyrosine Space group P 2 1 2 1 2 1 P -42 1 m P 2 1 2 1 2 1 Unit cell a , b , c (Å) 5.7691(4), 5.9494(4), 12.2453(7) 5.6308(4), 5.6308(4), 4.7145(10) 5.8283(9), 6.8709(12), 21.136(4) Angles α, β, γ (°) 90, 90, 90 90, 90, 90 90, 90, 90 Volume (Å 3 ) 420.29(4) 149.48(3) 846.4(2) Resolution (Å) 0.44 0.53 0.59 Completeness (%) 99 95.5 90.3 R int obs (%) 12.51 16.26 16.65 Dynamical IAM Refinement Rsg 0.66 0.7 0.66 Thickness model wedge wedge wedge Thickness (Å) 2468.72 2110.34 3000.74 Tilt correction -0.063 0.086 0.473 Isotropic mosaicity (°) 0.018 0.023 0.0001 Reflection used obs [ I > 3σ(I) ]/ all 5473/10640 1368/2663 5708/7864 Constraints/ Restraints/ Parameters 0/0/178 0/0/91 0/0/265 R 1 obs [ I > 3σ(I) ]/ all (%) 8.00/10.49 8.15/12.17 5.30/6.26 wR 1 obs [ I > 3σ(I) ]/ all (%) 8.82/9.08 9.06/9.42 5.74/5.92 No. of reflection after symmetry averaging (obs [ I > 3σ(I) ]/all) 2902/5027 380/588 3323/3989 M R 1 obs [ I > 3σ(I) ]/ M R 1 all /M wR 1 all (%) 6.15/7.89/7.18 6.61/8.80/7.22 4.68/5.19/5.28 GooF obs/all 3.27/2.41 3.06/2.28 1.80/1.58 Residual potential max./min. (e Å −1 ) 0.274/-0.313 0.314/-0.264 0.228/-0.245 Dynamical multipole refinement Thickness (Å) 2646.55 2217.54 3099.52 Tilt correction -0.051 0.084 0.492 Isotropic mosaicity (°) 0.020 0.041 0.0001 Reflection used obs [ I > 3σ(I) ]/ all 5475/10642 1373/2668 5708/7864 Constraints/ Restraints/ Parameters 0/0/215 0/0/113 0/0/348 R 1 obs [ I > 3σ(I) ]/ all (%) 7.35/9.75 7.36/11.0 4.08/4.99 wR 1 obs [ I > 3σ(I) ]/ all (%) 8.10/8.35 8.08/8.40 4.30/4.52 No. of reflection after symmetry averaging (obs [ I > 3σ(I) ]/ all) 2902/5027 380/588 3323/3989 M R 1 obs [ I > 3σ(I) ]/ M R 1 all/ M wR 1 all (%) 5.41/7.06/6.36 5.43/7.36/6.28 3.50/3.99/3.82 GooF obs/all 3.01/2.22 2.77/2.06 1.36/1.21 Residual potential max./min. (e Å −1 ) 0.253/-0.239 0.241/0.218 0.147/-0.141 Urea IAM refinement Consistent with the L-alanine refinement protocol, no restraints or constraints were applied to the atomic coordinates or ADPs of any atoms during the eIAM exp refinement. Following the eIAM exp refinement, the ADPs for all atoms were positive definite (Fig. 4 a), with M R 1 (obs) value of 6.61% and the residual electrostatic potential map (Fig. 4 b) maximum and minimum peaks of + 0.314 e Å - 1 and − 0.264 e Å −1 , respectively. Multipole refinement The eMM exp refinement of urea resulted in the improvement of the refinement statistics (Table 1 ) and a better structural model (Fig. 4 c-d). The M R 1 (obs) was 5.43%. The 3D Fourier maps (Fig. 4 e) showed a dramatic improvement after the multipole refinement compared to eIAM exp (Fig. 4 b), indicating a better fit of the model to experimental 3D ED data. The N–H bond lengths became shorter by 0.09 Å after the multipole refinement compared to eIAM exp (Fig. 4 c, Table S6 ), one of the bonds approached the reference values from eMM theo and xMM exp , the second became too short by 0.05 Å. The ADPs of hydrogen atoms were visibly improved after the multipole refinement (Fig. 4 d ) , although ellipsoids representing them were not ideally oriented and still slightly elongated in one direction. The U eq values of both non-hydrogen and hydrogen atoms of eMM exp were comparable to neutron diffraction data 52 collected at 123 K ( Fig. S7 ). The chemically appropriate atomic charges confirmed the accuracy of the multipole model of eMM exp, and those were similar to the charges of eMM theo and xMM exp , with a RMSD of 0.21 e and 0.16 e ( Table S6 ), which is within ca. one e.s.d. for P val (Fig. 4 f). The κ and κ' values of eMM exp were also in the physically acceptable ranges and similar to reference eMM theo and xMM exp (Fig. 4 g-h). Especially the κ' values were closer to the reference eMM theo (RMSD of 0.14) than the values of xMM exp (RMSD of 0.21). Deformation electron density, electrostatic potential and QTAIM topology properties The 2D deformation density maps (Fig. 5 a-c, Fig. S8 ) highlighted the accurate features of chemical bonding and lone electron pairs in the urea molecule. While the C-N bond density in the eMM exp map showed minor imperfections, it remained within an acceptable range for qualitative analysis. The electrostatic potentials on the urea molecular surfaces in all three models (eMM exp , eMM theo and xMM exp ) were qualitatively similar (Fig. 5 d-f) showing positive regions near hydrogen atoms and negative regions near electronegative oxygen atoms. Quantitatively, the positive surface potentials from eMM exp were comparable to eMM theo and xMM exp positive potentials, but the negative surface potentials were distinct ( Tables S7 ). Topological analysis of the eMM exp electron density revealed bonding paths for all expected covalent bonds and all hydrogen bonding interactions (Fig. 6 a, Fig. S9a-b ). Qualitatively, maps of ▽ 2 ρ bcp for eMM exp show all characteristic features of covalent bonds and electron pairs, with the exception of the lack of separate maxima for the C1 atom in the directions of the N1 atoms (Fig. 6 b, Fig. S9c-d ). Nevertheless, the topological values of ρ bcp at BCPs of covalent bonds and hydrogen bonding interactions for eMM exp were in the acceptable range (Fig. 6 c-e, Table S8-S9 ) and similar to the reference eMM theo and xMM exp (with RMSDs of 0.32 e Å −3 and 0.42 e Å −3 , respectively, for covalent bonds, and 0.03 e Å −3 and 0.04 e Å −3 , respectively, for H···Acceptor interactions, Table S6 ). The differences between the two reference models were almost the same (RMDS 0.26 e Å −3 ) for covalent bonds and slightly smaller (0.01 e Å −3 ) for H···Acceptor interactions. The values for ▽ 2 ρ bcp at BCPs agreed relatively well with the reference (Fig. 6 d-f, Table S8-S9 ) only for non-hydrogen covalent bonds, with a difference of 10.56 e Å −5 and 19.08 e Å −5 from eMM theo and xMM exp , respectively, where the difference between eMM theo and xMM exp was 11.90 e Å −5 ( Table S6 ). ▽ 2 ρ bcp values for the N–H covalent bonds and the H···Acceptor interactions for eMM exp were distinct from the reference values. The bond path lengths ( R ij ) for covalent bond and H···Acceptor interactions of eMM exp were similar to the reference models (Fig. S10) L-tyrosine IAM refinement During the eIAM exp refinement of L-tyrosine, atomic coordinates and ADPs of all atoms, including hydrogen, were refined freely without restraints or constraints. All refined ADPs were positive definite, except for two hydrogen atoms (Fig. 7 a). The M R 1 (obs) was 4.68% and the residual electrostatic potential maximum and minimum values were 0.228/-0.245 e Å −1 with the corresponding 3D Fourier map of the electrostatic potential showing many unmodelled negative peaks in the molecule region (Fig. 7 b). Multipole model refinement In the case of L-tyrosine, multipole model parameters − specifically the spherical harmonic coefficients ( P lm ) and expansion/contraction parameters ( κ and κ’ ) − were constrained to be identical for chemically equivalent atom types to maintain chemical consistency and reduce the number of independent parameters during the refinement. The eMM exp refinement significantly improved both the statistical indicators (Table 1 ) and the overall quality of the structural model (Fig. 7 c-d). The M R 1 (obs) improved to 3.50% and maximum and minimum residual potential peaks reduced to 0.147/-0.141 e Å −1 . The enhanced quality of the Fourier maps after the eMM exp refinement (Fig. 7 e) demonstrates a markedly improved fit of the model to the experimental 3D ED data. The X–H bond lengths were refined to more accurate values compared to those obtained from the eIAM exp model; they shortened by 0.04 Å (Fig. 7 c, Table S10 ). While bond lengths from eMM exp remained slightly longer than those from eMM theo and xMM exp (by 0.02 Å), they still showed clear improvement. Notably, the ADPs of hydrogen atoms became more reliable and positive definite after multipole refinement (Fig. 7 d). The magnitude of ADPs for non-hydrogen atoms were, however, slightly larger than the reference xMM exp , as judged from the U eq values ( Fig. S11 ). The accuracy of the final eMM exp model was further validated through the charges based on P val , and κ and κ' values. The charge values matched the eMM theo and xMM exp values well (Fig. 7 f-g), with the RMSD of 0.21 e in both cases ( Table S10 ). Interestingly, only a slightly smaller spread of values was observed also between eMM theo and xMM exp refinements (RMSD 0.17 e). The κ and κ' values for non-hydrogen atoms from eMM exp were also in an acceptable range and similar to eMM theo and xMM exp, with the possible exception of κ' (C7) (Fig. 7 h,j). The RMSDs for κ parameters were 0.02 and 0.02, respectively, and for κ' parameters were 0.11 and 0.19, respectively ( Table S10 ), comparable to the RMSDs between the two reference models (0.02 for κ and 0.12 for κ' ). The RMSDs among κ and κ' values for hydrogen atoms were somewhat bigger for κ (0.04 and 0.07 for eMM theo and xMM exp , respectively) and similar for κ' (0.13 and 0.10 for eMM theo and xMM exp , respectively), but still comparable to RMSDs between the two reference models (0.09 for κ and 0.05 for κ' ) (Fig. 7 i,k). Deformation electron density, electrostatic potential and QTAIM topology properties Deformation electron density features of L-tyrosine, such as bond charge accumulation and lone-pair localization, were clearly observed in the eMM exp model (Fig. 8 a,b, Fig. S12a ). In particular, the lone-pair electron density on the carboxyl and hydroxyl oxygen atoms was distinctly resolved in the eMM exp map and was in qualitative agreement with the eMM theo (Fig. 8 c-d, Fig. S12b ) and xMM exp (Fig. 8 e-f, Fig. S12c ) models. The deformation density across the aromatic ring in eMM exp also revealed π-electron delocalization and chemically meaningful bonding features, with exception of the C7 atom which appeared less aspherical. The electrostatic potential for L-tyrosine calculated from the eMM exp model (Fig. 8 g ) showed regions of negative potential localized around the carboxyl and hydroxyl oxygen atoms, while regions of positive potential were centred on hydrogen atoms. The π-system of the aromatic ring exhibited a near-neutral to slightly negative potential, consistent with delocalized electron density. Qualitatively, the electrostatic potential of eMM exp model mapped on the molecular surface agreed very well with the reference (Fig. 8 h-i). Quantitatively, the positive and negative surface potentials from eMM exp and eMM theo agreed very well ( Table S11 ), while the negative potentials of xMM exp were slightly shifted. The small differences may reflect the fact that X-ray scattering exhibits different sensitivity to charge distribution than electron scattering. It might also result from the usage of fixed, averaged neutron diffraction hydrogen positions. Topological analysis of eMM exp revealed all covalent bond paths, and all intermolecular hydrogen bonding seen in the reference models (Fig. 9 a, Fig. S13a-b ). The overall distribution of ∇² ρ bcp for eMM exp qualitatively agrees with the reference distributions, reproducing well regions of positive and negative ∇² ρ bcp , and the presence of local maxima ∇² ρ bcp associated with electron pairs (Fig. 9 b, Fig. S14a-e ). While ρ bcp and ∇² ρ bcp of covalent bonds derived from eMM exp for L-tyrosine were generally lower than those from the eMM theo and xMM exp (by 0.21 e Å −3 and 0.31 e Å −3 , respectively, for ρ bcp and by 7.93 e Å −5 and 10.41 e Å −5 , respectively, for ∇² ρ bcp ), they exhibited similar overall trends and remained within physically acceptable ranges (Fig. 9 c-f, Table S12 ). The RMSDs between the two reference models were only ca . twice smaller (0.15 e Å −3 for ρ bcp and 5.15 e Å −5 for ∇² ρ bcp ). For intermolecular hydrogen bonding, the eMM exp model reproduced quite well the ρ bcp and ∇² ρ bcp values at BCPs of H···Acceptor interactions seen in both reference eMM theo and xMM exp models, with the exception of the H9···O2 contact (Fig. 9 g-h, Table S13) . The bond path lengths ( R ij ) for covalent bond and H···Acceptor interactions of eMM exp were similar to the reference models (Fig. S11) Discussion This study establishes the feasibility of performing full multipole charge density analysis using 3D ED data for organic nanocrystals. A central procedural challenge is the complexity of the refinement, which necessitated starting from (TAAM) rather than the conventional IAM. Multipole refinement involves optimization of a large number of correlated parameters (e.g., P lm , P val , κ , κ′ , ADPs). This creates a rugged refinement landscape with numerous local minima and makes the refinement highly sensitive to the initial conditions. Starting from the IAM, which is a poor approximation of the aspherical charge distribution, frequently leads to trapping of the refinement in false minima with non-physical parameters. The TAAM, by providing a chemically-informed and physically realistic starting point, effectively guides the refinement toward the global minimum, ensuring convergence to a meaningful and stable charge density model. While the final M R 1 (obs) values for eMM exp refinements (ranging from 3.50–5.43%) were significantly lower than for dynamical IAM models, they remained higher than typical values seen in X-ray-based charge density studies. This discrepancy arises mainly from the intrinsic differences in the scattering mechanisms: 3D ED data are influenced by strong dynamical diffraction effects, which are inherently more challenging to model than X-ray data for which the kinematical approximation is sufficient. Additionally, the impossibility to collect highly redundant data that could improve the signal-to-noise ratio, and the sensitivity of electron diffraction to the crystal imperfections lead to less ideal data statistics. A direct comparison of the three compounds is revealing: L-tyrosine, which was crystallized in situ and exhibited the lowest isotropic mosaicity (0.0001 º), yielded the best R-factor (M R 1 (obs) = 3.50%). Conversely, L-alanine and urea, which were mechanically ground and had higher mosaicity values, resulted in poorer R -factors. This strongly suggests that a major source of residual error is physical crystal imperfections − such as strain, defects, and complex mosaic spread − that may not be entirely adequately parameterized by the simplified Gaussian mosaicity model. In spite of these limitations, the results of the refinements show that the ED data combined with the dynamical refinement can be successfully used to extract reliable charge-density information and improve the models. The residual electrostatic potential maps after multipole refinement show that the multipole model more accurately accounts for the aspherical features of the electron density, which are neglected in the IAM refinement and cause increased noise in the residual potential maps. The successful free refinement of hydrogen positions and ADPs using 3D ED data is another notable achievement, facilitated by the strong interaction of electrons with the electrostatic potential, which is generated by both electrons and protons. However, some issues persist. For example, small discrepancies in atomic charges or κ and κ′ parameters were observed in certain atoms (e.g., N1 in L-alanine or C7 in L-tyrosine). These are likely influenced by parameter correlations, the sensitivity of 3D ED to dynamical effects, and noise. Additionally, some hydrogen ADPs remained at the edge of physical plausibility, indicating the need for further improvements in modelling protocols or data collection strategies. The close alignment of atomic charges, κ/κ′ parameters, deformation electron density features, and electrostatic potentials among the three models demonstrates that 3D ED, when processed with appropriate dynamical refinement, can yield reliable charge density models. For example, the values of ρ bcp and ∇² ρ bcp for covalent and hydrogen bonds from eMM exp differed from the reference models by amounts comparable to or only slightly larger than the internal variation between eMM theo and xMM exp . The electrostatic potential, deformation electron density and Laplacian of electron density of all three compounds were qualitatively consistent across models, capturing essential chemical features such as lone pairs, covalent bonds, hydrogen bonding interactions, and π-delocalization. The implications of this work extend far beyond the specific systems studied, opening the door to investigating the electronic structure of materials that have remained stubbornly out of reach. This includes, for example, metastable polymorphs that only form as nanocrystals, complex multicomponent systems like drug-target cocrystals, metal-organic frameworks displaying functional properties in nanocrystalline form, and organic optoelectronic materials whose optical properties depend on the size of the crystal. By establishing the viability of quantitative charge density analysis at the nanoscale, this study provides a new tool for fundamental discovery in chemistry, pharmacology, and materials science. It heralds a new chapter in quantum crystallography, where the intricate details of chemical bonding are no longer hidden by the challenge of growing an ideal large crystal. Herein, we establish the feasibility of performing full multipole refinement on 3D ED data. While the procedure is demanding, necessitating exceptionally high-quality data and meticulous analysis, the resulting models are robust and suitable for drawing conclusions about the chemical bonding environment. In specific instances, the reliability of the obtained results approaches that of conventional XRD and theoretical DFT calculations. However, additional work is required to further improve the fits, resolve remaining discrepancies in fitting the experimental data, and thereby enhance the stability and accuracy of the multipole refinement. Methods Sample preparation and data collection L-alanine, urea, and L-tyrosine were obtained from commercial suppliers and used without further purification. Crystals of L-alanine and urea were grown by slow evaporation of their respective solvents: a 1:1 (v/v) ethanol–water mixture for L-alanine, and distilled water for urea. For L-tyrosine, a saturated aqueous solution was prepared at room temperature, and a small droplet was deposited onto a holey carbon TEM grid. After allowing the droplet to sit undisturbed for approximately 30 seconds, the excess solution was gently blotted to induce crystal formation via evaporation. 3D ED measurements for L-alanine and urea were performed on two Rigaku XtaLAB Synergy-ED diffractometers, equipped with a LaB 6 source operating at 200 kV (λ = 0.0251 Å) and a Rigaku HyPix-ED detector. A small amount of each sample was first gently crushed in a mortar and pestle to reduce the crystal size. Then, the crystalline powders were deposited on carbon coated copper TEM grids coated (ultrathin continuous carbon from EMS for L-alanine and holey carbon from Pelco for urea). The samples were mounted on a Gatan Elsa™ 698 Cryo-transfer holder and cooled at 173 K prior to the insertion in the diffractometer, then cooled to 100 K in a vacuum (ca. 10 − 5 Pa). Diffraction patterns were collected on one single crystal of each compound using a selected area aperture (apparent diameter ca. 2 µm) during continuous rotation of the crystals over ca. 120°, with a shutterless scan and frame width of 0.15 ° (L-alanine) or 0.2 ° (urea). The beam flux density was optimized for a minimally required dose and kept in the range 0.003 to 0.01 e s − 1 Å −2 . The program CrysAlis Pro (Rigaku OD, 2024) was used to control the data collection. The camera length was calibrated with the help of an evaporated aluminum diffraction standard grid. 3D ED data for L-tyrosine were collected at 95 K on an FEI Tecnai G2 20 TEM (LaB₆ filament, 200 kV, λ = 0.0251 Å) equipped with a Medipix 3 ASI Cheetah hybrid pixel detector. Crystals were crystallized on copper TEM grids with holey carbon film and mounted on a single-tilt holder. Data collection was performed in continuous-rotation mode, controlled by custom scripts within the iTEM software, with crystal tracking during goniometer tilting facilitated by the Fast-ADT routine 53 . All measurements were conducted under cryogenic conditions to minimize thermal vibration. Data processing and IAM refinement PETS2 software 54 was used for the unit-cell parameter determination, optical distortion refinement, frame orientation optimization, integration of the reflection intensities and data reduction 55 , 56 . For dynamical refinement, the intensities were integrated by the concept of overlapping virtual frames 44 . Noise parameters 3 and 0 were used for L-alanine and urea, respectively and 4.2, and 0 for L-tyrosine. For L-alanine, calibration constant was adjusted to obtain more accurate unit cell parameters. Frames that showed any shadow by the specimen support were excluded from the data processing. The final resolution of the data was determined based on completeness (> 90%), redundancy (> 3), R int (obs) ( 1) and CC 1/2 (> 30%) in the last resolution shell. The solution and refinement of all three structures were done using the JANA2020 software 57 . Each compound’s structure was first solved using the charge-flipping algorithm implemented in Superflip 58 . Initial refinements employed the IAM under the kinematical approximation, followed by dynamical refinements. In these dynamical refinements, reflections were filtered using the R Sg parameter, which quantifies how well a reflection is sampled around the Bragg condition, ensuring that only reliably integrated intensities were included in the refinement 44 , 59 . Refinements were based on F amplitudes and the Wilson’s modification weighting scheme was used. Refinement quality was assessed using R-factors and the residual features in electrostatic potential difference maps. To account for variations in the crystal thickness − particularly critical in dynamical refinement − an idealized geometrical models (i.e. a wedge) was applied to approximate the probability distribution of thickness across the crystal. During the 3D ED experiment, tilting the crystal changes the effective thickness along the electron beam. To account for this, an empirical correction was applied that interpolates between two extremes: a flat plate model where thickness increases with tilt (t(α) = t₀ / cosα) and an isometric model where thickness remains constant (t(α) = t₀), with α the tilt angle. The final correction uses a tunable parameter C (0 ≤ C ≤ 1) to represent the actual behavior as t(θ) = t₀ / [(1 – C) + C·cosθ], providing a flexible and physically realistic model of thickness variation during tilting 46 . In addition to geometric and tilt-based corrections, we refined the average incoherent isotropic mosaicity for all compounds. This parameter accounts for angular spread due to slight misorientations of mosaic blocks within a crystal, which can impact the accuracy of calculated diffraction intensities in dynamical refinement. Including mosaicity improved overall agreement between observed and calculated intensities, the stability of the multipole refinement and the accuracy of the resulting mode 60 . Multipole model refinement on 3D ED data The multipole model refinements were performed using the Hansen-Coppens multipole formalism 17 in the JANA2020 software. During each refinement cycle, JANA2020 computes model-based X-ray structure factors from the current multipole electron density, incorporating both spherical and aspherical contributions using Slater-type orbitals. These structure factors are then converted into electron structure factors using the Mott–Bethe formula. Based on these electron structure factors, dynamical diffraction intensities are calculated using the Bloch-wave formalism, which accounts for multiple scattering, crystal thickness, and orientation. The refinement minimises the difference between these calculated dynamical intensities and the experimental electron diffraction intensities via least-squares optimisation. Importantly, this is a fully dynamical refinement against the raw experimental 3D ED data, not against transformed or corrected X-ray-equivalent data. All relevant parameters, including atomic coordinates, ADPs, and multipole model parameters ( P val , κ , κ' , P lm ), are refined simultaneously. This approach distinguishes itself from earlier methods that either applied kinematical multipole refinements to corrected 3D ED data or refined multipole parameters alone against pseudo-X-ray structure factors. The multipole refinements were carried out using the Su-Coppens radial functions for the core and spherical valence electron density terms 61 . The initial models for multipole refinements were obtained from the IAM structures fully refined with dynamical approach. These models provided a physically realistic starting point that incorporates multiple scattering effects and accurate crystal thickness estimations. Retaining the same dynamical diffraction framework ensured consistency between IAM and multipole refinements. First, dynamical TAAM refinements 45 were carried out using the fixed multipole model parameter values transferred from the MATTS data bank 62 , 63 using the discambMATTS2tsc program 64 . In dynamical TAAM refienements, the same set of parameters was refined as in dynamical IAM, but with multipolar scatteringa factors computed from TAAM. After that, dynamical multipole model refinements were performed in a step-wise and iterative-block refinement manner (Fig. S16) . First, only P val and κ parameters were allowed to be refined, still with P lm and κ' values constrained at values from the MATTS data bank. The multipole expansion was refined up to the octupole level for non-H atoms. For H-atoms, only bond-directed dipoles and quadrupoles were refined. The κ and κ' parameters were refined individually for all the non-H atoms. For H-atoms, κ and κ' parameters were assigned to be the same for the chemically equivalent types of atoms and refined. Importantly, the positions and anisotropic displacement parameters (ADPs) of all hydrogen atoms were freely refined throughout the refinement process. The inclusion of hydrogen ADPs is especially significant in electron diffraction, where hydrogen atoms scatter more strongly than in XRD, allowing for improved accuracy in modelling light atom behaviour and hydrogen bonding interactions. Multipole model refinement on X-ray data For L-alanine 25 (CCDC No. 2443207) and urea 48 (CCDC No. 1047783), the available high-resolution XRD data were used for the reference experimental charge density analyses. In the case of L-tyrosine, high-resolution X-ray data were collected for good-quality single crystal ( Fig. S17 ) on an in-house instrument and used for the reference experimental charge density analysis ( details in SI , Table S14 ). The resolution of the XRD data was cut to reach the same resolutions as were observed for the 3D ED data, these were 0.44 Å, 0.53 Å and 0.59 Å for L-alanine, urea and L-tyrosine, respectively. The multipole model refinements were performed in the JANA2020 software using the same settings (except for dynamical scattering) and refinement strategy as used for the multipole refinement on the 3D ED data, with the following exceptions. The anisotropic displacement parameters (ADPs) of hydrogen atoms for L-alanine and L-tyrosine were estimated using the SHADE2.1server 65 and for urea, the ADPs from neutron diffraction data were used 52 . These values were incorporated and kept fixed during the refinements. First, the scale factor refinements were performed using all reflections (Fig S16) . Next, high-order refinements for the non-H atoms were performed to determine the accurate positional and displacement parameters, while the positions of the H atoms were derived with a riding model with the X–H bond lengths constrained to the mean neutron values 49 . For the H atoms, the refinement of κ' parameters was not stable, therefore the parameters were constrained at the MATTS data bank values. Refinements were based on F amplitudes and the Wilson’s modification weighting scheme was used. Crystal data and multipole refinment parameters of xMM exp for all three molecules are listed in Table S15 . Computational methods The crystal structure of L-alanine (CCDC No. 1009312) from XRD experimental studies performed at 100 K was used for the theoretical calculation 66 . For urea, the crystal structure from neutron diffraction studies performed at 123 K (CCDC No. 1278500) was used for the theoretical calculations 52 . In the case of L-tyrosine, the crystal structure determined in this work from multipole refinement on high-resolution XRD data was used. To obtain the theoretical structure factors, the experimental geometries (atomic coordinates) of all three molecules were optimized with frozen unit-cell parameters by applying periodic DFT calculations using CRYSTAL17 67 (the details of Geometry optimization and X-ray static structure factor calculation are discussed in the SI). The calculated X-ray static structure factors were converted into kinematical electron static structure factors by application of the Motte-Bethe formula 68 using the dedicated DiSCaMB utility program 64 . Then, the electron static structure factors were imported into Jana2020 and the multipole model refinements were performed for L-alanine, urea and L-tyrosine using the same strategy as for multipole model refinements on experimental 3D ED data, with the exception of the atomic positions – these were constrained to the optimized geometry positions and the ADPs were set to zero and not refined (Fig S16) . All refinements were carried out on F using unit weights and kinematical approximation. Crystal data and multipole refinment parameters of eMM theo for all three molecules are listed in Table S16 . Topological and Electrostatic Potential Analysis The topological analysis of electron density based on Bader’s QTAIM theory and deformation density maps of the molecules was performed using the MoPro Viewer program as implemented in the MoPro suite 69 . For the covalent and non-covalent interactions, the topological properties such as R ij of bonding path, ρ bcp and ∇² ρ bcp were calculated. The electrostatic potential was computed from the refined multipole model of electron density of studied molecules using XD2024 70 and mapped on the iso-contour of molecular electron density using the MoleCoolQt 71 . Declarations Data availability All the data needed to evaluate the conclusion in the paper are present in the paper and/or the Supplementary Materials. Raw data, the data reduction and processing files, the kinematical, dynamical IAM and dynamical multipole refinements files of 3D ED data, the multipole refinement files for theoretical electron static structure factors, the multipole refinement files for experimental X-ray diffraction, X-ray diffraction raw data, data processing and refinements files for L-tyrosine and CIF files of all the compounds used in this study are available online using the following doi: https://doi.org/10.18150/VNLTKK , https://doi.org/10.18150/FNLNWC , https://doi.org/10.18150/VTBPGP [RepOD ( https://repod.icm.edu.pl/ ), Repository for Open Data, Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw, Warsaw, Poland] and https://doi.org/10.5281/zenodo.16752042 (a repository hosted by Zenodo). The CIF files with results from all dynamical IAM and dynamical multipole refinements (3D ED) and L-tyrosine (X-ray IAM refinement) presented in this work can be retrieved free-of-charge from the Cambridge Structural Database (CSD) (deposition numbers: CCDC 2479735–2479739 and 2480319–2480320). Competing interests The authors declare no competing interests. Funding The National Science Center, Poland, provided the funding for the research presented in this work under the grant 2020/39/I/ST4/02904. The work is also supported by the H2020 ITN project NanED, grant agreement No. 956099. Acknowledgment is also extended to the Polish high-performance computing infrastructure PLGrid (HPC Centers: ACK Cyfronet AGH, WCSS) for providing computer facilities and support within the computational grant no. PLG/2024/017098. Part of the electron diffraction experiments are supported by Novo Nordisk Foundation Research Infrastructure grant n. NNF220C0074439. Author contributions Concept: P.M.D., L.P., A.K.; 3D ED Data collection: A.K., A.L., J.W., P.B; XRD Data collection: A.K., D.T.; 3D ED data reduction, processing and refinements: A.K., A.S.; Multipole refinement of experiment 3D ED data: A.K., A.S.; Multipole refinement on theortical and XRD data: A.K., Topological analysis: A.K.; Theoretical calculations: A.K.; Writing original draft: A.K., A.S.; Supervision: P.M.D., L.P.; Writing review & editing: All authors contributed to the review and editing collaboratively. Acknowledgement We thank Felix Hennersdorf, Maurycy Nowak, Anna Hoser and Anna Makal for support during initial 3D ED data collections attempts. References Gillet JM, Koritsanszky T (2012) Past, present and future of charge density and density matrix refinements. Mod Charge-Density Anal Pawledzio S, Einkauf J, Custelcean R, Wang X (2025) Intermolecular Interactions in Direct Air Capture Materials: Insights from Charge Density Analysis. J Am Chem Soc Koch D et al (2024) The Analysis of Electron Densities: From Basics to Emergent Applications. Chem Rev 124:12661–12737 Kasai H et al (2018) X-ray electron density investigation of chemical bonding in van der Waals materials. Nat Mater 17:249–252 Zhurova EA, Matta CF, Wu N, Zhurov VV, Pinkerton AA (2006) Experimental and Theoretical Electron Density Study of Estrone. J Am Chem Soc 128:8849–8861 Kumar A, Mohanty B, Munshi P (2023) Probing Diversity in Binding Affinities of Polymorphs of an Anticancer Agent against Human γ-Enolase: A Quantum Crystallographic Perspective. Cryst Growth Des 23:580–591 Jha KK et al (2019) Structure–Property Relationship in an Organic Semiconductor: Insights from Energy Frameworks, Charge Density Analysis, and Diode Devices. Cryst Growth Des 19:3019–3029 Flaig R, Koritsanszky T, Dittrich B, Wagner A, Luger P (2002) Intra- and Intermolecular Topological Properties of Amino Acids: A Comparative Study of Experimental and Theoretical Results. J Am Chem Soc 124:3407–3417 Coppens P et al (1999) Experimental Charge Densities and Intermolecular Interactions: Electrostatic and Topological Analysis of dl-Histidine. J Am Chem Soc 121:2585–2593 Münch A et al (2020) Insight into the Bonding and Aggregation of Alkyllithiums by Experimental Charge Density Studies and Energy Decomposition Analyses. J Am Chem Soc 142:15897–15906 Eraković M, Cinčić D, Molčanov K, Stilinović VA (2019) Crystallographic Charge Density Study of the Partial Covalent Nature of Strong N⋅⋅⋅Br Halogen Bonds. Angew Chemie 131:15849–15853 Sarkar S et al (2022) X-ray Electron Density Study of the Chemical Bonding Origin of Glass Formation in Metal–Organic Frameworks**. Angew Chemie Int Ed 61 Fournier B et al (2009) Charge Density and Electrostatic Interactions of Fidarestat, an Inhibitor of Human Aldose Reductase. J Am Chem Soc 131:10929–10941 Pavan MS, Durga Prasad K (2013) Guru Row, T. N. Halogen bonding in fluorine: experimental charge density study on intermolecular F⋯F and F⋯S donor–acceptor contacts. Chem Commun 49:7558 Singla L, Kumar A, Robertson CM, Munshi P (2023) Roy Choudhury, A. Investigation of C–F···F–C Interactions Using Experimental and Theoretical Charge Density Analyses. Cryst Growth Des 23:853–861 Coppens P et al (1979) Net atomic charges and molecular dipole moments from spherical-atom X-ray refinements, and the relation between atomic charge and shape. Acta Crystallogr Sect A 35:63–72 Hansen NK, Coppens P (1978) Testing aspherical atom refinements on small-molecule data sets. Acta Crystallogr Sect A 34:909–921 Koritsanszky TS, Coppens P (2001) Chemical Applications of X-ray Charge-Density Analysis. Chem Rev 101:1583–1628 Krawczuk A, Macchi P (2014) Charge density analysis for crystal engineering. Chem Cent J 8:68 Saleh G, Gatti C, Lo Presti L, Contreras-García J (2012) Revealing Non‐covalent Interactions in Molecular Crystals through Their Experimental Electron Densities. Chem – Eur J 18:15523–15536 Stalke D (2011) Meaningful Structural Descriptors from Charge Density. Chem – Eur J 17:9264–9278 Kleemiss F et al (2021) Similarities and Differences between Crystal and Enzyme Environmental Effects on the Electron Density of Drug Molecules. Chem – Eur J 27:3407–3419 Yearley EJ, Zhurova EA, Zhurov VV, Pinkerton AA (2007) Binding of Genistein to the Estrogen Receptor Based on an Experimental Electron Density Study. J Am Chem Soc 129:15013–15021 Korlyukov AA et al (2020) Charge density view on bicalutamide molecular interactions in the monoclinic polymorph and androgen receptor binding pocket. IUCrJ 7:71–82 Hayashi M, Nishioka T, Kasai H, Nishibori E (2025) Accurate temperature dependence of structure factors of L-alanine and taurine for quantum crystallography. IUCrJ 12:384–392 Zhurov VV, Pinkerton AA (2015) Inter- and Intramolecular Interactions in Crystalline 2-Nitrobenzoic Acid—An Experimental and Theoretical QTAIM Analysis. J Phys Chem A 119:13092–13100 Jones CG et al (2018) The CryoEM Method MicroED as a Powerful Tool for Small Molecule Structure Determination. ACS Cent Sci 4:1587–1592 Palatinus L et al (2017) Hydrogen positions in single nanocrystals revealed by electron diffraction. Sci (80-) 355:166–169 Kolb U, Gorelik T, Otten MT (2008) Towards automated diffraction tomography. Part II—Cell parameter determination. Ultramicroscopy 108:763–772 Gemmi M et al (2019) 3D Electron Diffraction: The Nanocrystallography Revolution. ACS Cent Sci 5:1315–1329 Gruene T, Mugnaioli E (2021) 3D Electron Diffraction for Chemical Analysis: Instrumentation Developments and Innovative Applications. Chem Rev 121:11823–11834 Yonekura K, Maki-Yonekura S (2016) Refinement of cryo-EM structures using scattering factors of charged atoms. J Appl Crystallogr 49:1517–1523 Yuan S et al (2018) [Ti 8 Zr 2 O 12 (COO) 16 ] Cluster: An Ideal Inorganic Building Unit for Photoactive Metal–Organic Frameworks. ACS Cent Sci 4:105–111 Cichocka MO, Ångström J, Wang B, Zou X, Smeets S (2018) High-throughput continuous rotation electron diffraction data acquisition via software automation. J Appl Crystallogr 51:1652–1661 Clabbers MTB, Hattne J, Martynowycz MW, Gonen T (2025) Energy filtering enables macromolecular MicroED data at sub-atomic resolution. Nat Commun 16:2247 Nannenga BL, Gonen T (2019) The cryo-EM method microcrystal electron diffraction (MicroED). Nat Methods 16:369–379 Gruza B, Chodkiewicz ML, Krzeszczakowska J, Dominiak PM (2020) Refinement of organic crystal structures with multipolar electron scattering factors. Acta Crystallogr Sect Found Adv 76:92–109 Yonekura K, Kato K, Ogasawara M, Tomita M, Toyoshima C (2015) Electron crystallography of ultrathin 3D protein crystals: Atomic model with charges. Proc. Natl. Acad. Sci. 112, 3368–3373 Bochtler M (2024) X-rays, electrons, and neutrons as probes of atomic matter. Structure 32:630–643e6 Kumar A et al (2024) TAAM refinement on high-resolution experimental and simulated 3D ED/MicroED data for organic molecules. Acta Crystallogr Sect C Struct Chem 80:264–277 Avilov AS (2003) The quantitative analysis of electrostatic potential and study of chemical bonding by electron diffraction structure analysis. Z fur Krist 218:247–258 Zuo JM, Kim M, O’Keeffe M, Spence JCH (1999) Direct observation of d-orbital holes and Cu–Cu bonding in Cu 2 O. Nature 401:49–52 Wu JS, Spence JCH (2003) Structure and bonding in α-copper phthalocyanine by electron diffraction. Acta Crystallogr Sect Found Crystallogr 59:495–505 Klar PB et al (2023) Accurate structure models and absolute configuration determination using dynamical effects in continuous-rotation 3D electron diffraction data. Nat Chem 15:848–855 Olech B, Brázda P, Palatinus L, Dominiak PM (2024) Dynamical refinement with multipolar electron scattering factors. IUCrJ 11:309–324 Suresh A et al (2024) Ionisation of atoms determined by kappa refinement against 3D electron diffraction data. Nat Commun 15:9066 Destro R, Soave R, Barzaghi M (2008) Physicochemical Properties of Zwitterionic L- and DL-alanine Crystals from Their Experimental and Theoretical Charge Densities. J Phys Chem B 112:5163–5174 Birkedal H et al (2004) The charge density of urea from synchrotron diffraction data. Acta Crystallogr Sect Found Crystallogr 60:371–381 Allen FH, Bruno IJ (2010) Bond lengths in organic and metal-organic compounds revisited: X —H bond lengths from neutron diffraction data. Acta Crystallogr Sect B Struct Sci 66:380–386 Wilson CC, Myles D, Ghosh M, Johnson LN, Wang W (2005) Neutron diffraction investigations of l- and d-alanine at different temperatures: the search for structural evidence for parity violation. New J Chem 29:1318 Bader RF (1991) W. A quantum theory of molecular structure and its applications. Chem Rev 91:893–928 Swaminathan S, Craven BM, McMullan RK (1984) The crystal structure and molecular thermal motion of urea at 12, 60 and 123 K from neutron diffraction. Acta Crystallogr Sect B Struct Sci 40:300–306 Plana-Ruiz S et al (2020) Fast-ADT: A fast and automated electron diffraction tomography setup for structure determination and refinement. Ultramicroscopy 211:112951 Palatinus L et al (2019) Specifics of the data processing of precession electron diffraction tomography data and their implementation in the program PETS2.0. Acta Crystallogr Sect B Struct Sci Cryst Eng Mater 75:512–522 Brázda P, Klementová M, Krysiak Y, Palatinus L (2022) Accurate lattice parameters from 3D electron diffraction data. I. Optical distortions. IUCrJ 9:735–755 Brázda P, Palatinus L, Babor M (2019) Electron diffraction determines molecular absolute configuration in a pharmaceutical nanocrystal. Sci (80-) 364:667–669 Petříček V, Palatinus L, Plášil J, Dušek M (2023) Jana2020 – a new version of the crystallographic computing system Jana. Z für Krist - Cryst Mater 238:271–282 Palatinus L, Chapuis G (2007) SUPERFLIP – a computer program for the solution of crystal structures by charge flipping in arbitrary dimensions. J Appl Crystallogr 40:786–790 Palatinus L, Petříček V, Corrêa CA (2015) Structure refinement using precession electron diffraction tomography and dynamical diffraction: theory and implementation. Acta Crystallogr Sect Found Adv 71:235–244 Palatinus L (2024) Including mosaicity effects in the dynamical refinement against 3D ED data. Acta Crystallogr Sect Found Adv 80:e225–e225 Su Z, Coppens P (1992) On the mapping of electrostatic properties from the multipole description of the charge density. Acta Crystallogr Sect Found Crystallogr 48:188–197 Jha KK et al (2022) Multipolar Atom Types from Theory and Statistical Clustering (MATTS) Data Bank: Restructurization and Extension of UBDB. J Chem Inf Model 62:3752–3765 Rybicka PM, Kulik M, Chodkiewicz ML, Dominiak PM (2022) Multipolar Atom Types from Theory and Statistical Clustering (MATTS) Data Bank: Impact of Surrounding Atoms on Electron Density from Cluster Analysis. J Chem Inf Model 62:3766–3783 Chodkiewicz ML et al (2018) DiSCaMB: a software library for aspherical atom model X-ray scattering factor calculations with CPUs and GPUs. J Appl Crystallogr 51:193–199 Munshi P, Madsen AØ, Spackman MA, Larsen S, Destro R (2008) Estimated H-atom anisotropic displacement parameters: a comparison between different methods and with neutron diffraction results. Acta Crystallogr Sect Found Crystallogr 64:465–475 Escudero-Adán EC, Benet-Buchholz J, Ballester P (2014) The use of Mo K α radiation in the assignment of the absolute configuration of light-atom molecules; the importance of high-resolution data. Acta Crystallogr Sect B Struct Sci Cryst Eng Mater 70:660–668 Dovesi R et al (2018) Quantum-mechanical condensed matter simulations with CRYSTAL. WIREs Comput Mol Sci 8 The scattering of electrons by atoms. Proc. R. Soc. London. Ser. A, Contain. Pap. a Math. Phys. Character 127, 658–665 (1930) Jelsch C, Guillot B, Lagoutte A, Lecomte C (2005) Advances in protein and small-molecule charge-density refinement methods using MoPro. J Appl Crystallogr 38:38–54 Koritsanszky T, Volkov A, Farrugia LJ, Mallinson PR, Macchi P, Gatti C, Richter T XD (2024). A computer program package for multipole refinement, topological analysis of charge densities and evaluation of intermolecular energies from experimental and theoretical structure factors.(2024). A computer program package for multipole refinement, topological analysis of charge densities and evaluation of intermolecular energies from experimental and theoretical structure factors.(2024) Hübschle CB, Dittrich B (2011) MoleCoolQt – a molecule viewer for charge-density research. J Appl Crystallogr 44:238–240 Additional Declarations There is NO Competing Interest. Supplementary Files 3DEDmultipolarESI.pdf Supplementary Information GA.png Graphical Abstract Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7433721","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":506557607,"identity":"fa42295d-982e-4813-99af-c1e9250cf389","order_by":0,"name":"Paulina Dominiak","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1UlEQVRIiWNgGAWjYFCCBBCyYTCACxwA4geEtaShaUkgpIWB4TAJWszZk49ueLjjvLw5e3cCM28bgxzfjQS2B/i0WPY8S7uReOa24c6esxtAWowlbySwG+DTYnAjx+xGYtvtBIMbuUAt2xgSNwBtkSBCy7kEg/tvwVrqidVyAGgLL1gLkEFAC8QvbcmGG87kbjg495+E4cwzD9vx+gUYYsdu/myzkzc4fnbjgzdnbOT5jicfe/ABn8OQOQcYGCSAFGMbHg1oWmCADa+WUTAKRsEoGHEAAO93VgVH84bbAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-1466-1243","institution":"University of Warsaw","correspondingAuthor":true,"prefix":"","firstName":"Paulina","middleName":"","lastName":"Dominiak","suffix":""},{"id":506557608,"identity":"9e529a30-0615-4d51-bc61-41ace2034b14","order_by":1,"name":"Anil Kumar","email":"","orcid":"https://orcid.org/0009-0005-8471-2690","institution":"University of Warsaw","correspondingAuthor":false,"prefix":"","firstName":"Anil","middleName":"","lastName":"Kumar","suffix":""},{"id":506557609,"identity":"043a41e3-b460-42b3-b465-b701ce1d3697","order_by":2,"name":"Ashwin Suresh","email":"","orcid":"https://orcid.org/0000-0002-9042-8603","institution":"Institute of Physics of the CAS","correspondingAuthor":false,"prefix":"","firstName":"Ashwin","middleName":"","lastName":"Suresh","suffix":""},{"id":506557610,"identity":"d0de6ce0-a7ca-42a5-82b8-df86daace2c5","order_by":3,"name":"Arianna Lanza","email":"","orcid":"https://orcid.org/0000-0002-7820-907X","institution":"University of Copenhagen","correspondingAuthor":false,"prefix":"","firstName":"Arianna","middleName":"","lastName":"Lanza","suffix":""},{"id":506557611,"identity":"2a44503a-e1c8-49da-8483-c994cd0c8bff","order_by":4,"name":"Jakub Wojciechowski","email":"","orcid":"","institution":"Rigaku Europe SE","correspondingAuthor":false,"prefix":"","firstName":"Jakub","middleName":"","lastName":"Wojciechowski","suffix":""},{"id":506557612,"identity":"fe6a1bd0-3ead-44a9-9abc-ca72f9256496","order_by":5,"name":"Damian Trzybiński","email":"","orcid":"","institution":"University of Warsaw","correspondingAuthor":false,"prefix":"","firstName":"Damian","middleName":"","lastName":"Trzybiński","suffix":""},{"id":506557613,"identity":"c8cd0a09-2448-43bd-9bee-1c9f0e0fa074","order_by":6,"name":"Petr Brazda","email":"","orcid":"","institution":"Institute of Physics of the CAS, v.v.i.","correspondingAuthor":false,"prefix":"","firstName":"Petr","middleName":"","lastName":"Brazda","suffix":""},{"id":506557614,"identity":"90aa0e45-8c01-4664-937b-34edca233e25","order_by":7,"name":"Lukas Palatinus","email":"","orcid":"https://orcid.org/0000-0002-8987-8164","institution":"Institute of Physics of the CAS","correspondingAuthor":false,"prefix":"","firstName":"Lukas","middleName":"","lastName":"Palatinus","suffix":""}],"badges":[],"createdAt":"2025-08-22 10:50:49","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7433721/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7433721/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":90321710,"identity":"bdbf6486-7197-4048-a4c2-aa6bc01fe1cc","added_by":"auto","created_at":"2025-09-01 10:56:30","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":268637,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison of charge density models for L-alanine crystal.\u003c/strong\u003e\u0026nbsp;\u003cstrong\u003ea\u003c/strong\u003e,\u0026nbsp;\u003cstrong\u003ed\u003c/strong\u003e\u0026nbsp;Atomic displacement ellipsoids (50% probability) for the eIAM\u003csub\u003eexp\u003c/sub\u003e and eMM\u003csub\u003eexp\u003c/sub\u003e, respectively.\u0026nbsp;\u003cstrong\u003eb\u003c/strong\u003e,\u0026nbsp;\u003cstrong\u003ee\u003c/strong\u003e\u0026nbsp;3D difference Fourier map of the residual electrostatic potential for the eIAM\u003csub\u003eexp\u003c/sub\u003e \u003cstrong\u003e(b)\u003c/strong\u003e and eMM\u003csub\u003eexp\u003c/sub\u003e\u003cstrong\u003e(e)\u003c/strong\u003e models. Positive (yellow) and negative (blue) contours are drawn at ±0.166 e Å\u003csup\u003e−1\u003c/sup\u003e.\u0026nbsp;\u003cstrong\u003ec\u003c/strong\u003e\u0026nbsp;Comparison of refined X–H bond lengths. \u003cstrong\u003ef–h\u003c/strong\u003e\u0026nbsp;Comparison of refined atomic parameters from different multipole models: (\u003cstrong\u003ef\u003c/strong\u003e) atomic charges, (\u003cstrong\u003eg\u003c/strong\u003e) \u003cem\u003eκ\u003c/em\u003e parameters, and (\u003cstrong\u003eh\u003c/strong\u003e) \u003cem\u003eκ'\u003c/em\u003e parameters. Error bars represent estimated standard deviations.\u003c/p\u003e","description":"","filename":"Picture1.png","url":"https://assets-eu.researchsquare.com/files/rs-7433721/v1/343332a5af542ab764c60d9e.png"},{"id":90319758,"identity":"2894e88b-7ba5-433e-b276-1ae43d0b34b8","added_by":"auto","created_at":"2025-09-01 10:40:29","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":408021,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDeformation electron density and electrostatic potential for L-alanine crystal.\u003c/strong\u003e\u0026nbsp;\u003cstrong\u003ea–c\u003c/strong\u003e, 2D static deformation electron density map in the plane of the carboxylate group for the eMM\u003csub\u003eexp\u003c/sub\u003e (\u003cstrong\u003ea\u003c/strong\u003e), eMM\u003csub\u003etheo\u003c/sub\u003e (\u003cstrong\u003eb\u003c/strong\u003e), and xMM\u003csub\u003eexp\u003c/sub\u003e (\u003cstrong\u003ec\u003c/strong\u003e) models. The positive (blue) and negative (red) contours are drawn at ± 0.1 e Å\u003csup\u003e−3\u003c/sup\u003e.\u0026nbsp; \u003cstrong\u003ed–f\u003c/strong\u003e, Molecular electrostatic potential (Bohr Å\u003csup\u003e−1\u003c/sup\u003e) mapped onto the electron density isosurface of 0.05 Bohr Å\u003csup\u003e−3\u003c/sup\u003e for the eMM\u003csub\u003eexp\u003c/sub\u003e (\u003cstrong\u003ed\u003c/strong\u003e), eMM\u003csub\u003etheo\u003c/sub\u003e (\u003cstrong\u003ee\u003c/strong\u003e) and xMM\u003csub\u003eexp\u003c/sub\u003e (\u003cstrong\u003ef\u003c/strong\u003e) models. The molecule is oriented as in Fig. 1.\u003c/p\u003e","description":"","filename":"Picture2.png","url":"https://assets-eu.researchsquare.com/files/rs-7433721/v1/ff509c1fea1a42590269ddb9.png"},{"id":90319759,"identity":"9ac7aa8d-91de-4494-b2ba-94f88dffd561","added_by":"auto","created_at":"2025-09-01 10:40:29","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":471926,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTopological analysis of electron density for L-alanine crystal.\u003c/strong\u003e\u0026nbsp;\u003cstrong\u003ea\u003c/strong\u003e, Showing the covalent bonds and hydrogen intermolecular interactions in terms of bond critical points (magenta and green spheres, respectively) and bonding paths (intermolecular interactions only, green lines) for the eMM\u003csub\u003eexp\u003c/sub\u003e model. \u003cstrong\u003eb\u003c/strong\u003e, Laplacian map focusing on selected intermolecular interactions for the eMM\u003csub\u003eexp\u003c/sub\u003e model showing charge concentration (red) and depletion (blue). Positive (blue dotted lines) and negative (red solid lines) contours are drawn at the level of ± 2 × 10\u003csup\u003en\u003c/sup\u003e, ± 4 × 10\u003csup\u003en\u003c/sup\u003e, ± 8 × 10\u003csup\u003en\u003c/sup\u003e (n = -3 to +2) e Å\u003csup\u003e−5 \u003c/sup\u003e\u003cstrong\u003ec, d\u003c/strong\u003e, Electron density (\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e,\u003csub\u003e \u003c/sub\u003ee Å\u003csup\u003e−3\u003c/sup\u003e) and its Laplacian (∇²\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e,\u003cem\u003e \u003c/em\u003ee Å\u003csup\u003e−5\u003c/sup\u003e) at covalent bond critical points, respectively for the eMM\u003csub\u003eexp\u003c/sub\u003e, eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e models. \u003cstrong\u003ee, f\u003c/strong\u003e, Corresponding properties for hydrogen intermolecular interactions.\u003c/p\u003e","description":"","filename":"Picture3.png","url":"https://assets-eu.researchsquare.com/files/rs-7433721/v1/113995b8963bd0a814f85943.png"},{"id":90319762,"identity":"32c0fe70-6424-4b42-ad62-c5700735f856","added_by":"auto","created_at":"2025-09-01 10:40:30","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":179991,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison of charge density models for urea crystal.\u003c/strong\u003e\u0026nbsp;\u003cstrong\u003ea\u003c/strong\u003e,\u0026nbsp;\u003cstrong\u003ed\u003c/strong\u003e\u0026nbsp;Atomic displacement ellipsoids (50% probability) for the eIAM\u003csub\u003eexp\u003c/sub\u003e and eMM\u003csub\u003eexp\u003c/sub\u003e, respectively.\u0026nbsp;\u003cstrong\u003eb\u003c/strong\u003e,\u0026nbsp;\u003cstrong\u003ee\u003c/strong\u003e\u0026nbsp;3D difference Fourier map of the residual electrostatic potential for the eIAM\u003csub\u003eexp\u003c/sub\u003e (\u003cstrong\u003eb\u003c/strong\u003e) and eMM\u003csub\u003eexp\u003c/sub\u003e (\u003cstrong\u003ee\u003c/strong\u003e) models. Positive (yellow) and negative (blue) contours are drawn at ±0.166 e Å\u003csup\u003e−1\u003c/sup\u003e.\u0026nbsp;\u003cstrong\u003ec\u003c/strong\u003e\u0026nbsp;Comparison of refined X–H bond lengths. \u003cstrong\u003ef–h\u003c/strong\u003e\u0026nbsp;Comparison of refined atomic parameters from different multipole models: (\u003cstrong\u003ef\u003c/strong\u003e) atomic charges, (\u003cstrong\u003eg\u003c/strong\u003e) \u003cem\u003eκ\u003c/em\u003e parameters, and (\u003cstrong\u003eh\u003c/strong\u003e) \u003cem\u003eκ'\u003c/em\u003e parameters. Error bars represent estimated standard deviations.\u003c/p\u003e","description":"","filename":"Picture4.png","url":"https://assets-eu.researchsquare.com/files/rs-7433721/v1/aa3be9e4f6cce060261f3bea.png"},{"id":90320576,"identity":"a1208dfd-c8fa-48f3-9fcb-9994ab11e46d","added_by":"auto","created_at":"2025-09-01 10:48:30","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":382023,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDeformation electron density and electrostatic potential for urea crystals.\u003c/strong\u003e\u0026nbsp;\u003cstrong\u003ea–c\u003c/strong\u003e, 2D static deformation electron density map for the eMM\u003csub\u003eexp\u003c/sub\u003e (\u003cstrong\u003ea\u003c/strong\u003e), eMM\u003csub\u003etheo\u003c/sub\u003e (\u003cstrong\u003eb\u003c/strong\u003e), and xMM\u003csub\u003eexp\u003c/sub\u003e (\u003cstrong\u003ec\u003c/strong\u003e) models. The positive (blue) and negative (red) contours are drawn at ± 0.1 e Å\u003csup\u003e−3\u003c/sup\u003e.\u0026nbsp; \u003cstrong\u003ed–f\u003c/strong\u003e, Molecular electrostatic potential (Bohr Å\u003csup\u003e−1\u003c/sup\u003e) mapped onto the electron density isosurface of 0.05 Bohr Å\u003csup\u003e−3\u003c/sup\u003e for the eMM\u003csub\u003eexp\u003c/sub\u003e (\u003cstrong\u003ed\u003c/strong\u003e), eMM\u003csub\u003etheo\u003c/sub\u003e (\u003cstrong\u003ee\u003c/strong\u003e) and xMM\u003csub\u003eexp\u003c/sub\u003e (\u003cstrong\u003ef\u003c/strong\u003e) models.\u003c/p\u003e","description":"","filename":"Picture5.png","url":"https://assets-eu.researchsquare.com/files/rs-7433721/v1/816a47019f1e2f0c6c791cd9.png"},{"id":90319774,"identity":"060904b4-5d52-47e3-a6c2-038bc50481be","added_by":"auto","created_at":"2025-09-01 10:40:30","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":376034,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTopological analysis of electron density for urea crystal.\u003c/strong\u003e\u0026nbsp;\u003cstrong\u003ea\u003c/strong\u003e, Showing the covalent bonds and hydrogen intermolecular interactions in terms of bond critical points (magenta and green spheres, respectively) and bonding paths (intermolecular interactions only, green lines) for the eMM\u003csub\u003eexp\u003c/sub\u003e model. \u003cstrong\u003eb\u003c/strong\u003e, Laplacian map of covalent bonds and selected intermolecular interactions for eMM\u003csub\u003eexp\u003c/sub\u003e model showing charge concentration (red) and depletion (blue). Positive (blue dotted lines) and negative (red solid lines) contours are drawn at the level of ± 2 ×10\u003csup\u003en\u003c/sup\u003e, ± 4 × 10\u003csup\u003en\u003c/sup\u003e, ± 8 × 10\u003csup\u003en\u003c/sup\u003e (n = -3 to +2) e Å\u003csup\u003e−5\u003c/sup\u003e. \u003cstrong\u003ec, d\u003c/strong\u003e, Electron density (\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e,\u003csub\u003e \u003c/sub\u003ee Å\u003csup\u003e−3\u003c/sup\u003e) and its Laplacian (∇²\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e,\u003cem\u003e \u003c/em\u003ee Å\u003csup\u003e−5\u003c/sup\u003e) at covalent bond critical points, respectively for the eMM\u003csub\u003eexp\u003c/sub\u003e, eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e models. \u003cstrong\u003ee, f\u003c/strong\u003e, Corresponding properties for hydrogen intermolecular interactions.\u003c/p\u003e","description":"","filename":"Picture6.png","url":"https://assets-eu.researchsquare.com/files/rs-7433721/v1/0d2f0d7c95dd6d7af607b140.png"},{"id":90320574,"identity":"47116009-da5c-4fa6-86c1-6f5d64efaab8","added_by":"auto","created_at":"2025-09-01 10:48:30","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":317178,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison of charge density models for L-tyrosine crystal.\u003c/strong\u003e\u0026nbsp;\u003cstrong\u003ea\u003c/strong\u003e,\u0026nbsp;\u003cstrong\u003ed\u003c/strong\u003e\u0026nbsp;Atomic displacement ellipsoids (50% probability) for the eIAM\u003csub\u003eexp\u003c/sub\u003e and eMM\u003csub\u003eexp\u003c/sub\u003e, respectively.\u0026nbsp;\u003cstrong\u003eb\u003c/strong\u003e,\u0026nbsp;\u003cstrong\u003ee\u003c/strong\u003e\u0026nbsp;3D difference Fourier map of the residual electrostatic potential for the eIAM\u003csub\u003eexp\u003c/sub\u003e \u003cstrong\u003e(b)\u003c/strong\u003e and eMM\u003csub\u003eexp\u003c/sub\u003e\u003cstrong\u003e(e)\u003c/strong\u003e models. Positive (yellow) and negative (blue) contours are drawn at ±0.116 e Å\u003csup\u003e−1\u003c/sup\u003e.\u0026nbsp;\u003cstrong\u003ec,\u003c/strong\u003e\u0026nbsp;Comparison of refined X–H bond lengths. \u003cstrong\u003ef–k\u003c/strong\u003e\u0026nbsp;Comparison of refined atomic parameters (non-H and H-atoms, up and down, respectively) from different multipole models: (\u003cstrong\u003ef,g\u003c/strong\u003e) atomic charges, (\u003cstrong\u003eh,i\u003c/strong\u003e) \u003cem\u003eκ\u003c/em\u003e parameters, and (\u003cstrong\u003ej,k\u003c/strong\u003e) \u003cem\u003eκ'\u003c/em\u003e parameters. Error bars represent estimated standard deviations.\u003c/p\u003e","description":"","filename":"Picture7.png","url":"https://assets-eu.researchsquare.com/files/rs-7433721/v1/071a0f6ab9991606c3c6b2e2.png"},{"id":90320577,"identity":"e26f40e7-c54b-4c1c-8f93-ba2054d7f167","added_by":"auto","created_at":"2025-09-01 10:48:30","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":651500,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDeformation electron density and electrostatic potential for L-tyrosine crystal.\u003c/strong\u003e\u0026nbsp;\u003cstrong\u003ea–f\u003c/strong\u003e, 2D static deformation electron density map in the plane of the carboxylate group (first row) and benzene ring (second row) for the eMM\u003csub\u003eexp\u003c/sub\u003e (\u003cstrong\u003ea,b\u003c/strong\u003e), eMM\u003csub\u003etheo\u003c/sub\u003e (\u003cstrong\u003ec,d\u003c/strong\u003e), and xMM\u003csub\u003eexp\u003c/sub\u003e (\u003cstrong\u003ee,f\u003c/strong\u003e) models. The positive (blue) and negative (red) contours are drawn at ± 0.1 e Å\u003csup\u003e-3\u003c/sup\u003e.\u0026nbsp; \u003cstrong\u003eg–i\u003c/strong\u003e, Molecular electrostatic potential (Bohr Å\u003csup\u003e−1\u003c/sup\u003e) mapped onto the electron density isosurface of 0.05 Bohr Å\u003csup\u003e−3\u003c/sup\u003e for the eMM\u003csub\u003eexp\u003c/sub\u003e (\u003cstrong\u003eg\u003c/strong\u003e), eMM\u003csub\u003etheo\u003c/sub\u003e (\u003cstrong\u003eh\u003c/strong\u003e) and xMM\u003csub\u003eexp\u003c/sub\u003e (\u003cstrong\u003ei\u003c/strong\u003e) models.\u003c/p\u003e","description":"","filename":"Picture8.png","url":"https://assets-eu.researchsquare.com/files/rs-7433721/v1/b9208564d8c138556e5519b2.png"},{"id":90319808,"identity":"8e8e9de6-a321-42d5-afa4-223245a9c529","added_by":"auto","created_at":"2025-09-01 10:40:31","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":480780,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTopological analysis of electron density for L-tyrosine crystal.\u003c/strong\u003e\u0026nbsp;\u003cstrong\u003ea\u003c/strong\u003e, Showing the covalent bonds and hydrogen intermolecular interactions in terms of bond critical points (magenta and green spheres, respectively) and bonding paths (intermolecular interactions only, green lines) for the eMM\u003csub\u003eexp\u003c/sub\u003e model. \u003cstrong\u003eb\u003c/strong\u003e, Laplacian map focusing on selected intermolecular interactions for the eMM\u003csub\u003eexp\u003c/sub\u003e model showing charge concentration (red) and depletion (blue). Positive (blue dotted lines) and negative (red solid lines) contours are drawn at the level of ± 2 × 10\u003csup\u003en\u003c/sup\u003e, ± 4 × 10\u003csup\u003en\u003c/sup\u003e, ± 8 × 10\u003csup\u003en\u003c/sup\u003e (n = -3 to +2) e Å\u003csup\u003e−5\u003c/sup\u003e. Electron density (\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e, e Å\u003csup\u003e−3\u003c/sup\u003e) of non-H bonds \u003cstrong\u003e(c), \u003c/strong\u003eH-bonds\u003cstrong\u003e (d),\u003c/strong\u003e and its Laplacian (∇²\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e, e Å\u003csup\u003e−5\u003c/sup\u003e) of non-H bonds \u003cstrong\u003e(e),\u003c/strong\u003e H-bonds \u003cstrong\u003e(f)\u003c/strong\u003e at covalent bond critical points for the eMM\u003csub\u003eexp\u003c/sub\u003e, eMM\u003csub\u003etheo,\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e models. \u003cstrong\u003eg, h\u003c/strong\u003e, Electron density (\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e, e Å\u003csup\u003e−3\u003c/sup\u003e) \u003cstrong\u003e(g) \u003c/strong\u003eand its Laplacian (∇²\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e, e Å\u003csup\u003e−5\u003c/sup\u003e) \u003cstrong\u003e(h)\u003c/strong\u003e properties for hydrogen intermolecular interactions.\u003c/p\u003e","description":"","filename":"Picture9.png","url":"https://assets-eu.researchsquare.com/files/rs-7433721/v1/8b693e50673e0f179360349c.png"},{"id":94121682,"identity":"224f2a23-24e4-4417-8aec-24f7e233c92d","added_by":"auto","created_at":"2025-10-22 15:19:39","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5379848,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7433721/v1/0ee4b81a-f0e9-4a8e-b240-33b989b761db.pdf"},{"id":90319766,"identity":"61b6bc3a-df97-4b4a-94af-0310686f6c8a","added_by":"auto","created_at":"2025-09-01 10:40:30","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":3836747,"visible":true,"origin":"","legend":"Supplementary Information","description":"","filename":"3DEDmultipolarESI.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7433721/v1/e0eca68aabac8e50a9f71dc6.pdf"},{"id":90321709,"identity":"6a47bd4e-254c-4fc9-b57e-6c9a048300ea","added_by":"auto","created_at":"2025-09-01 10:56:29","extension":"png","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":160483,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eGraphical Abstract\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"GA.png","url":"https://assets-eu.researchsquare.com/files/rs-7433721/v1/ac15577c512ab095e7347d7d.png"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Experimental charge density of organic nanocrystals revealed by 3D electron diffraction","fulltext":[{"header":"Introduction","content":"\u003cp\u003eExperimental charge density analysis has become an important tool in modern crystallography for elucidating the underlying electronic structure of materials\u003csup\u003e\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. By mapping the detailed electron density distribution within molecules and crystals, this approach offers critical insights into interatomic interactions that govern chemical bonding and molecular assembly. Several fundamental properties of interactions can be analyzed using this approach. For example, the spatial distribution of electrons in molecules and crystals can be visualized, allowing for direct observation of both radial and angular deformations in electron charge\u003csup\u003e\u003cspan additionalcitationids=\"CR5 CR6 CR7 CR8\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. Additionally, the evaluation of topological features of the electron density and its associated Laplacian yields quantitative measures of bond strength and character, whether covalent, ionic, or intermediate\u003csup\u003e\u003cspan additionalcitationids=\"CR11\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. Moreover, visualizing and quantifying electrostatic potential distributions allows for evaluating the effects of local charge variations on inter- and intramolecular interactions clarifying the balance between attractive and repulsive forces and facilitates investigation of evolving electrostatic interactions with precise energetic measurements\u003csup\u003e\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. Collectively, these fundamental electronic properties are intrinsically linked to the macroscopic behaviour and overall properties of materials.\u003c/p\u003e\u003cp\u003eThe kappa formalism\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e improves upon the independent atom model (IAM), wherein crystals are treated as collections of non-interacting, neutral atoms. While retaining spherical symmetry, in the kappa formalism two additional parameters are refined against experimental data: the valence electron populations (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eval\u003c/em\u003e\u003c/sub\u003e) and valence electron density expansion-contraction parameter (\u003cem\u003eκ\u003c/em\u003e). This allows to describe charge transfer between atoms and estimate molecular dipole moments for example, overcoming the primary limitation of the IAM.\u003c/p\u003e\u003cp\u003eOne of the most widely adopted approaches for experimental charge density analysis is the multipolar model proposed by Hansen and Coppens\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. In the Hansen-Coppens multipole formalism, the atomic electron density is modelled as aspherical and decomposed into three terms, as outlined below.\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{\\rho\\:}_{at}\\left(\\varvec{r}\\right)=\\:{\\rho\\:}_{core}\\left(r\\right)+{P}_{val}{\\kappa\\:}^{3}{\\rho\\:}_{val}\\left(\\kappa\\:r\\right)+\\:\\sum\\:_{l=0}^{{l}_{max}}{\\kappa\\:}^{{\\prime\\:}3}{R}_{l}\\left({\\kappa\\:}^{{\\prime\\:}}r\\right)\\sum\\:_{m=0}^{+l}{P}_{lm}{d}_{lm\\pm\\:}(\\theta\\:,\\phi\\:)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe first term represents core electrons, assumed to remain unperturbed and non-interacting. The second term captures partial charge transfer via valence electron population (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eval\u003c/em\u003e\u003c/sub\u003e) and valence electron density expansion/contraction (\u003cem\u003eκ\u003c/em\u003e) coefficients, constituting the kappa formalism. The third term models valence electron asphericity using a radial function \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003el\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003eκ'r\u003c/em\u003e) and spherical harmonics \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003elm\u0026plusmn;\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(θ,φ)\u003c/em\u003e, together with their expansion/contraction (\u003cem\u003eκ'\u003c/em\u003e), and population (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003elm\u003c/em\u003e\u003c/sub\u003e) coefficients.\u003c/p\u003e\u003cp\u003eCharge density analysis based on the multipole formalism applied to high-resolution XRD data is well established and plays a crucial role in crystal engineering and pharmaceutical sciences by enhancing our understanding of non-covalent interactions and drug-receptor complex interactions\u003csup\u003e\u003cspan additionalcitationids=\"CR19 CR20 CR21 CR22 CR23\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. Despite its significant contributions, this approach has notable limitations. First, high-resolution XRD requires relatively large crystals of high quality \u0026ndash;a major challenge when working with small organic molecules and macromolecules. Second, the time consuming data collection time poses further difficulties, although the use of synchrotron radiation can mitigate this issue to some extent\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. Moreover, a critical drawback of XRD data is that it is hardly possible to perform free refinement of hydrogen atom positions and atomic displacement parameters simultaneously with multipole model parameters\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eThree-dimensional electron diffraction (3D ED), also known as MicroED, is a recent addition to the structural science toolbox that effectively addresses challenges associated with analyzing micro- and nanocrystals\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e and the accurate localization of hydrogen atoms\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e. Initially introduced by Kolb et al.\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e and subsequently adapted into several variants\u003csup\u003e\u003cspan additionalcitationids=\"CR31 CR32 CR33 CR34 CR35\" citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. 3D ED has advanced significantly over the past decade, driven by ultrafast data acquisition from nanocrystals. The technique is particularly well suited for studying micro- and nanocrystals because electrons, as charged particles, interact with matter approximately 10\u003csup\u003e4\u003c/sup\u003e times more strongly than X-rays. Electrons are scattered by the electrostatic (Coulombic) potential of the sample, which arises from both atomic nuclei and electron clouds. Since the positive potential of nuclei is largely cancelled by the negative potential of electrons, 3D ED in fact probes the difference between these two contributions. Consequently, hydrogen atom localization is facilitated, as protons are largely de-shielded due to the absence of core electrons and the high polarization of their valence electrons towards covalent partners. Moreover, electron charge transfer between atoms leads to significant changes in their electrostatic potential and thus their scattering power, particularly at low scattering angles\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e,\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. This effect is only weakly dependent on the atomic number and may remain still relatively large for heavier elements\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. Thus, 3D ED data may allow for the free refinement of hydrogen atom positions and anisotropic atomic displacement parameters (ADPs) along with electron density-deformation parameters. Moreover, valence electron charge transfer as well as radial and angular deformations of the valence electron charge density distribution should be easier to capture by multipole model refinement, even for atoms dominated by the core electron density.\u003c/p\u003e\u003cp\u003eOne reason why 3D ED is not yet widely used for charge density studies is that it is significantly impacted by dynamical diffraction. When this effect is neglected, and only the kinematic approximation is used, the resulting fit to the experimental data is poor, the refinement results in poor refinement statistics, the structural models may suffer from large inaccuracies and extracting detailed structure information becomes exceedingly difficult, making kinematical refinement unsuitable for charge density studies\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. Pioneering experimental charge density studies using electron diffraction data for inorganic crystals\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e,\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e were initially performed as full multipole model refinement under the kinematical approximation or dynamically corrected CBED data combined with XRD data. A possibility to study chemical bonding in organic crystal using 3D ED data by refinemenent of spherical charge density model involving a mid-bond charge-clouds complemented with dynamical diffraction theory was shown for the first time by Wu and Spence\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e. Recently, advanced computational methods based on Bloch wave calculations have enabled the dynamical refinement of 3D ED data, routinely yielding improved structural models\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e,\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e and making dynamical kappa refinement on inorganic crystals possible\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e. Combined with the current ability to collect high-resolution, high-quality 3D ED data with limited beam damage\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e, these developments now open the possibility of performing full multipole model refinements also on organic crystals using the dynamical refinement approach, thereby extending charge density analysis to nanocrystalline samples.\u003c/p\u003e\u003cp\u003eIn this study, we performed the experimental charge density analysis using 3D ED data on three organic crystals. High-resolution 3D ED data for L-alanine, urea and L-tyrosine were collected and subjected to full multipole refinement using the dynamical diffraction approach. We compare our results with multipole refinement results obtained from simulated electron diffraction data based on DFT calculations as well as high-resolution experimental XRD data, thereby validating the obtained models and elucidating the differences and similarities between 3D ED and XRD.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eExperimental charge density analysis requires good-quality high-resolution diffraction data. We have selected L-alanine, urea and L-tyrosine molecules for the experimental charge density analysis on 3D ED data primarily because their crystals are relatively stable under the electron beam, i.e., they are less prone to radiation damage. Moreover, the experimental charge density analyses for L-alanine and urea from XRD data are well documented in the literature\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e,\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e, constituting excellent reference data as well as proving that good quality crystals can be grown for these compounds. Surprisingly, there was no experimental charge density analysis for L-tyrosine molecules from XRD data available in the literature. Therefore, for this work, we additionally collected high-quality high-resolution XRD data for L-tyrosine and performed the experimental charge density analysis for reference. Excellent quality single crystals of the compounds L-alanine, urea and L-tyrosine (\u003cb\u003eFig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/b\u003e) were selected for the 3D ED data collection in the continuous rotation mode at a temperature of 100 K. The data were extracted up to the resolution of 0.44 \u0026Aring;, 0.53 \u0026Aring;, and 0.59 \u0026Aring;, respectively (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). At these resolutions, relatively high completeness was achieved for all three compounds (around 90%). The \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eint\u003c/em\u003e\u003c/sub\u003e values of all three data sets, in the range of 12.5\u0026ndash;16.7%, are quite low for electron diffraction data, and indicate a high data quality, although it should be noted that the \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eint\u003c/em\u003e\u003c/sub\u003e has only a limited predictive power in the presence of strong dynamical effects.\u003c/p\u003e\u003cp\u003eThe kinematical IAM refinements were performed on the 3D ED data for crystals of all three compounds and yielded figures of merit (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e-factors) in the range of 15.2\u0026ndash;18.4% (\u003cb\u003eTable \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/b\u003e) and structure models of quality not satisfactory to perform the charge density analysis. In all subsequent steps, the dynamical effects were taken into account, and both dynamical IAM and, subsequently, dynamical multipole model refinements were performed using the dynamical refinement approach. During the dynamical refinements, the thickness, shape and mosaicity of the crystal were taken into account.\u003c/p\u003e\u003cp\u003eThe multipole refinements were initiated from the results of a Transferable Aspherical Atom Model (TAAM) refinements, utilizing multipole parameters taken from the MATTS data bank (see Materials and SI for further details). These parameters provided a physically meaningful and chemically realistic starting point for the dynamical multipole model refinements. This initial step is essential because multipole model refinements involve optimizing a large number of correlated parameters on top of the, already computationally expensive, dynamical refinement. Starting from MATTS-derived parameters speeds up the convergence and improves the likelihood of converging to a physically reasonable and global or near-global minimum, rather than trapping the refinement in nonphysical local minima. The quality of the multipole model refinements on experimental 3D ED data was evaluated by analyzing the residual Fourier maps and merged R-factors\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e (MR-factors, calculated by performing symmetry-averaging of intensities) to judge the quality of the model fit to the data, and by analyzing the physical correctness of the refined multipole models. For the latter, we focused on atomic charges computed from \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eval\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eq\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eva\u003c/em\u003el\u003c/sub\u003e \u0026ndash; \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eval\u003c/em\u003e\u003c/sub\u003e, where \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eval\u003c/em\u003e\u003c/sub\u003e is the number of valence electrons in a neutral atom), \u003cem\u003eκ\u003c/em\u003e and \u003cem\u003eκ'\u003c/em\u003e values, deformation electron density, electrostatic potential and electron density topology. The results were compared with the properties computed from the multipole models refined against theoretical electron static structure factors obtained from periodic DFT calculation and experimental high-resolution XRD data. The details of the qualitative and quantitative charge density analyses for each compound are discussed in the following subsections. From now on, the multipole model refinements against experimental 3D ED data, against theoretical electron static structure factors, and against experimental XRD data will be referred to as eMM\u003csub\u003eexp\u003c/sub\u003e, eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e, respectively. Similarly, the dynamical IAM refinements against 3D ED data are denoted eIAM\u003csub\u003eexp\u003c/sub\u003e.\u003c/p\u003e\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eL-alanine\u003c/h2\u003e\u003cdiv id=\"Sec4\" class=\"Section3\"\u003e\u003ch2\u003eIAM refinement\u003c/h2\u003e\u003cp\u003eIn the eIAM\u003csub\u003eexp\u003c/sub\u003e refinement of L-alanine, the coordinates and anisotropic ADPs of all the atoms, including hydrogen, were refined freely, i.e. no restraints or constraints were used during the refinement. After eIAM\u003csub\u003eexp\u003c/sub\u003e refinement, the ADPs of all the atoms were positive definite (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea\u003cb\u003e)\u003c/b\u003e. The M\u003cem\u003eR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e (obs) was 6.15%, and the residual electrostatic potential maximum and minimum values were 0.274/-0.313 e \u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The 3D Fourier map of the residual electrostatic potential showed that despite the relatively good model and model-to-data fit, some unmodelled information was still present in the data (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb), justifying the usage of more sophisticated multipole model.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\n\u003ch3\u003eMultipole model refinement\u003c/h3\u003e\n\u003cp\u003eFor L-alanine, the refinement of multipole parameters associated with the oxygen atoms required special handling due to convergence issues and parameter correlations. Initially, the spherical harmonic coefficients \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003elm\u003c/em\u003e\u003c/sub\u003e for oxygen were constrained to their values from the MATTS data bank to stabilize the refinement. Following the convergence of all other parameters, the \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003elm\u003c/em\u003e\u003c/sub\u003e values for oxygen along with their associated valence population (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eval\u003c/em\u003e\u003c/sub\u003e), and expansion/contraction parameters (\u003cem\u003eκ\u003c/em\u003e and \u003cem\u003eκ\u0026prime;\u003c/em\u003e) were released and refined. Subsequently, the remaining parameters were refined again with the updated \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003elm\u003c/em\u003e\u003c/sub\u003e values of oxygen atoms fixed, ensuring internal consistency and stability in the final model. The eMM\u003csub\u003eexp\u003c/sub\u003e refinement resulted in improvements in the refinement statistics (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) and better structural model (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec-d). The Fourier residual electrostatic potential maps (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee) clearly indicated the better fit of the eMM\u003csub\u003eexp\u003c/sub\u003e model to the data compared to eIAM\u003csub\u003eexp\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb). The X\u0026ndash;H bond lengths (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec) obtained from the eMM\u003csub\u003eexp\u003c/sub\u003e were systematically shorter compared to eIAM\u003csub\u003eexp\u003c/sub\u003e, by 0.04 \u0026Aring; (\u003cb\u003eTable S2\u003c/b\u003e), and more similar to the reference bond lengths from eMM\u003csub\u003etheo\u003c/sub\u003e (RMSD of 0.01 \u0026Aring;) and from xMM\u003csub\u003eexp\u003c/sub\u003e (RMSD by 0.01 \u0026Aring;). It is worth noticing that in the eMM\u003csub\u003etheo\u003c/sub\u003e, model the X\u0026ndash;H bond lengths resulted from the DFT geometry optimization, and in the xMM\u003csub\u003eexp\u003c/sub\u003e model the mean values from neutron\u003csup\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e diffraction were used as constraints. The anisotropic ADPs of H-atoms were improved after the multipole refinement (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed\u003cb\u003e)\u003c/b\u003e, though some still resulted in ellipsoids having their orientation and shape at the border of being physically correct. The resulting \u003cem\u003eU\u003c/em\u003e\u003csub\u003e\u003cem\u003eeq\u003c/em\u003e\u003c/sub\u003e of the H-atoms of eMM\u003csub\u003eexp\u003c/sub\u003e falls in between the \u003cem\u003eU\u003c/em\u003e\u003csub\u003e\u003cem\u003eeq\u003c/em\u003e\u003c/sub\u003e values from neutron diffraction data\u003csup\u003e\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e collected at 60 K and 295 K, and much closer to the 60 K \u003cb\u003e(Fig. S2\u003c/b\u003e), indicating that overall magnitudes of hydrogen atom displacements were physically correct. \u003cem\u003eU\u003c/em\u003e\u003csub\u003e\u003cem\u003eeq\u003c/em\u003e\u003c/sub\u003e for non-hydrogen atoms of eMM\u003csub\u003eexp\u003c/sub\u003e also had an appropriate magnitude compared to neutron diffraction data and were very similar to \u003cem\u003eU\u003c/em\u003e\u003csub\u003e\u003cem\u003eeq\u003c/em\u003e\u003c/sub\u003e from xMM\u003csub\u003eexp\u003c/sub\u003e. The chemically plausible atomic charges confirmed the accuracy of the eMM\u003csub\u003eexp\u003c/sub\u003e model. The majority of the atoms followed the same trend as seen in the reference eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e models, except N1 and C2 atoms (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef). The root mean square differences in atomic charges between eMM\u003csub\u003eexp\u003c/sub\u003e and any of the reference models (0.14 e and 0.10 e for eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e, respectively, except the N1 and C2, (\u003cb\u003eTable S2\u003c/b\u003e) were not larger than the RMSD between the two reference models (0.14 e), and only slightly larger than the mean e.s.d. for \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eval\u003c/em\u003e\u003c/sub\u003e parameters from eMM\u003csub\u003eexp\u003c/sub\u003e. Moreover, the \u003cem\u003eκ\u003c/em\u003e and \u003cem\u003eκ'\u003c/em\u003e values from eMM\u003csub\u003eexp\u003c/sub\u003e were in the physically acceptable range (oscillating around 1.0) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eg-h) and the agreement with the eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e (RMSDs of 0.07 and 0.10 for \u003cem\u003eκ\u003c/em\u003e and \u003cem\u003eκ'\u003c/em\u003e, respectively) is comparable with the agreement between the two reference models (RMSD of 0.06 and 0.09 for \u003cem\u003eκ\u003c/em\u003e and \u003cem\u003eκ'\u003c/em\u003e, respectively).\u003c/p\u003e\n\u003ch3\u003eDeformation electron density, electrostatic potential and QTAIM topology properties (dup: abstract ?)\u003c/h3\u003e\n\u003cp\u003eThe deformation of electron density maps of L-alanine computed from eMM\u003csub\u003eexp\u003c/sub\u003e highlighted the accurate features of covalent bond densities, locations, and orientations of the lone electron pairs (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea) and regions of depletion of electron densities around the molecule (\u003cb\u003eFig. S3a\u003c/b\u003e), which is confirmed by qualitative agreement with the reference eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb-c, \u003cb\u003eFig. S3b-c\u003c/b\u003e).\u003c/p\u003e\u003cp\u003eThe molecular electrostatic potential of L-alanine calculated from the eMM\u003csub\u003eexp\u003c/sub\u003e and plotted on the molecular surface allowed to identify the electropositive, neutral, and electronegative regions in the molecule, helping to understand the nature of the intermolecular interactions (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed\u003cb\u003e)\u003c/b\u003e. The oxygen atoms of the carboxyl group and hydrogen atoms of the ammonium group had electronegative and electropositive surfaces, respectively, whereas the methyl group had a neutral potential surface, which agreed with the reference eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e models (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed-e). Quantitatively, the surface potential maxima and minima from eMM\u003csub\u003eexp\u003c/sub\u003e and eMM\u003csub\u003etheo\u003c/sub\u003e agreed very well (\u003cb\u003eTable S3\u003c/b\u003e), while xMM\u003csub\u003eexp\u003c/sub\u003e potentials were slightly shifted towards negative values. The small differences may be the result of the different sensitivity of X-ray radiation to the charge distribution as well as the usage of fixed averaged neutron-diffraction H positions and estimated ADPs.\u003c/p\u003e\u003cp\u003eThe QTAIM\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e topological analysis of electron density calculated from the eMM\u003csub\u003eexp\u003c/sub\u003e of L-alanine crystal showed to be useful to further characterize the nature of covalent and intermolecular interactions. Bonding paths (BP) for all expected covalent bonds were identified, and all hydrogen bonding interactions were found (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea\u003cb\u003e)\u003c/b\u003e as observed in the reference models (\u003cb\u003eFig. S4a-b\u003c/b\u003e). The maps of ▽\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e showed all characteristic features of covalent bonds, electron pairs and hydrogen bonding interactions (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb, \u003cb\u003eFig. S5a-e\u003c/b\u003e). The topological values at bond critical points (BCPs) (\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e, ▽\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e and \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e) obtained from eMM\u003csub\u003eexp\u003c/sub\u003e were comparable with the reference values from eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec-f, \u003cb\u003eFig. S6\u003c/b\u003e, \u003cb\u003eTable S4-S5\u003c/b\u003e). They clearly indicated, especially by the sign of ▽\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e at the BCP, which interactions were covalent (▽\u003csup\u003e2\u003c/sup\u003e\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0) and which were of closed-shell nature (▽\u003csup\u003e2\u003c/sup\u003e\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0). For covalent bonds, the differences between topological values from eMM\u003csub\u003eexp\u003c/sub\u003e and the reference eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e were not much larger than the difference between the eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e themselves (0.2 e \u0026Aring;\u003csup\u003e\u0026minus;3\u003c/sup\u003e vs. 0.1 e \u0026Aring;\u003csup\u003e\u0026minus;3\u003c/sup\u003e for \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e, and 6\u0026ndash;8 e \u0026Aring;\u003csup\u003e\u0026minus;5\u003c/sup\u003e vs. 4 e \u0026Aring;\u003csup\u003e\u0026minus;5\u003c/sup\u003e for ▽\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e, \u003cb\u003eTable S2\u003c/b\u003e). In the case of hydrogen bonding, the topological values of eMM\u003csub\u003eexp\u003c/sub\u003e for the H\u0026middot;\u0026middot;\u0026middot;Acceptor interactions were on average slightly closer to the reference eMM\u003csub\u003etheo\u003c/sub\u003e (0.03e \u0026Aring;\u003csup\u003e\u0026minus;3\u003c/sup\u003e for \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e and 0.3 e \u0026Aring;\u003csup\u003e\u0026minus;5\u003c/sup\u003e for ▽\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e) than the xMM\u003csub\u003eexp\u003c/sub\u003e was to eMM\u003csub\u003etheo\u003c/sub\u003e (by 0.04 e \u0026Aring;\u003csup\u003e\u0026minus;3\u003c/sup\u003e for \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e and 0.4 e \u0026Aring;\u003csup\u003e\u0026minus;5\u003c/sup\u003e for ▽\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e). This proves that the refinement of hydrogen atomic positions and anisotropic ADPs leads not only to improved geometry but also improved electron density properties.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eCrystal data and refinement parameters against 3D ED data for dynamical IAM and multipole refinement\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eParameters\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL-alanine\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eUrea\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eL-tyrosine\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSpace group\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003eP\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e2\u003csub\u003e1\u003c/sub\u003e2\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cem\u003eP\u003c/em\u003e-42\u003csub\u003e1\u003c/sub\u003e\u003cem\u003em\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cem\u003eP\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e2\u003csub\u003e1\u003c/sub\u003e2\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUnit cell \u003cem\u003ea\u003c/em\u003e, \u003cem\u003eb\u003c/em\u003e, \u003cem\u003ec\u003c/em\u003e (\u0026Aring;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e5.7691(4), 5.9494(4), 12.2453(7)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e5.6308(4), 5.6308(4), 4.7145(10)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e5.8283(9), 6.8709(12), 21.136(4)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAngles α, β, γ (\u0026deg;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e90, 90, 90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e90, 90, 90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e90, 90, 90\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVolume (\u0026Aring;\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e420.29(4)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e149.48(3)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e846.4(2)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eResolution (\u0026Aring;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.44\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.53\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.59\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCompleteness (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e95.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e90.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003eint\u003c/sub\u003e obs (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e12.51\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e16.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e16.65\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e\u003cp\u003e\u003cb\u003eDynamical IAM Refinement\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRsg\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.66\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.66\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eThickness model\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ewedge\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ewedge\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ewedge\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eThickness (\u0026Aring;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2468.72\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2110.34\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3000.74\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTilt correction\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-0.063\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.086\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.473\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIsotropic mosaicity (\u0026deg;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.018\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.023\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0001\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eReflection used obs [\u003cem\u003eI\u0026thinsp;\u0026gt;\u0026thinsp;3σ(I)\u003c/em\u003e]/ all\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e5473/10640\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1368/2663\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e5708/7864\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eConstraints/ Restraints/ Parameters\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0/0/178\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0/0/91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0/0/265\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e obs [\u003cem\u003eI\u0026thinsp;\u0026gt;\u0026thinsp;3σ(I)\u003c/em\u003e]/ all (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e8.00/10.49\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e8.15/12.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e5.30/6.26\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003ewR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e obs [\u003cem\u003eI\u0026thinsp;\u0026gt;\u0026thinsp;3σ(I)\u003c/em\u003e]/ all (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e8.82/9.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e9.06/9.42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e5.74/5.92\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNo. of reflection after symmetry averaging (obs [\u003cem\u003eI\u0026thinsp;\u0026gt;\u0026thinsp;3σ(I)\u003c/em\u003e]/all)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2902/5027\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e380/588\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3323/3989\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eM\u003cem\u003eR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e obs [\u003cem\u003eI\u0026thinsp;\u0026gt;\u0026thinsp;3σ(I)\u003c/em\u003e]/ M\u003cem\u003eR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e all /M\u003cem\u003ewR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e all (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e6.15/7.89/7.18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e6.61/8.80/7.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e4.68/5.19/5.28\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eGooF\u003c/em\u003e \u003csub\u003eobs/all\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3.27/2.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.06/2.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.80/1.58\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eResidual potential max./min. (e \u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.274/-0.313\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.314/-0.264\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.228/-0.245\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e\u003cp\u003e\u003cb\u003eDynamical multipole refinement\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eThickness (\u0026Aring;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2646.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2217.54\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3099.52\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTilt correction\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-0.051\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.084\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.492\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIsotropic mosaicity (\u0026deg;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.020\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.041\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0001\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eReflection used obs [\u003cem\u003eI\u0026thinsp;\u0026gt;\u0026thinsp;3σ(I)\u003c/em\u003e]/ all\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e5475/10642\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1373/2668\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e5708/7864\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eConstraints/ Restraints/ Parameters\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0/0/215\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0/0/113\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0/0/348\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e obs [\u003cem\u003eI\u0026thinsp;\u0026gt;\u0026thinsp;3σ(I)\u003c/em\u003e]/ all (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e7.35/9.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e7.36/11.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e4.08/4.99\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003ewR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e obs [\u003cem\u003eI\u0026thinsp;\u0026gt;\u0026thinsp;3σ(I)\u003c/em\u003e]/ all (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e8.10/8.35\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e8.08/8.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e4.30/4.52\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNo. of reflection after symmetry averaging (obs [\u003cem\u003eI\u0026thinsp;\u0026gt;\u0026thinsp;3σ(I)\u003c/em\u003e]/ all)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2902/5027\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e380/588\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3323/3989\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eM\u003cem\u003eR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e obs [\u003cem\u003eI\u0026thinsp;\u0026gt;\u0026thinsp;3σ(I)\u003c/em\u003e]/ M\u003cem\u003eR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e all/ M\u003cem\u003ewR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e all (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e5.41/7.06/6.36\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e5.43/7.36/6.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3.50/3.99/3.82\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eGooF\u003c/em\u003e \u003csub\u003eobs/all\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3.01/2.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.77/2.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.36/1.21\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eResidual potential max./min. (e \u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.253/-0.239\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.241/0.218\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.147/-0.141\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\n\u003ch3\u003eUrea\u003c/h3\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003eIAM refinement\u003c/h2\u003e\u003cp\u003eConsistent with the L-alanine refinement protocol, no restraints or constraints were applied to the atomic coordinates or ADPs of any atoms during the eIAM\u003csub\u003eexp\u003c/sub\u003e refinement. Following the eIAM\u003csub\u003eexp\u003c/sub\u003e refinement, the ADPs for all atoms were positive definite (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea), with M\u003cem\u003eR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e (obs) value of 6.61% and the residual electrostatic potential map (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb) maximum and minimum peaks of +\u0026thinsp;0.314 e \u0026Aring;\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e and \u0026minus;\u0026thinsp;0.264 e \u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e, respectively.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eMultipole refinement\u003c/h3\u003e\n\u003cp\u003eThe eMM\u003csub\u003eexp\u003c/sub\u003e refinement of urea resulted in the improvement of the refinement statistics (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) and a better structural model (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec-d). The M\u003cem\u003eR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e (obs) was 5.43%. The 3D Fourier maps (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee) showed a dramatic improvement after the multipole refinement compared to eIAM\u003csub\u003eexp\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb), indicating a better fit of the model to experimental 3D ED data. The N\u0026ndash;H bond lengths became shorter by 0.09 \u0026Aring; after the multipole refinement compared to eIAM\u003csub\u003eexp\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec, \u003cb\u003eTable S6\u003c/b\u003e), one of the bonds approached the reference values from eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e, the second became too short by 0.05 \u0026Aring;. The ADPs of hydrogen atoms were visibly improved after the multipole refinement (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed\u003cb\u003e)\u003c/b\u003e, although ellipsoids representing them were not ideally oriented and still slightly elongated in one direction. The \u003cem\u003eU\u003c/em\u003e\u003csub\u003e\u003cem\u003eeq\u003c/em\u003e\u003c/sub\u003e values of both non-hydrogen and hydrogen atoms of eMM\u003csub\u003eexp\u003c/sub\u003e were comparable to neutron diffraction data\u003csup\u003e\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e collected at 123 K (\u003cb\u003eFig. S7\u003c/b\u003e). The chemically appropriate atomic charges confirmed the accuracy of the multipole model of eMM\u003csub\u003eexp,\u003c/sub\u003e and those were similar to the charges of eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e, with a RMSD of 0.21 e and 0.16 e (\u003cb\u003eTable S6\u003c/b\u003e), which is within \u003cem\u003eca.\u003c/em\u003e one e.s.d. for \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eval\u003c/em\u003e\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ef). The \u003cem\u003eκ\u003c/em\u003e and \u003cem\u003eκ'\u003c/em\u003e values of eMM\u003csub\u003eexp\u003c/sub\u003e were also in the physically acceptable ranges and similar to reference eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eg-h). Especially the \u003cem\u003eκ'\u003c/em\u003e values were closer to the reference eMM\u003csub\u003etheo\u003c/sub\u003e (RMSD of 0.14) than the values of xMM\u003csub\u003eexp\u003c/sub\u003e (RMSD of 0.21).\u003c/p\u003e\n\u003ch3\u003eDeformation electron density, electrostatic potential and QTAIM topology properties\u003c/h3\u003e\n\u003cp\u003eThe 2D deformation density maps (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea-c, \u003cb\u003eFig. S8\u003c/b\u003e) highlighted the accurate features of chemical bonding and lone electron pairs in the urea molecule. While the C-N bond density in the eMM\u003csub\u003eexp\u003c/sub\u003e map showed minor imperfections, it remained within an acceptable range for qualitative analysis.\u003c/p\u003e\u003cp\u003eThe electrostatic potentials on the urea molecular surfaces in all three models (eMM\u003csub\u003eexp\u003c/sub\u003e, eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e) were qualitatively similar (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed-f) showing positive regions near hydrogen atoms and negative regions near electronegative oxygen atoms. Quantitatively, the positive surface potentials from eMM\u003csub\u003eexp\u003c/sub\u003e were comparable to eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e positive potentials, but the negative surface potentials were distinct (\u003cb\u003eTables S7\u003c/b\u003e).\u003c/p\u003e\u003cp\u003eTopological analysis of the eMM\u003csub\u003eexp\u003c/sub\u003e electron density revealed bonding paths for all expected covalent bonds and all hydrogen bonding interactions (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea, \u003cb\u003eFig. S9a-b\u003c/b\u003e). Qualitatively, maps of ▽\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e for eMM\u003csub\u003eexp\u003c/sub\u003e show all characteristic features of covalent bonds and electron pairs, with the exception of the lack of separate maxima for the C1 atom in the directions of the N1 atoms (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb, \u003cb\u003eFig. S9c-d\u003c/b\u003e). Nevertheless, the topological values of \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e at BCPs of covalent bonds and hydrogen bonding interactions for eMM\u003csub\u003eexp\u003c/sub\u003e were in the acceptable range (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ec-e, \u003cb\u003eTable S8-S9\u003c/b\u003e) and similar to the reference eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e (with RMSDs of 0.32 e \u0026Aring;\u003csup\u003e\u0026minus;3\u003c/sup\u003e and 0.42 e \u0026Aring;\u003csup\u003e\u0026minus;3\u003c/sup\u003e, respectively, for covalent bonds, and 0.03 e \u0026Aring;\u003csup\u003e\u0026minus;3\u003c/sup\u003e and 0.04 e \u0026Aring;\u003csup\u003e\u0026minus;3\u003c/sup\u003e, respectively, for H\u0026middot;\u0026middot;\u0026middot;Acceptor interactions, \u003cb\u003eTable S6\u003c/b\u003e). The differences between the two reference models were almost the same (RMDS 0.26 e \u0026Aring;\u003csup\u003e\u0026minus;3\u003c/sup\u003e) for covalent bonds and slightly smaller (0.01 e \u0026Aring;\u003csup\u003e\u0026minus;3\u003c/sup\u003e) for H\u0026middot;\u0026middot;\u0026middot;Acceptor interactions. The values for ▽\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e at BCPs agreed relatively well with the reference (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed-f, \u003cb\u003eTable S8-S9\u003c/b\u003e) only for non-hydrogen covalent bonds, with a difference of 10.56 e \u0026Aring;\u003csup\u003e\u0026minus;5\u003c/sup\u003e and 19.08 e \u0026Aring;\u003csup\u003e\u0026minus;5\u003c/sup\u003e from eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e, respectively, where the difference between eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e was 11.90 e \u0026Aring;\u003csup\u003e\u0026minus;5\u003c/sup\u003e (\u003cb\u003eTable S6\u003c/b\u003e). ▽\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e values for the N\u0026ndash;H covalent bonds and the H\u0026middot;\u0026middot;\u0026middot;Acceptor interactions for eMM\u003csub\u003eexp\u003c/sub\u003e were distinct from the reference values. The bond path lengths (\u003cem\u003eR\u003c/em\u003e\u003csub\u003eij\u003c/sub\u003e) for covalent bond and H\u0026middot;\u0026middot;\u0026middot;Acceptor interactions of eMM\u003csub\u003eexp\u003c/sub\u003e were similar to the reference models \u003cb\u003e(Fig. S10)\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003eL-tyrosine\u003c/h2\u003e\u003cdiv id=\"Sec12\" class=\"Section3\"\u003e\u003ch2\u003eIAM refinement\u003c/h2\u003e\u003cp\u003eDuring the eIAM\u003csub\u003eexp\u003c/sub\u003e refinement of L-tyrosine, atomic coordinates and ADPs of all atoms, including hydrogen, were refined freely without restraints or constraints. All refined ADPs were positive definite, except for two hydrogen atoms (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea). The M\u003cem\u003eR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e (obs) was 4.68% and the residual electrostatic potential maximum and minimum values were 0.228/-0.245 e \u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e with the corresponding 3D Fourier map of the electrostatic potential showing many unmodelled negative peaks in the molecule region (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eb).\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003eMultipole model refinement\u003c/h2\u003e\u003cp\u003eIn the case of L-tyrosine, multipole model parameters\u0026thinsp;\u0026minus;\u0026thinsp;specifically the spherical harmonic coefficients (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003elm\u003c/em\u003e\u003c/sub\u003e) and expansion/contraction parameters (\u003cem\u003eκ\u003c/em\u003e and \u003cem\u003eκ\u0026rsquo;\u003c/em\u003e)\u0026thinsp;\u0026minus;\u0026thinsp;were constrained to be identical for chemically equivalent atom types to maintain chemical consistency and reduce the number of independent parameters during the refinement. The eMM\u003csub\u003eexp\u003c/sub\u003e refinement significantly improved both the statistical indicators (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) and the overall quality of the structural model (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ec-d). The M\u003cem\u003eR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e (obs) improved to 3.50% and maximum and minimum residual potential peaks reduced to 0.147/-0.141 e \u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e. The enhanced quality of the Fourier maps after the eMM\u003csub\u003eexp\u003c/sub\u003e refinement (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ee) demonstrates a markedly improved fit of the model to the experimental 3D ED data. The X\u0026ndash;H bond lengths were refined to more accurate values compared to those obtained from the eIAM\u003csub\u003eexp\u003c/sub\u003e model; they shortened by 0.04 \u0026Aring; (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ec, \u003cb\u003eTable S10\u003c/b\u003e). While bond lengths from eMM\u003csub\u003eexp\u003c/sub\u003e remained slightly longer than those from eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e (by 0.02 \u0026Aring;), they still showed clear improvement. Notably, the ADPs of hydrogen atoms became more reliable and positive definite after multipole refinement (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ed). The magnitude of ADPs for non-hydrogen atoms were, however, slightly larger than the reference xMM\u003csub\u003eexp\u003c/sub\u003e, as judged from the \u003cem\u003eU\u003c/em\u003e\u003csub\u003e\u003cem\u003eeq\u003c/em\u003e\u003c/sub\u003e values (\u003cb\u003eFig. S11\u003c/b\u003e). The accuracy of the final eMM\u003csub\u003eexp\u003c/sub\u003e model was further validated through the charges based on \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eval\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eκ\u003c/em\u003e and \u003cem\u003eκ'\u003c/em\u003e values. The charge values matched the eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e values well (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ef-g), with the RMSD of 0.21 e in both cases (\u003cb\u003eTable S10\u003c/b\u003e). Interestingly, only a slightly smaller spread of values was observed also between eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e refinements (RMSD 0.17 e). The \u003cem\u003eκ\u003c/em\u003e and \u003cem\u003eκ'\u003c/em\u003e values for non-hydrogen atoms from eMM\u003csub\u003eexp\u003c/sub\u003e were also in an acceptable range and similar to eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp,\u003c/sub\u003e with the possible exception of \u003cem\u003eκ'\u003c/em\u003e(C7) (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eh,j). The RMSDs for \u003cem\u003eκ\u003c/em\u003e parameters were 0.02 and 0.02, respectively, and for \u003cem\u003eκ'\u003c/em\u003e parameters were 0.11 and 0.19, respectively (\u003cb\u003eTable S10\u003c/b\u003e), comparable to the RMSDs between the two reference models (0.02 for \u003cem\u003eκ\u003c/em\u003e and 0.12 for \u003cem\u003eκ'\u003c/em\u003e). The RMSDs among \u003cem\u003eκ\u003c/em\u003e and \u003cem\u003eκ'\u003c/em\u003e values for hydrogen atoms were somewhat bigger for \u003cem\u003eκ\u003c/em\u003e (0.04 and 0.07 for eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e, respectively) and similar for \u003cem\u003eκ'\u003c/em\u003e (0.13 and 0.10 for eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e, respectively), but still comparable to RMSDs between the two reference models (0.09 for \u003cem\u003eκ\u003c/em\u003e and 0.05 for \u003cem\u003eκ'\u003c/em\u003e ) (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ei,k).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003eDeformation electron density, electrostatic potential and QTAIM topology properties\u003c/h2\u003e\u003cp\u003eDeformation electron density features of L-tyrosine, such as bond charge accumulation and lone-pair localization, were clearly observed in the eMM\u003csub\u003eexp\u003c/sub\u003e model (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea,b, \u003cb\u003eFig. S12a\u003c/b\u003e). In particular, the lone-pair electron density on the carboxyl and hydroxyl oxygen atoms was distinctly resolved in the eMM\u003csub\u003eexp\u003c/sub\u003e map and was in qualitative agreement with the eMM\u003csub\u003etheo\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ec-d, \u003cb\u003eFig. S12b\u003c/b\u003e) and xMM\u003csub\u003eexp\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ee-f, \u003cb\u003eFig. S12c\u003c/b\u003e) models. The deformation density across the aromatic ring in eMM\u003csub\u003eexp\u003c/sub\u003e also revealed π-electron delocalization and chemically meaningful bonding features, with exception of the C7 atom which appeared less aspherical.\u003c/p\u003e\u003cp\u003eThe electrostatic potential for L-tyrosine calculated from the eMM\u003csub\u003eexp\u003c/sub\u003e model (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eg ) showed regions of negative potential localized around the carboxyl and hydroxyl oxygen atoms, while regions of positive potential were centred on hydrogen atoms. The π-system of the aromatic ring exhibited a near-neutral to slightly negative potential, consistent with delocalized electron density. Qualitatively, the electrostatic potential of eMM\u003csub\u003eexp\u003c/sub\u003e model mapped on the molecular surface agreed very well with the reference (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eh-i). Quantitatively, the positive and negative surface potentials from eMM\u003csub\u003eexp\u003c/sub\u003e and eMM\u003csub\u003etheo\u003c/sub\u003e agreed very well (\u003cb\u003eTable S11\u003c/b\u003e), while the negative potentials of xMM\u003csub\u003eexp\u003c/sub\u003e were slightly shifted. The small differences may reflect the fact that X-ray scattering exhibits different sensitivity to charge distribution than electron scattering. It might also result from the usage of fixed, averaged neutron diffraction hydrogen positions.\u003c/p\u003e\u003cp\u003eTopological analysis of eMM\u003csub\u003eexp\u003c/sub\u003e revealed all covalent bond paths, and all intermolecular hydrogen bonding seen in the reference models (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ea, \u003cb\u003eFig. S13a-b\u003c/b\u003e). The overall distribution of \u0026nabla;\u0026sup2;\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e for eMM\u003csub\u003eexp\u003c/sub\u003e qualitatively agrees with the reference distributions, reproducing well regions of positive and negative \u0026nabla;\u0026sup2;\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e, and the presence of local maxima \u0026nabla;\u0026sup2;\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e associated with electron pairs (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eb, \u003cb\u003eFig. S14a-e\u003c/b\u003e). While \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e and \u0026nabla;\u0026sup2;\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e of covalent bonds derived from eMM\u003csub\u003eexp\u003c/sub\u003e for L-tyrosine were generally lower than those from the eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e (by 0.21 e \u0026Aring;\u003csup\u003e\u0026minus;3\u003c/sup\u003e and 0.31 e \u0026Aring;\u003csup\u003e\u0026minus;3\u003c/sup\u003e, respectively, for \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e and by 7.93 e \u0026Aring;\u003csup\u003e\u0026minus;5\u003c/sup\u003e and 10.41 e \u0026Aring;\u003csup\u003e\u0026minus;5\u003c/sup\u003e, respectively, for \u0026nabla;\u0026sup2;\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e), they exhibited similar overall trends and remained within physically acceptable ranges (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ec-f, \u003cb\u003eTable S12\u003c/b\u003e). The RMSDs between the two reference models were only \u003cem\u003eca\u003c/em\u003e. twice smaller (0.15 e \u0026Aring;\u003csup\u003e\u0026minus;3\u003c/sup\u003e for \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e and 5.15 e \u0026Aring;\u003csup\u003e\u0026minus;5\u003c/sup\u003e for \u0026nabla;\u0026sup2;\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e). For intermolecular hydrogen bonding, the eMM\u003csub\u003eexp\u003c/sub\u003e model reproduced quite well the \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e and \u0026nabla;\u0026sup2;\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e values at BCPs of H\u0026middot;\u0026middot;\u0026middot;Acceptor interactions seen in both reference eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e models, with the exception of the H9\u0026middot;\u0026middot;\u0026middot;O2 contact (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eg-h, \u003cb\u003eTable S13)\u003c/b\u003e. The bond path lengths (\u003cem\u003eR\u003c/em\u003e\u003csub\u003eij\u003c/sub\u003e) for covalent bond and H\u0026middot;\u0026middot;\u0026middot;Acceptor interactions of eMM\u003csub\u003eexp\u003c/sub\u003e were similar to the reference models \u003cb\u003e(Fig. S11)\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study establishes the feasibility of performing full multipole charge density analysis using 3D ED data for organic nanocrystals.\u003c/p\u003e\u003cp\u003eA central procedural challenge is the complexity of the refinement, which necessitated starting from (TAAM) rather than the conventional IAM. Multipole refinement involves optimization of a large number of correlated parameters (e.g., \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003elm\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eval\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eκ\u003c/em\u003e, \u003cem\u003eκ\u0026prime;\u003c/em\u003e, ADPs). This creates a rugged refinement landscape with numerous local minima and makes the refinement highly sensitive to the initial conditions. Starting from the IAM, which is a poor approximation of the aspherical charge distribution, frequently leads to trapping of the refinement in false minima with non-physical parameters. The TAAM, by providing a chemically-informed and physically realistic starting point, effectively guides the refinement toward the global minimum, ensuring convergence to a meaningful and stable charge density model.\u003c/p\u003e\u003cp\u003eWhile the final M\u003cem\u003eR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e (obs) values for eMM\u003csub\u003eexp\u003c/sub\u003e refinements (ranging from 3.50\u0026ndash;5.43%) were significantly lower than for dynamical IAM models, they remained higher than typical values seen in X-ray-based charge density studies. This discrepancy arises mainly from the intrinsic differences in the scattering mechanisms: 3D ED data are influenced by strong dynamical diffraction effects, which are inherently more challenging to model than X-ray data for which the kinematical approximation is sufficient. Additionally, the impossibility to collect highly redundant data that could improve the signal-to-noise ratio, and the sensitivity of electron diffraction to the crystal imperfections lead to less ideal data statistics. A direct comparison of the three compounds is revealing: L-tyrosine, which was crystallized \u003cem\u003ein situ\u003c/em\u003e and exhibited the lowest isotropic mosaicity (0.0001 \u0026ordm;), yielded the best R-factor (M\u003cem\u003eR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e (obs)\u0026thinsp;=\u0026thinsp;3.50%). Conversely, L-alanine and urea, which were mechanically ground and had higher mosaicity values, resulted in poorer \u003cem\u003eR\u003c/em\u003e-factors. This strongly suggests that a major source of residual error is physical crystal imperfections\u0026thinsp;\u0026minus;\u0026thinsp;such as strain, defects, and complex mosaic spread\u0026thinsp;\u0026minus;\u0026thinsp;that may not be entirely adequately parameterized by the simplified Gaussian mosaicity model.\u003c/p\u003e\u003cp\u003eIn spite of these limitations, the results of the refinements show that the ED data combined with the dynamical refinement can be successfully used to extract reliable charge-density information and improve the models. The residual electrostatic potential maps after multipole refinement show that the multipole model more accurately accounts for the aspherical features of the electron density, which are neglected in the IAM refinement and cause increased noise in the residual potential maps.\u003c/p\u003e\u003cp\u003eThe successful free refinement of hydrogen positions and ADPs using 3D ED data is another notable achievement, facilitated by the strong interaction of electrons with the electrostatic potential, which is generated by both electrons and protons. However, some issues persist. For example, small discrepancies in atomic charges or \u003cem\u003eκ\u003c/em\u003e and \u003cem\u003eκ\u0026prime;\u003c/em\u003e parameters were observed in certain atoms (e.g., N1 in L-alanine or C7 in L-tyrosine). These are likely influenced by parameter correlations, the sensitivity of 3D ED to dynamical effects, and noise. Additionally, some hydrogen ADPs remained at the edge of physical plausibility, indicating the need for further improvements in modelling protocols or data collection strategies.\u003c/p\u003e\u003cp\u003eThe close alignment of atomic charges, \u003cem\u003eκ/κ\u0026prime;\u003c/em\u003e parameters, deformation electron density features, and electrostatic potentials among the three models demonstrates that 3D ED, when processed with appropriate dynamical refinement, can yield reliable charge density models. For example, the values of \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e and \u0026nabla;\u0026sup2;\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e for covalent and hydrogen bonds from eMM\u003csub\u003eexp\u003c/sub\u003e differed from the reference models by amounts comparable to or only slightly larger than the internal variation between eMM\u003csub\u003etheo\u003c/sub\u003e and xMM\u003csub\u003eexp\u003c/sub\u003e. The electrostatic potential, deformation electron density and Laplacian of electron density of all three compounds were qualitatively consistent across models, capturing essential chemical features such as lone pairs, covalent bonds, hydrogen bonding interactions, and π-delocalization.\u003c/p\u003e\u003cp\u003eThe implications of this work extend far beyond the specific systems studied, opening the door to investigating the electronic structure of materials that have remained stubbornly out of reach. This includes, for example, metastable polymorphs that only form as nanocrystals, complex multicomponent systems like drug-target cocrystals, metal-organic frameworks displaying functional properties in nanocrystalline form, and organic optoelectronic materials whose optical properties depend on the size of the crystal. By establishing the viability of quantitative charge density analysis at the nanoscale, this study provides a new tool for fundamental discovery in chemistry, pharmacology, and materials science. It heralds a new chapter in quantum crystallography, where the intricate details of chemical bonding are no longer hidden by the challenge of growing an ideal large crystal.\u003c/p\u003e\u003cp\u003eHerein, we establish the feasibility of performing full multipole refinement on 3D ED data. While the procedure is demanding, necessitating exceptionally high-quality data and meticulous analysis, the resulting models are robust and suitable for drawing conclusions about the chemical bonding environment. In specific instances, the reliability of the obtained results approaches that of conventional XRD and theoretical DFT calculations. However, additional work is required to further improve the fits, resolve remaining discrepancies in fitting the experimental data, and thereby enhance the stability and accuracy of the multipole refinement.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\u003cdiv id=\"Sec17\" class=\"Section3\"\u003e\u003ch2\u003eSample preparation and data collection\u003c/h2\u003e\u003cp\u003eL-alanine, urea, and L-tyrosine were obtained from commercial suppliers and used without further purification. Crystals of L-alanine and urea were grown by slow evaporation of their respective solvents: a 1:1 (v/v) ethanol\u0026ndash;water mixture for L-alanine, and distilled water for urea. For L-tyrosine, a saturated aqueous solution was prepared at room temperature, and a small droplet was deposited onto a holey carbon TEM grid. After allowing the droplet to sit undisturbed for approximately 30 seconds, the excess solution was gently blotted to induce crystal formation via evaporation. 3D ED measurements for L-alanine and urea were performed on two Rigaku XtaLAB Synergy-ED diffractometers, equipped with a LaB\u003csub\u003e6\u003c/sub\u003e source operating at 200 kV (λ\u0026thinsp;=\u0026thinsp;0.0251 \u0026Aring;) and a Rigaku HyPix-ED detector. A small amount of each sample was first gently crushed in a mortar and pestle to reduce the crystal size. Then, the crystalline powders were deposited on carbon coated copper TEM grids coated (ultrathin continuous carbon from EMS for L-alanine and holey carbon from Pelco for urea). The samples were mounted on a Gatan Elsa\u0026trade; 698 Cryo-transfer holder and cooled at 173 K prior to the insertion in the diffractometer, then cooled to 100 K in a vacuum (ca. 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e Pa). Diffraction patterns were collected on one single crystal of each compound using a selected area aperture (apparent diameter ca. 2 \u0026micro;m) during continuous rotation of the crystals over ca. 120\u0026deg;, with a shutterless scan and frame width of 0.15 \u0026deg; (L-alanine) or 0.2 \u0026deg; (urea). The beam flux density was optimized for a minimally required dose and kept in the range 0.003 to 0.01 e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e \u0026Aring;\u003csup\u003e\u0026minus;2\u003c/sup\u003e. The program CrysAlis\u003csup\u003ePro\u003c/sup\u003e (Rigaku OD, 2024) was used to control the data collection. The camera length was calibrated with the help of an evaporated aluminum diffraction standard grid. 3D ED data for L-tyrosine were collected at 95 K on an FEI Tecnai G2 20 TEM (LaB₆ filament, 200 kV, λ\u0026thinsp;=\u0026thinsp;0.0251 \u0026Aring;) equipped with a Medipix 3 ASI Cheetah hybrid pixel detector. Crystals were crystallized on copper TEM grids with holey carbon film and mounted on a single-tilt holder. Data collection was performed in continuous-rotation mode, controlled by custom scripts within the iTEM software, with crystal tracking during goniometer tilting facilitated by the Fast-ADT routine\u003csup\u003e\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e. All measurements were conducted under cryogenic conditions to minimize thermal vibration.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e\u003ch2\u003eData processing and IAM refinement\u003c/h2\u003e\u003cp\u003ePETS2 software\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e was used for the unit-cell parameter determination, optical distortion refinement, frame orientation optimization, integration of the reflection intensities and data reduction\u003csup\u003e\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e,\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e\u003c/sup\u003e. For dynamical refinement, the intensities were integrated by the concept of overlapping virtual frames\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e. Noise parameters 3 and 0 were used for L-alanine and urea, respectively and 4.2, and 0 for L-tyrosine. For L-alanine, calibration constant was adjusted to obtain more accurate unit cell parameters. Frames that showed any shadow by the specimen support were excluded from the data processing. The final resolution of the data was determined based on completeness (\u0026gt;\u0026thinsp;90%), redundancy (\u0026gt;\u0026thinsp;3), \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eint\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(obs)\u003c/em\u003e (\u0026lt;\u0026thinsp;20%), \u003cem\u003eI/σ(I)\u003c/em\u003e (\u0026gt;\u0026thinsp;1) and \u003cem\u003eCC\u003c/em\u003e\u003csub\u003e1/2\u003c/sub\u003e (\u0026gt;\u0026thinsp;30%) in the last resolution shell.\u003c/p\u003e\u003cp\u003eThe solution and refinement of all three structures were done using the JANA2020 software\u003csup\u003e\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/sup\u003e. Each compound\u0026rsquo;s structure was first solved using the charge-flipping algorithm implemented in Superflip\u003csup\u003e\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e\u003c/sup\u003e. Initial refinements employed the IAM under the kinematical approximation, followed by dynamical refinements. In these dynamical refinements, reflections were filtered using the \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eSg\u003c/em\u003e\u003c/sub\u003e parameter, which quantifies how well a reflection is sampled around the Bragg condition, ensuring that only reliably integrated intensities were included in the refinement\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e,\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e. Refinements were based on \u003cem\u003eF\u003c/em\u003e amplitudes and the Wilson\u0026rsquo;s modification weighting scheme was used. Refinement quality was assessed using R-factors and the residual features in electrostatic potential difference maps. To account for variations in the crystal thickness\u0026thinsp;\u0026minus;\u0026thinsp;particularly critical in dynamical refinement\u0026thinsp;\u0026minus;\u0026thinsp;an idealized geometrical models (i.e. a wedge) was applied to approximate the probability distribution of thickness across the crystal. During the 3D ED experiment, tilting the crystal changes the effective thickness along the electron beam. To account for this, an empirical correction was applied that interpolates between two extremes: a flat plate model where thickness increases with tilt (t(α)\u0026thinsp;=\u0026thinsp;t₀ / cosα) and an isometric model where thickness remains constant (t(α)\u0026thinsp;=\u0026thinsp;t₀), with α the tilt angle. The final correction uses a tunable parameter C (0\u0026thinsp;\u0026le;\u0026thinsp;C\u0026thinsp;\u0026le;\u0026thinsp;1) to represent the actual behavior as t(θ)\u0026thinsp;=\u0026thinsp;t₀ / [(1 \u0026ndash; C)\u0026thinsp;+\u0026thinsp;C\u0026middot;cosθ], providing a flexible and physically realistic model of thickness variation during tilting\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e. In addition to geometric and tilt-based corrections, we refined the average incoherent isotropic mosaicity for all compounds. This parameter accounts for angular spread due to slight misorientations of mosaic blocks within a crystal, which can impact the accuracy of calculated diffraction intensities in dynamical refinement. Including mosaicity improved overall agreement between observed and calculated intensities, the stability of the multipole refinement and the accuracy of the resulting mode\u003csup\u003e\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec19\" class=\"Section2\"\u003e\u003ch2\u003eMultipole model refinement on 3D ED data\u003c/h2\u003e\u003cp\u003eThe multipole model refinements were performed using the Hansen-Coppens multipole formalism\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e in the JANA2020 software. During each refinement cycle, JANA2020 computes model-based X-ray structure factors from the current multipole electron density, incorporating both spherical and aspherical contributions using Slater-type orbitals. These structure factors are then converted into electron structure factors using the Mott\u0026ndash;Bethe formula. Based on these electron structure factors, dynamical diffraction intensities are calculated using the Bloch-wave formalism, which accounts for multiple scattering, crystal thickness, and orientation.\u003c/p\u003e\u003cp\u003eThe refinement minimises the difference between these calculated dynamical intensities and the experimental electron diffraction intensities via least-squares optimisation. Importantly, this is a fully dynamical refinement against the raw experimental 3D ED data, not against transformed or corrected X-ray-equivalent data. All relevant parameters, including atomic coordinates, ADPs, and multipole model parameters (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eval\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eκ\u003c/em\u003e, \u003cem\u003eκ'\u003c/em\u003e, \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003elm\u003c/em\u003e\u003c/sub\u003e), are refined simultaneously. This approach distinguishes itself from earlier methods that either applied kinematical multipole refinements to corrected 3D ED data or refined multipole parameters alone against pseudo-X-ray structure factors. The multipole refinements were carried out using the Su-Coppens radial functions for the core and spherical valence electron density terms\u003csup\u003e\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e\u003c/sup\u003e. The initial models for multipole refinements were obtained from the IAM structures fully refined with dynamical approach. These models provided a physically realistic starting point that incorporates multiple scattering effects and accurate crystal thickness estimations. Retaining the same dynamical diffraction framework ensured consistency between IAM and multipole refinements. First, dynamical TAAM refinements\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e were carried out using the fixed multipole model parameter values transferred from the MATTS data bank\u003csup\u003e\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e,\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e\u003c/sup\u003e using the discambMATTS2tsc program\u003csup\u003e\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e\u003c/sup\u003e. In dynamical TAAM refienements, the same set of parameters was refined as in dynamical IAM, but with multipolar scatteringa factors computed from TAAM. After that, dynamical multipole model refinements were performed in a step-wise and iterative-block refinement manner \u003cb\u003e(Fig. S16)\u003c/b\u003e. First, only \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eval\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eκ\u003c/em\u003e parameters were allowed to be refined, still with \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003elm\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eκ'\u003c/em\u003e values constrained at values from the MATTS data bank. The multipole expansion was refined up to the octupole level for non-H atoms. For H-atoms, only bond-directed dipoles and quadrupoles were refined. The \u003cem\u003eκ\u003c/em\u003e and \u003cem\u003eκ'\u003c/em\u003e parameters were refined individually for all the non-H atoms. For H-atoms, \u003cem\u003eκ\u003c/em\u003e and \u003cem\u003eκ'\u003c/em\u003e parameters were assigned to be the same for the chemically equivalent types of atoms and refined. Importantly, the positions and anisotropic displacement parameters (ADPs) of all hydrogen atoms were freely refined throughout the refinement process. The inclusion of hydrogen ADPs is especially significant in electron diffraction, where hydrogen atoms scatter more strongly than in XRD, allowing for improved accuracy in modelling light atom behaviour and hydrogen bonding interactions.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec20\" class=\"Section2\"\u003e\u003ch2\u003eMultipole model refinement on X-ray data\u003c/h2\u003e\u003cp\u003eFor L-alanine\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e (CCDC No. 2443207) and urea\u003csup\u003e\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e (CCDC No. 1047783), the available high-resolution XRD data were used for the reference experimental charge density analyses. In the case of L-tyrosine, high-resolution X-ray data were collected for good-quality single crystal (\u003cb\u003eFig. S17\u003c/b\u003e) on an in-house instrument and used for the reference experimental charge density analysis (\u003cb\u003edetails in SI\u003c/b\u003e, \u003cb\u003eTable S14\u003c/b\u003e). The resolution of the XRD data was cut to reach the same resolutions as were observed for the 3D ED data, these were 0.44 \u0026Aring;, 0.53 \u0026Aring; and 0.59 \u0026Aring; for L-alanine, urea and L-tyrosine, respectively. The multipole model refinements were performed in the JANA2020 software using the same settings (except for dynamical scattering) and refinement strategy as used for the multipole refinement on the 3D ED data, with the following exceptions. The anisotropic displacement parameters (ADPs) of hydrogen atoms for L-alanine and L-tyrosine were estimated using the SHADE2.1server\u003csup\u003e\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e\u003c/sup\u003e and for urea, the ADPs from neutron diffraction data were used\u003csup\u003e\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e. These values were incorporated and kept fixed during the refinements. First, the scale factor refinements were performed using all reflections \u003cb\u003e(Fig S16)\u003c/b\u003e. Next, high-order refinements for the non-H atoms were performed to determine the accurate positional and displacement parameters, while the positions of the H atoms were derived with a riding model with the X\u0026ndash;H bond lengths constrained to the mean neutron values\u003csup\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e. For the H atoms, the refinement of \u003cem\u003eκ'\u003c/em\u003e parameters was not stable, therefore the parameters were constrained at the MATTS data bank values. Refinements were based on \u003cem\u003eF\u003c/em\u003e amplitudes and the Wilson\u0026rsquo;s modification weighting scheme was used. Crystal data and multipole refinment parameters of xMM\u003csub\u003eexp\u003c/sub\u003e for all three molecules are listed in \u003cb\u003eTable S15\u003c/b\u003e.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e\u003ch2\u003eComputational methods\u003c/h2\u003e\u003cp\u003eThe crystal structure of L-alanine (CCDC No. 1009312) from XRD experimental studies performed at 100 K was used for the theoretical calculation\u003csup\u003e\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e\u003c/sup\u003e. For urea, the crystal structure from neutron diffraction studies performed at 123 K (CCDC No. 1278500) was used for the theoretical calculations\u003csup\u003e\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e. In the case of L-tyrosine, the crystal structure determined in this work from multipole refinement on high-resolution XRD data was used.\u003c/p\u003e\u003cp\u003eTo obtain the theoretical structure factors, the experimental geometries (atomic coordinates) of all three molecules were optimized with frozen unit-cell parameters by applying periodic DFT calculations using CRYSTAL17\u003csup\u003e67\u003c/sup\u003e (the details of Geometry optimization and X-ray static structure factor calculation are discussed in the SI). The calculated X-ray static structure factors were converted into kinematical electron static structure factors by application of the Motte-Bethe formula\u003csup\u003e\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e\u003c/sup\u003e using the dedicated DiSCaMB utility program\u003csup\u003e\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e\u003c/sup\u003e. Then, the electron static structure factors were imported into Jana2020 and the multipole model refinements were performed for L-alanine, urea and L-tyrosine using the same strategy as for multipole model refinements on experimental 3D ED data, with the exception of the atomic positions \u0026ndash; these were constrained to the optimized geometry positions and the ADPs were set to zero and not refined \u003cb\u003e(Fig S16)\u003c/b\u003e. All refinements were carried out on \u003cem\u003eF\u003c/em\u003e using unit weights and kinematical approximation. Crystal data and multipole refinment parameters of eMM\u003csub\u003etheo\u003c/sub\u003e for all three molecules are listed in \u003cb\u003eTable S16\u003c/b\u003e.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec22\" class=\"Section2\"\u003e\u003ch2\u003eTopological and Electrostatic Potential Analysis\u003c/h2\u003e\u003cp\u003eThe topological analysis of electron density based on Bader\u0026rsquo;s QTAIM theory and deformation density maps of the molecules was performed using the MoPro Viewer program as implemented in the MoPro suite\u003csup\u003e\u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e69\u003c/span\u003e\u003c/sup\u003e. For the covalent and non-covalent interactions, the topological properties such as \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e of bonding path, \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e and \u0026nabla;\u0026sup2;\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ebcp\u003c/sub\u003e were calculated. The electrostatic potential was computed from the refined multipole model of electron density of studied molecules using XD2024\u003csup\u003e70\u003c/sup\u003e and mapped on the iso-contour of molecular electron density using the MoleCoolQt\u003csup\u003e\u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cdiv id=\"Sec23\" class=\"Section3\"\u003e\u003ch2\u003eData availability\u003c/h2\u003e\u003cp\u003eAll the data needed to evaluate the conclusion in the paper are present in the paper and/or the Supplementary Materials. Raw data, the data reduction and processing files, the kinematical, dynamical IAM and dynamical multipole refinements files of 3D ED data, the multipole refinement files for theoretical electron static structure factors, the multipole refinement files for experimental X-ray diffraction, X-ray diffraction raw data, data processing and refinements files for L-tyrosine and CIF files of all the compounds used in this study are available online using the following doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.18150/VNLTKK\u003c/span\u003e\u003cspan address=\"10.18150/VNLTKK\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.18150/FNLNWC\u003c/span\u003e\u003cspan address=\"10.18150/FNLNWC\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.18150/VTBPGP\u003c/span\u003e\u003cspan address=\"10.18150/VTBPGP\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e [RepOD (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://repod.icm.edu.pl/\u003c/span\u003e\u003cspan address=\"https://repod.icm.edu.pl/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e), Repository for Open Data, Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw, Warsaw, Poland] and \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.5281/zenodo.16752042\u003c/span\u003e\u003cspan address=\"10.5281/zenodo.16752042\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (a repository hosted by Zenodo).\u003c/p\u003e\u003cp\u003eThe CIF files with results from all dynamical IAM and dynamical multipole refinements (3D ED) and L-tyrosine (X-ray IAM refinement) presented in this work can be retrieved free-of-charge from the Cambridge Structural Database (CSD) (deposition numbers: CCDC 2479735\u0026ndash;2479739 and 2480319\u0026ndash;2480320).\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\n\u003ch2\u003eCompeting interests\u003c/h2\u003e\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e\u003cp\u003eThe National Science Center, Poland, provided the funding for the research presented in this work under the grant 2020/39/I/ST4/02904. The work is also supported by the H2020 ITN project NanED, grant agreement No. 956099. Acknowledgment is also extended to the Polish high-performance computing infrastructure PLGrid (HPC Centers: ACK Cyfronet AGH, WCSS) for providing computer facilities and support within the computational grant no. PLG/2024/017098. Part of the electron diffraction experiments are supported by Novo Nordisk Foundation Research Infrastructure grant n. NNF220C0074439.\u003c/p\u003e\u003ch2\u003eAuthor contributions\u003c/h2\u003e\u003cp\u003eConcept: P.M.D., L.P., A.K.; 3D ED Data collection: A.K., A.L., J.W., P.B; XRD Data collection: A.K., D.T.; 3D ED data reduction, processing and refinements: A.K., A.S.; Multipole refinement of experiment 3D ED data: A.K., A.S.; Multipole refinement on theortical and XRD data: A.K., Topological analysis: A.K.; Theoretical calculations: A.K.; Writing original draft: A.K., A.S.; Supervision: P.M.D., L.P.; Writing review \u0026amp; editing: All authors contributed to the review and editing collaboratively.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eWe thank Felix Hennersdorf, Maurycy Nowak, Anna Hoser and Anna Makal for support during initial 3D ED data collections attempts.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eGillet JM, Koritsanszky T (2012) Past, present and future of charge density and density matrix refinements. Mod Charge-Density Anal\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePawledzio S, Einkauf J, Custelcean R, Wang X (2025) Intermolecular Interactions in Direct Air Capture Materials: Insights from Charge Density Analysis. J Am Chem Soc\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKoch D et al (2024) The Analysis of Electron Densities: From Basics to Emergent Applications. Chem Rev 124:12661\u0026ndash;12737\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKasai H et al (2018) X-ray electron density investigation of chemical bonding in van der Waals materials. Nat Mater 17:249\u0026ndash;252\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhurova EA, Matta CF, Wu N, Zhurov VV, Pinkerton AA (2006) Experimental and Theoretical Electron Density Study of Estrone. J Am Chem Soc 128:8849\u0026ndash;8861\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKumar A, Mohanty B, Munshi P (2023) Probing Diversity in Binding Affinities of Polymorphs of an Anticancer Agent against Human γ-Enolase: A Quantum Crystallographic Perspective. Cryst Growth Des 23:580\u0026ndash;591\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJha KK et al (2019) Structure\u0026ndash;Property Relationship in an Organic Semiconductor: Insights from Energy Frameworks, Charge Density Analysis, and Diode Devices. Cryst Growth Des 19:3019\u0026ndash;3029\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eFlaig R, Koritsanszky T, Dittrich B, Wagner A, Luger P (2002) Intra- and Intermolecular Topological Properties of Amino Acids: A Comparative Study of Experimental and Theoretical Results. J Am Chem Soc 124:3407\u0026ndash;3417\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eCoppens P et al (1999) Experimental Charge Densities and Intermolecular Interactions: Electrostatic and Topological Analysis of dl-Histidine. J Am Chem Soc 121:2585\u0026ndash;2593\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eM\u0026uuml;nch A et al (2020) Insight into the Bonding and Aggregation of Alkyllithiums by Experimental Charge Density Studies and Energy Decomposition Analyses. J Am Chem Soc 142:15897\u0026ndash;15906\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eEraković M, Cinčić D, Molčanov K, Stilinović VA (2019) Crystallographic Charge Density Study of the Partial Covalent Nature of Strong N\u0026sdot;\u0026sdot;\u0026sdot;Br Halogen Bonds. Angew Chemie 131:15849\u0026ndash;15853\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSarkar S et al (2022) X-ray Electron Density Study of the Chemical Bonding Origin of Glass Formation in Metal\u0026ndash;Organic Frameworks**. Angew Chemie Int Ed 61\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eFournier B et al (2009) Charge Density and Electrostatic Interactions of Fidarestat, an Inhibitor of Human Aldose Reductase. J Am Chem Soc 131:10929\u0026ndash;10941\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePavan MS, Durga Prasad K (2013) Guru Row, T. N. Halogen bonding in fluorine: experimental charge density study on intermolecular F⋯F and F⋯S donor\u0026ndash;acceptor contacts. Chem Commun 49:7558\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSingla L, Kumar A, Robertson CM, Munshi P (2023) Roy Choudhury, A. Investigation of C\u0026ndash;F\u0026middot;\u0026middot;\u0026middot;F\u0026ndash;C Interactions Using Experimental and Theoretical Charge Density Analyses. Cryst Growth Des 23:853\u0026ndash;861\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eCoppens P et al (1979) Net atomic charges and molecular dipole moments from spherical-atom X-ray refinements, and the relation between atomic charge and shape. Acta Crystallogr Sect A 35:63\u0026ndash;72\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHansen NK, Coppens P (1978) Testing aspherical atom refinements on small-molecule data sets. Acta Crystallogr Sect A 34:909\u0026ndash;921\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKoritsanszky TS, Coppens P (2001) Chemical Applications of X-ray Charge-Density Analysis. Chem Rev 101:1583\u0026ndash;1628\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKrawczuk A, Macchi P (2014) Charge density analysis for crystal engineering. Chem Cent J 8:68\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSaleh G, Gatti C, Lo Presti L, Contreras-Garc\u0026iacute;a J (2012) Revealing Non‐covalent Interactions in Molecular Crystals through Their Experimental Electron Densities. Chem \u0026ndash; Eur J 18:15523\u0026ndash;15536\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eStalke D (2011) Meaningful Structural Descriptors from Charge Density. Chem \u0026ndash; Eur J 17:9264\u0026ndash;9278\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKleemiss F et al (2021) Similarities and Differences between Crystal and Enzyme Environmental Effects on the Electron Density of Drug Molecules. Chem \u0026ndash; Eur J 27:3407\u0026ndash;3419\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYearley EJ, Zhurova EA, Zhurov VV, Pinkerton AA (2007) Binding of Genistein to the Estrogen Receptor Based on an Experimental Electron Density Study. J Am Chem Soc 129:15013\u0026ndash;15021\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKorlyukov AA et al (2020) Charge density view on bicalutamide molecular interactions in the monoclinic polymorph and androgen receptor binding pocket. IUCrJ 7:71\u0026ndash;82\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHayashi M, Nishioka T, Kasai H, Nishibori E (2025) Accurate temperature dependence of structure factors of L-alanine and taurine for quantum crystallography. IUCrJ 12:384\u0026ndash;392\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhurov VV, Pinkerton AA (2015) Inter- and Intramolecular Interactions in Crystalline 2-Nitrobenzoic Acid\u0026mdash;An Experimental and Theoretical QTAIM Analysis. J Phys Chem A 119:13092\u0026ndash;13100\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJones CG et al (2018) The CryoEM Method MicroED as a Powerful Tool for Small Molecule Structure Determination. ACS Cent Sci 4:1587\u0026ndash;1592\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePalatinus L et al (2017) Hydrogen positions in single nanocrystals revealed by electron diffraction. Sci (80-) 355:166\u0026ndash;169\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKolb U, Gorelik T, Otten MT (2008) Towards automated diffraction tomography. Part II\u0026mdash;Cell parameter determination. Ultramicroscopy 108:763\u0026ndash;772\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGemmi M et al (2019) 3D Electron Diffraction: The Nanocrystallography Revolution. ACS Cent Sci 5:1315\u0026ndash;1329\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGruene T, Mugnaioli E (2021) 3D Electron Diffraction for Chemical Analysis: Instrumentation Developments and Innovative Applications. Chem Rev 121:11823\u0026ndash;11834\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYonekura K, Maki-Yonekura S (2016) Refinement of cryo-EM structures using scattering factors of charged atoms. J Appl Crystallogr 49:1517\u0026ndash;1523\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYuan S et al (2018) [Ti\u003csub\u003e8\u003c/sub\u003e Zr\u003csub\u003e2\u003c/sub\u003e O\u003csub\u003e12\u003c/sub\u003e (COO)\u003csub\u003e16\u003c/sub\u003e] Cluster: An Ideal Inorganic Building Unit for Photoactive Metal\u0026ndash;Organic Frameworks. ACS Cent Sci 4:105\u0026ndash;111\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eCichocka MO, \u0026Aring;ngstr\u0026ouml;m J, Wang B, Zou X, Smeets S (2018) High-throughput continuous rotation electron diffraction data acquisition via software automation. J Appl Crystallogr 51:1652\u0026ndash;1661\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eClabbers MTB, Hattne J, Martynowycz MW, Gonen T (2025) Energy filtering enables macromolecular MicroED data at sub-atomic resolution. Nat Commun 16:2247\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNannenga BL, Gonen T (2019) The cryo-EM method microcrystal electron diffraction (MicroED). Nat Methods 16:369\u0026ndash;379\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGruza B, Chodkiewicz ML, Krzeszczakowska J, Dominiak PM (2020) Refinement of organic crystal structures with multipolar electron scattering factors. Acta Crystallogr Sect Found Adv 76:92\u0026ndash;109\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYonekura K, Kato K, Ogasawara M, Tomita M, Toyoshima C (2015) Electron crystallography of ultrathin 3D protein crystals: Atomic model with charges. \u003cem\u003eProc. Natl. Acad. Sci.\u003c/em\u003e 112, 3368\u0026ndash;3373\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBochtler M (2024) X-rays, electrons, and neutrons as probes of atomic matter. Structure 32:630\u0026ndash;643e6\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKumar A et al (2024) TAAM refinement on high-resolution experimental and simulated 3D ED/MicroED data for organic molecules. Acta Crystallogr Sect C Struct Chem 80:264\u0026ndash;277\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAvilov AS (2003) The quantitative analysis of electrostatic potential and study of chemical bonding by electron diffraction structure analysis. Z fur Krist 218:247\u0026ndash;258\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZuo JM, Kim M, O\u0026rsquo;Keeffe M, Spence JCH (1999) Direct observation of d-orbital holes and Cu\u0026ndash;Cu bonding in Cu\u003csub\u003e2\u003c/sub\u003eO. Nature 401:49\u0026ndash;52\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWu JS, Spence JCH (2003) Structure and bonding in α-copper phthalocyanine by electron diffraction. Acta Crystallogr Sect Found Crystallogr 59:495\u0026ndash;505\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKlar PB et al (2023) Accurate structure models and absolute configuration determination using dynamical effects in continuous-rotation 3D electron diffraction data. Nat Chem 15:848\u0026ndash;855\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eOlech B, Br\u0026aacute;zda P, Palatinus L, Dominiak PM (2024) Dynamical refinement with multipolar electron scattering factors. IUCrJ 11:309\u0026ndash;324\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSuresh A et al (2024) Ionisation of atoms determined by kappa refinement against 3D electron diffraction data. Nat Commun 15:9066\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eDestro R, Soave R, Barzaghi M (2008) Physicochemical Properties of Zwitterionic L- and DL-alanine Crystals from Their Experimental and Theoretical Charge Densities. J Phys Chem B 112:5163\u0026ndash;5174\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBirkedal H et al (2004) The charge density of urea from synchrotron diffraction data. Acta Crystallogr Sect Found Crystallogr 60:371\u0026ndash;381\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAllen FH, Bruno IJ (2010) Bond lengths in organic and metal-organic compounds revisited: X \u0026mdash;H bond lengths from neutron diffraction data. Acta Crystallogr Sect B Struct Sci 66:380\u0026ndash;386\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWilson CC, Myles D, Ghosh M, Johnson LN, Wang W (2005) Neutron diffraction investigations of l- and d-alanine at different temperatures: the search for structural evidence for parity violation. New J Chem 29:1318\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBader RF (1991) W. A quantum theory of molecular structure and its applications. Chem Rev 91:893\u0026ndash;928\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSwaminathan S, Craven BM, McMullan RK (1984) The crystal structure and molecular thermal motion of urea at 12, 60 and 123 K from neutron diffraction. Acta Crystallogr Sect B Struct Sci 40:300\u0026ndash;306\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePlana-Ruiz S et al (2020) Fast-ADT: A fast and automated electron diffraction tomography setup for structure determination and refinement. Ultramicroscopy 211:112951\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePalatinus L et al (2019) Specifics of the data processing of precession electron diffraction tomography data and their implementation in the program PETS2.0. Acta Crystallogr Sect B Struct Sci Cryst Eng Mater 75:512\u0026ndash;522\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBr\u0026aacute;zda P, Klementov\u0026aacute; M, Krysiak Y, Palatinus L (2022) Accurate lattice parameters from 3D electron diffraction data. I. Optical distortions. IUCrJ 9:735\u0026ndash;755\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBr\u0026aacute;zda P, Palatinus L, Babor M (2019) Electron diffraction determines molecular absolute configuration in a pharmaceutical nanocrystal. Sci (80-) 364:667\u0026ndash;669\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePetř\u0026iacute;ček V, Palatinus L, Pl\u0026aacute;šil J, Dušek M (2023) Jana2020 \u0026ndash; a new version of the crystallographic computing system Jana. Z f\u0026uuml;r Krist - Cryst Mater 238:271\u0026ndash;282\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePalatinus L, Chapuis G (2007) SUPERFLIP \u0026ndash; a computer program for the solution of crystal structures by charge flipping in arbitrary dimensions. J Appl Crystallogr 40:786\u0026ndash;790\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePalatinus L, Petř\u0026iacute;ček V, Corr\u0026ecirc;a CA (2015) Structure refinement using precession electron diffraction tomography and dynamical diffraction: theory and implementation. Acta Crystallogr Sect Found Adv 71:235\u0026ndash;244\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePalatinus L (2024) Including mosaicity effects in the dynamical refinement against 3D ED data. Acta Crystallogr Sect Found Adv 80:e225\u0026ndash;e225\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSu Z, Coppens P (1992) On the mapping of electrostatic properties from the multipole description of the charge density. Acta Crystallogr Sect Found Crystallogr 48:188\u0026ndash;197\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJha KK et al (2022) Multipolar Atom Types from Theory and Statistical Clustering (MATTS) Data Bank: Restructurization and Extension of UBDB. J Chem Inf Model 62:3752\u0026ndash;3765\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eRybicka PM, Kulik M, Chodkiewicz ML, Dominiak PM (2022) Multipolar Atom Types from Theory and Statistical Clustering (MATTS) Data Bank: Impact of Surrounding Atoms on Electron Density from Cluster Analysis. J Chem Inf Model 62:3766\u0026ndash;3783\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eChodkiewicz ML et al (2018) DiSCaMB: a software library for aspherical atom model X-ray scattering factor calculations with CPUs and GPUs. J Appl Crystallogr 51:193\u0026ndash;199\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMunshi P, Madsen A\u0026Oslash;, Spackman MA, Larsen S, Destro R (2008) Estimated H-atom anisotropic displacement parameters: a comparison between different methods and with neutron diffraction results. Acta Crystallogr Sect Found Crystallogr 64:465\u0026ndash;475\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eEscudero-Ad\u0026aacute;n EC, Benet-Buchholz J, Ballester P (2014) The use of Mo K α radiation in the assignment of the absolute configuration of light-atom molecules; the importance of high-resolution data. Acta Crystallogr Sect B Struct Sci Cryst Eng Mater 70:660\u0026ndash;668\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eDovesi R et al (2018) Quantum-mechanical condensed matter simulations with CRYSTAL. WIREs Comput Mol Sci 8\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eThe scattering of electrons by atoms. Proc. R. Soc. London. Ser. A, Contain. Pap. a Math. Phys. Character 127, 658\u0026ndash;665 (1930)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJelsch C, Guillot B, Lagoutte A, Lecomte C (2005) Advances in protein and small-molecule charge-density refinement methods using MoPro. J Appl Crystallogr 38:38\u0026ndash;54\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKoritsanszky T, Volkov A, Farrugia LJ, Mallinson PR, Macchi P, Gatti C, Richter T \u003cem\u003eXD\u003c/em\u003e(2024). A computer program package for multipole refinement, topological analysis of charge densities and evaluation of intermolecular energies from experimental and theoretical structure factors.(2024). A computer program package for multipole refinement, topological analysis of charge densities and evaluation of intermolecular energies from experimental and theoretical structure factors.(2024)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eH\u0026uuml;bschle CB, Dittrich B (2011) MoleCoolQt \u0026ndash; a molecule viewer for charge-density research. J Appl Crystallogr 44:238\u0026ndash;240\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7433721/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7433721/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCharge density analysis is a cornerstone of quantum crystallography, offering deep insights into electron densities and chemical bonding in crystals, traditionally relying on high-resolution X-ray diffraction (XRD). Three-dimensional electron diffraction (3D ED) emerges as a powerful alternative, uniquely suited for micro- and nanocrystals and accurate hydrogen atoms localization due to a strong electron-matter interaction. This study presents a comprehensive experimental charge density analysis of L-alanine, urea, and L-tyrosine crystals using 3D ED. Incorporating dynamical scattering into multipole refinement allowed to model accurately electron density and simultaneously to reliably refine hydrogen positions and anisotropic displacements−beyond XRD limitations. Results align well with DFT and experimental XRD data, validating the approach. These findings establish 3D ED as a powerful and viable method for full charge density analysis for organic crystals, particularly in cases where conventional XRD is limited by small crystal size, difficulty in resolving hydrogen atoms, or reduced sensitivity to subtle electron density features.\u003c/p\u003e","manuscriptTitle":"Experimental charge density of organic nanocrystals revealed by 3D electron diffraction","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-01 10:40:25","doi":"10.21203/rs.3.rs-7433721/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"428d1a2a-b580-458c-a39b-c433bacf52f7","owner":[],"postedDate":"September 1st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":53807344,"name":"Physical sciences/Chemistry/Physical chemistry"},{"id":53807345,"name":"Physical sciences/Chemistry/Theoretical chemistry/Quantum chemistry"}],"tags":[],"updatedAt":"2026-03-05T21:55:25+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-01 10:40:25","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7433721","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7433721","identity":"rs-7433721","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}