Selective Stabilization of β-Blockers within Cationic Vesicles: A DFT Study of Propranolol, Atenolol, and Metoprolol

Selective Stabilization of β-Blockers within Cationic Vesicles: A DFT Study of Propranolol, Atenolol, and Metoprolol | 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 Research Article Selective Stabilization of β-Blockers within Cationic Vesicles: A DFT Study of Propranolol, Atenolol, and Metoprolol Nurendra Chhetri, Moazzam Ali This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7575992/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Theoretical investigation on the interaction between a cationic, double tailed vesicle-forming surfactant dioctadecyldimethylammonium bromide (DDOAB) and three non-selective β-blocker drugs: propranolol (PPL), atenolol (ATL), and metoprolol (MPL), have been carried out using Density Functional Theory (DFT). The primary aim is to elucidate the molecular mechanisms governing drug-surfactant complex formation, stability, and electronic behaviour in gas phase, thereby providing foundational insights into their potential relevance in drug delivery systems. PPL-DDOAB system exhibited the most stable complex, followed by ATL-DDOAB and MPL-DDOAB, based on relative stabilization energies. Frontier Molecular Orbital (FMO) analysis revealed significant changes in the HOMO–LUMO energy levels upon complex formation. The energy gap (ΔE) decreased for all drug-surfactant complexes compared to the isolated drugs, indicating enhanced electronic interaction and altered reactivity. Notably, the PPL-DDOAB complex showed the lowest energy gap (4.67 eV), suggesting improved electron mobility and the highest charge transfer potential among the studied systems. Quantum molecular descriptors (QMDs), calculated from HOMO and LUMO energies, further supported these findings. The chemical hardness (η) of DDOAB decreased upon complexation, with the lowest value in the PPL-DDOAB complex, implying increased reactivity and stabilization. Electrophilicity (ω) and softness values (S) also varied among the complexes, highlighting subtle differences in chemical behaviour. Non-Covalent Interaction (NCI) analysis, combined with Reduced Density Gradient (RDG) plots, visually and quantitatively identified van der Waals forces, steric repulsions, and hydrogen bonding as the main contributors to complex stabilization. Overall, the findings underscore the critical role of non-covalent interactions in the formation and stability of drug-surfactant complexes. These insights are vital for the rational design of vesicle-based drug delivery systems, where optimized molecular interactions can significantly influence drug loading, release, and bioavailability. β- blockers vesicle DFT HOMO-LUMO non-covalent Figures Figure 1 Figure 2 Figure 3 1. Introduction Micelles and vesicles, the two predominant self-assembled surfactant structures, differ fundamentally in their morphology and molecular organization. These structural distinctions strongly influence how drug molecules partition within the system, associate with the surfactant assembly, and ultimately manifest their interactions. Vesicles are structurally and functionally closer to biological membranes than micelles because they consist of a lipid bilayer arranged tail-to-tail, creating two aqueous compartments that mimic the inside and outside of a cell, whereas micelles have only a single layer with no compartmentalization. This bilayer organization in vesicles allows them to exhibit lamellar phases, gel-to-fluid transitions, and membrane-like permeability, as well as to support processes such as fusion, transport, and insertion of proteins or lipids, making them highly suitable as model membranes [ 1 – 3 ]. Vesicles are thus better model systems for biological membranes than micelles. Furthermore, the larger size and bilayer curvature of vesicles allow for cooperative binding effects and more complex interaction patterns, making them superior platforms for probing drug–membrane interactions relevant to drug delivery and pharmacokinetics [ 4 ]. Vesicles prepared from the natural phospholipids surfactants are widely employed both as model membranes and as drug delivery vehicles [ 5 , 6 ]. However, vesicles formed from the synthetic cationic surfactants such as dimethyldioctadecylammonium bromide (DDOAB) are particularly notable for their biocompatibility, permeability, surface potential, and close resemblance to natural membranes [ 7 , 8 ]. While such systems have been extensively explored in experimental studies, theoretical investigations remain comparatively limited [ 9 – 12 ]. The interaction of a drug with a membrane is governed by several factors, the most critical being its molecular shape, size, pKa, and hydrophobicity [ 13 , 14 ]. A clear understanding of drug–vesicle interactions is crucial for improving the efficacy and stability of many pharmaceutical formulations. β-blockers rank among the most effective therapeutic agents for managing heart failure, certain types of arrhythmias, hypertension, and myocardial infarction [ 15 ]. Propranolol (PPL), atenolol (ATL), and metoprolol (MPL) are widely used non-selective β-blockers in the treatment of cardiovascular disorders [ 16 ]. Notably, propranolol has been shown to exert membrane-stabilizing effects, indicating that its interaction with membranes [ 17 ] may be a significant factor in understanding its toxicity, particularly under overdose conditions [ 18 ]. Given these pharmacological properties, numerous studies have explored the interaction of β-blockers with lipid membranes using a variety of experimental techniques. Krill et al. [ 19 ] investigated several β-blocker drugs, including propranolol, oxprenolol, nadolol, and metoprolol, and reported that these compounds alter the thermotropic phase behaviour of dimyristoylphosphatidylcholine (DMPC) bilayers in a manner dependent on their lipophilicity. Likewise, the interactions of β-blockers such as propranolol, oxprenolol, and acebutolol with palmitoyloleoylphosphatidylcholine (POPC) membranes have been examined using time-dependent fluorescence shift (TDFS) and generalized polarization (GP) measurements [ 20 ]. This study demonstrated that increasing β-blocker concentrations lead to a rigidification of the lipid bilayers at both the glycerol backbone and headgroup regions, with propranolol producing the most pronounced effect. Experimental techniques such as calorimetry, spectroscopy, and microscopy have greatly advanced our understanding of key parameters in drug–membrane systems, including partitioning, drug release, and membrane fluidity [ 21 – 23 ]. However, these methods often fall short in providing detailed insights into the electronic aspects of drug–surfactant interactions such as charge transfer, frontier orbital overlap, specific interaction types, and the stability of drug–membrane complexes. To bridge this gap, computational approaches like Density Functional Theory (DFT) offer valuable tools for probing the electronic nature of molecular interactions as they provide atomic-level insight into the nature and strength of non-covalent forces, including hydrogen bonding, electrostatic, π–π, and van der Waals interactions. DFT enables accurate evaluation of binding and interaction energies, charge distribution, and electron density changes, thereby clarifying the molecular basis of drug localization and stabilization within the environment of organised medium [ 24 ]. Moreover, theoretical predictions of vibrational, electronic, and NMR parameters can be directly correlated with experimental spectra, facilitating interpretation of spectral shifts upon complex formation [ 25 ] By isolating specific interaction modes in a controlled virtual environment, DFT helps overcome limitations of experimental techniques in complex multicomponent systems. Therefore, the aim of this study is to elucidate the nature of interactions between PPL, ATL, and MPL with DDOAB vesicles at the DFT level, providing insights into orbital contributions, stabilization energies, and non-covalent interaction patterns that can aid in the rational design of more effective drug delivery systems. 2. Computational methods The theoretical computations were carried out using the DFT approach[ 26 ]. All structural optimization and calculations for PPL, MPL, ATL and their complexes with DDOAB in gas phase were carried out using Gaussian 09 software package [ 27 ]. Additionally, the B3LYP functional, which combines Becke’s three parameters exchange and the Lee -Yang-Parr correlation functionals[ 28 , 29 ] has been used for the study along with the 6-31G (D, P) basic set, implemented in Gaussian 09 software within the framework of Density functional theory (DFT). The B3LYP functional is widely recognized as a reliable choice in drug design, owing to its proven ability to accurately predict the structural, electronic, and magnetic properties of drug molecules. It is often regarded as a “workhorse” functional in quantum chemistry, offering an effective balance between computational accuracy and cost [ 30 ]. Furthermore, non-covalent interaction (NCI) and reduced density gradient (RDG) analyses were carried out using Multiwfn, gnuplot, IrfanView, and VMD software[ 31 ] to visualize and evaluate weak interactions, including hydrogen bonding, van der Waals forces, and steric effects. 3. Results and Discussion 3.1. Optimised structures and their energies The molecular geometries of the individual β-blocker drug molecules propranolol (PPL), atenolol (ATL), and metoprolol (MTL) as well as the vesicle-forming double-tailed surfactant dioctadecyldimethylammonium bromide (DDOAB) were optimized using density functional theory (DFT). The optimisation energies are presented in Table 1 . Subsequently, the corresponding drug–surfactant complexes (PPL–DDOAB, ATL–DDOAB, and MTL–DDOAB) were also optimized, and their optimisation energies are also presented in Table 1 . In all cases, the energies of the drug–DDOAB complexes were significantly lower than the energies of the individual drug and surfactant molecules, clearly indicating the spontaneous formation of more stable supramolecular assemblies. The total electronic energies of the PPL–DDOAB, ATL–DDOAB, and MTL–DDOAB complexes were found to be -62.45 x 10 5 kJ/mol, -63.87 x 10 5 kJ/mol, and − 63.48 x 10 5 kJ/mol, respectively, suggesting that propranolol interacts more favorably with the vesicular surfactant, resulting in the most stable complex. This observation is consistent with the intrinsic hydrophobic character of propranolol, which enhances its affinity toward the hydrophobic microenvironment provided by the DDOAB vesicle. Previous studies have likewise demonstrated that propranolol exhibits stronger interactions with single-chain cationic surfactants as the alkyl chain length increases, primarily due to enhanced hydrophobic interactions between the surfactant tail and the hydrophobic naphthalene moiety of propranolol [ 32 ]. To gain deeper insight into complex stability, interaction (stabilization) energies (Table 1 ) were calculated as the difference between the total energy of the complex and the sum of the energies of the individual drug and surfactant molecules. The calculated stabilization energies for all three drug–DDOAB systems were negative, confirming that their association is thermodynamically favourable. A negative interaction energy signifies stabilizing complexation, while a positive value would indicate negligible binding. Among the systems studied, the interaction energies follow the order DDOAB–PPL (− 0.59 eV) > DDOAB–ATL (− 0.73 eV) > DDOAB–MTL (− 0.77 eV), indicating that propranolol exhibits the strongest affinity toward DDOAB, followed by atenolol and metoprolol. The stronger stabilization of the PPL–DDOAB complex can be attributed to the high hydrophobicity of propranolol, which facilitates deeper accommodation within the nonpolar microenvironment of the DDOAB bilayer. In addition to van der Waals stabilization, hydrophobic interactions and possible cation–π interactions between the aromatic naphthalene ring of PPL and the positively charged surfactant headgroup further enhance the binding affinity. In comparison, atenolol and metoprolol, with higher polarity and hydrogen-bond donor/acceptor functionalities, results in relatively weaker overall stabilization compared to propranolol. These results are in line with previous reports that highlight the preferential association of propranolol with cationic surfactant assemblies owing to its amphiphilic character and favorable partitioning into hydrophobic domains [ 33 ]. Table 1 The energy of the individual molecules, complexes, and the stabilization energy. System Energy in kJ/mol stabilizing energy (kJ/mol) DDOAB -40.72 x 10 5 PPL -21.72 x 10 5 ATL -23.15 x 10 5 MPL -22.76 x 10 5 DDOAB-PPL -62.45 x 10 5 -57.23 DDOAB-ATL -63.87 x 10 5 -70.88 DDOAB-MPL -63.48 x 10 5 -74.51 3.2 Frontier Molecular Orbitals (FMOs) and HOMO–LUMO Gap Analysis Frontier Molecular Orbital (FMO) theory provides valuable insights into molecular reactivity by analyzing the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) [ 34 ]. The HOMO energy reflects a molecule’s electron-donating ability (ionization potential), while the LUMO energy relates to its electron-accepting capacity (electron affinity) [ 35 ]. The energy gap (ΔE = E LUMO − E HOMO ) is a key descriptor of stability and reactivity: larger ΔE values correspond to harder, less polarizable molecules, whereas smaller ΔE values indicate more reactive systems with enhanced potential for charge transfer [ 36 ]. For the individual β-blockers, clear differences were observed. PPL exhibited the smallest HOMO–LUMO gap, with its HOMO localized on the naphthalene ring, hydroxyl substituent, and secondary amine, and its LUMO spread across the naphthalene–OH region. In contrast, atenolol ATL and MPL showed larger gaps, with HOMOs delocalized over their aromatic ring and hydroxyl groups, and in ATL additionally extending onto the acetamide moiety. Their LUMOs were primarily localized around the aromatic rings. These distinct orbital distributions likely contribute to the differences in their respective energy gaps. Notably, the smaller energy gap in PPL may indicate a more reactive geometry, as minimal ΔE values are often associated with enhanced chemical reactivity and potential for interaction [ 37 ]. The surfactant DDOAB exhibits a higher ΔE value (− 6.152 eV) compared to the individual drug molecules PPL, ATL, and MPL. This difference can be attributed to the spatial distribution of the frontier molecular orbitals in DDOAB, where the HOMO is predominantly localized along the hydrocarbon alkyl chain, approximately five carbon atoms away from the head group, while the LUMO is concentrated over the head group containing the quaternary ammonium unit. A similar trend was observed in investigation involving single chain quaternary ammonium surfactants of varying alkyl chain lengths in the presence of PPL [ 38 ]. The calculated HOMO–LUMO gaps for the complexes were: PPL–DDOAB (4.67 eV) < ATL–DDOAB (5.46 eV) < MPL–DDOAB (6.01 eV). This order indicates that the PPL–DDOAB complex requires the least energy for electronic excitation and is therefore the most chemically reactive and polarizable. ATL–DDOAB exhibits moderate reactivity, while MPL–DDOAB has the largest gap, implying greater kinetic stability but weaker charge-transfer potential. The results indicate that the PPL–DDOAB complex exhibits pronounced intramolecular charge transfer and greater thermodynamic stability, arising from its reduced ΔE and aromatic-rich electronic framework, which stem from electron redistribution induced by the perturbation of HOMO and LUMO energy levels during complex formation [ 39 ]. The resulting change in electron distribution alters the HOMO–LUMO gap (ΔE), which directly influences chemical reactivity, polarizability, and stability [ 40 ]. Thus, the FMO analysis underscores the importance of drug structure in dictating electronic behavior upon complexation with vesicle-forming surfactants, with direct implications for drug delivery performance. 3.3 Quantum Molecular Descriptors (QMDs) Quantum molecular descriptors (QMDs) derived from frontier orbital energies offer quantitative measures of global stability and reactivity. Based on Koopmans’ theorem [ 41 ], key descriptors such as chemical potential (µ), electronegativity (χ), chemical hardness (η), softness (S), and electrophilicity index (ω) can be obtained from E HOMO and E LUMO values using equations (1)–(5). $$\:\begin{array}{c}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mu\:=\frac{\left({E}_{HOMO}+{E}_{LUMO}\right)}{2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(1\right)\end{array}$$ $$\:\begin{array}{c}\eta\:=\frac{\left({E}_{LUMO}+{E}_{HOMO}\right)}{2}\:\left(2\right)\end{array}$$ $$\:\begin{array}{c}S=\frac{1}{2{\eta\:}}\:\left(3\right)\end{array}$$ $$\:\begin{array}{c}\chi\:=\:\frac{-\left({E}_{LUMO}+{E}_{HOMO}\right)}{2}\:\left(4\right)\end{array}$$ $$\:\begin{array}{c}\omega\:=\:\frac{{{\mu\:}}^{2}}{2{\eta\:}}\:\left(5\right)\end{array}$$ These parameters complement the HOMO–LUMO gap (ΔE) analysis by providing a more detailed picture of how electronic properties change upon complexation. Generally, higher hardness (η) and lower softness (S) correspond to chemically stable systems, while lower hardness and higher softness signify greater reactivity and polarizability. The electrophilicity index (ω) reflects the ability of a system to stabilize additional electronic charge. The calculated QMD values for the individual molecules and their DDOAB complexes are summarized in Table 2 . Table 2 The E HOMO , E LUMO , Chemical potential (µ), Electronegativity (χ), Chemical hardness (η) values in eV, and Chemical softness (s) value in (ev − 1 ) from optimised structure in gas phase. System DDOAB PPL ATL MPL PPL/ DDOAB ATL/ DDOAB MPL/ DDOAB E HOMO 8.781 5.523 5.774 5.632 7.670 8.005 8.432 E LUMO 2.628 0.878 0.157 0.144 2.998 2.546 2.421 Chemical potential (µ) -5.704 -3.201 -2.966 -2.744 -5.334 -5.276 -5.427 Electronegativity (χ) 5.704 3.201 2.966 2.744 5.334 5.276 5.427 Chemical hardness (η) 3.076 2.322 2.808 2.888 2.336 2.729 3.005 Chemical softness (s) 0.163 0.215 0.178 0.173 0.214 0.183 0.166 Electrophilicity index (ω) 5.290 2.206 1.566 1.303 6.091 5.099 4.899 For isolated molecules, DDOAB displayed relatively high hardness (3.08 eV) and low softness (0.163 eV⁻¹), indicating strong resistance to electronic deformation. Among the drugs, propranolol (PPL) had the lowest hardness (2.32 eV) and highest softness (0.215 eV⁻¹), consistent with its smaller ΔE and higher chemical reactivity compared to atenolol (ATL, η = 2.81 eV) and metoprolol (MPL, η = 2.89 eV). Upon complexation with DDOAB, the hardness of the surfactant decreased in all cases, reflecting enhanced electronic delocalization at the drug–surfactant interface. The softness and electrophilicity values increased correspondingly, pointing to greater reactivity. The reduction in hardness was most pronounced for PPL–DDOAB (η = 2.34 eV), followed by ATL–DDOAB (2.73 eV) and MPL–DDOAB (3.01 eV). The higher softness and electrophilicity index (ω = 6.09) of PPL–DDOAB further reinforce its status as the most reactive complex, whereas MPL–DDOAB remains the hardest and least polarizable, suggesting stronger kinetic stability but weaker charge-transfer potential. The observed QMD trends align closely with the HOMO–LUMO analysis. The PPL–DDOAB complex, with the smallest energy gap, also exhibits the lowest hardness and highest softness, highlighting its enhanced susceptibility to electronic perturbation and greater potential for intramolecular charge transfer. Conversely, MPL–DDOAB, with the largest ΔE, shows the highest hardness and lowest softness, implying reduced reactivity. ATL–DDOAB occupies an intermediate position between the two. Taken together, QMD analysis corroborates the FMO results and confirms that complexation with DDOAB significantly alters the electronic properties of the drugs, with PPL–DDOAB emerging as the most reactive and polarizable system. This enhanced softness and electrophilicity may facilitate stronger binding and electron delocalization within the vesicle environment, offering mechanistic insights into its superior stabilization and potential in drug delivery applications. 3.4 Non-Covalent Interactions (NCI) and Reduced Density Gradient (RDG) Analysis Non-covalent interactions are key determinants of drug–surfactant complex stability [ 42 ]. To visualize and characterize these forces, NCI and RDG analyses were performed. The RDG method highlights weak interactions by plotting the reduced density gradient against the product of the electron density (ρ) and the second eigenvalue of the Hessian matrix (λ₂) [ 43 , 44 ]. Negative λ₂ρ values denote attractive interactions such as hydrogen bonding, values near zero indicate van der Waals interactions, and positive values correspond to steric repulsions. In the isosurface maps, these appear as blue (hydrogen bonding), green (van der Waals), and red (steric) regions. For the isolated drug molecules, distinct interaction patterns were observed. Propranolol (PPL) showed mainly van der Waals contacts around the aromatic naphthalene core, with negligible hydrogen bonding. Atenolol (ATL), owing to its amide side chain, exhibited prominent blue isosurfaces and sharp negative λ₂ρ spikes, consistent with strong hydrogen bonding. Metoprolol (MPL) displayed both hydrogen bonding and dispersion features, but weaker than ATL. These inherent differences reflect the polarity gradient among the drugs and precondition their interaction behavior with the cationic surfactant. Upon complexation with DDOAB, additional van der Waals regions appeared at the drug–surfactant interface in all cases, indicating hydrophobic contacts between the DDOAB tails and drug aromatic groups. The PPL–DDOAB complex was dominated by green isosurfaces, signifying stabilization primarily through van der Waals forces, consistent with its lipophilic character and deep bilayer penetration. In contrast, the ATL–DDOAB complex exhibited strong hydrogen-bonding signatures at the amide and hydroxyl groups near the surfactant headgroup, along with steric patches at the interface. MPL–DDOAB showed intermediate behavior, with mixed hydrogen bonding and dispersion forces. Overall, the strength of non-covalent interactions follows the order ATL–DDOAB > MPL–DDOAB > PPL–DDOAB. This hierarchy aligns with the polarity of the drugs [ 45 ]: ATL (most hydrophilic) engages strongly through hydrogen bonding, MPL shows balanced contributions, while PPL (most lipophilic) stabilizes mainly via hydrophobic dispersion. From a drug delivery standpoint, this suggests that PPL localizes deeply within the vesicle core, enhancing encapsulation; ATL remains near the surface through hydrogen bonding, which may affect release kinetics; and MPL adopts an intermediate interfacial position. These non-covalent interactions are fundamental to drug delivery mechanisms, as they play a key role in facilitating the controlled and efficient release of the drug at the target site [ 46 ]. Thus, NCI and RDG analyses provide molecular-level insights into how drug polarity and structure dictate binding strength and localization within vesicle-forming DDOAB assemblies 4. Conclusion The current investigation provides a thorough theoretical understanding of the interactions between the cationic DDOAB and β- blocker drugs -PPL, ATL, and MPL by utilizing frontier molecular orbital theory (FMO) analysis, quantum molecular descriptors (QMDs), and non-covalent interaction (NCI) analysis. The comparative HOMO-LUMO energy levels indicated that the energy gaps (ΔE) of the drugs decreased upon interacting with DDOAB, indicating that the intramolecular charge transfer and reactivity profiles were altered. Among the complexes, PPL-DDOAB exhibited the smallest gap, which suggest that it has the lowest energy for excitation and highest chemical stability. Additionally, the QMD results corroborate these findings, as the chemical hardness of DDOAB was diminished during complexation, particularly in PPL-DDOAB system. This suggests that the drug surfactant interaction was successful, as evident by the increased reactivity. In addition, the NCI analysis offered quantitative and visuals evidence of non-covalent forces that regulate the interactions between the drug and DDOAB. From RDG scatter plots, the presence and strength of hydrogen bonding in the drug-surfactant complexes, particularly in ATL-DDOAB and MPL-DDOAB were confirmed by notable shifts in sign λ2(ρ) values. As evident by more prominent shifts and distinct NCI features, ATL-DDOAB exhibited the strongest non-covalent interactions among all systems studied. In summary, these results underscore the importance of non-covalent interactions, particularly hydrogen bonding and van der Waals forces, in regulating the binding behaviour of β- blockers with DDPOAB. These interactions not only affect the physiochemical properties of the complexes but also have the potential to affect their behaviour in drug delivery systems. Declarations On behalf of all authors, the corresponding author states that there is no conflict of interest. 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Journal of Chemistry 2021(1):6674261. https://doi.org/10.1155/2021/6674261 Chhetri N, Shil S, Ali M (2025) Amino acid-based sodium n-lauroylsarcosinate as an optimised surfactant for propranolol interaction: comparative analysis of mixed micelle formation with cationic and zwitterionic surfactants. Journal of Molecular Liquids 5:127899. https://doi.org/10.1016/j.molliq.2025.127899 Chhetri N, Ali M (2025) Photophysical response of propranolol in biomimetic micellar media of alkyltrimethylammonium bromide surfactants: effect of pH and alkyl chain length. Journal of Fluorescence 35(7):5045-57. https://doi.org/10.1007/s10895-024-03896-2 Chhetri N, Ali M (2024) Exploring the pH-Responsive Interaction of β-Blocker drug Propranolol with Biomimetic Micellar Media: fluorescence and electronic absorption studies. Journal of Fluorescence 34(3):1291-306. https://doi.org/10.1007/s10895-023-03361-6 Yu J, Su NQ, Yang W (2022) Describing chemical reactivity with frontier molecular orbitalets. 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Mao Y, Head-Gordon M, Shao Y (2018) Unraveling substituent effects on frontier orbitals of conjugated molecules using an absolutely localized molecular orbital based analysis. Chemical science 9(45):8598-607. https://doi.org/10.1039/C8SC02990C Khajehzadeh M, Sadeghi N (2018) Molecular structure, the effect of solvent on UV–vis and NMR, FT–IR and FT–Raman spectra, NBO, frontier molecular orbital analysis of Mitomycin anticancer drug. Journal of Molecular Liquids 15;256:238-46. https://doi.org/10.1016/j.molliq.2018.01.099 Vijayaraj R, Subramanian V, Chattaraj PK (2009) Comparison of global reactivity descriptors calculated using various density functionals: a QSAR perspective. Journal of chemical theory and computation 13;5(10):2744-53. https://doi.org/10.1021/ct900347f Chhetri N, Ali M (2023) Effect of hydrophilic atenolol and lipophilic propranolol β-blockers on the surface and bulk aggregation of quaternary ammonium bromide surfactants: A comparative study. Journal of Molecular Liquids 15;382:121858. https://doi.org/10.1016/j.molliq.2023.121858 Contreras-García J, Johnson ER, Keinan S, Chaudret R, Piquemal JP, Beratan DN, Yang W (2011) NCIPLOT: a program for plotting noncovalent interaction regions. Journal of chemical theory and computation 8;7(3):625-32. https://doi.org/10.1021/ct100641a Medimagh M, Issaoui N, Gatfaoui S, Brandán SA, Al-Dossary O, Marouani H, Wojcik MJ (2021) Impact of non-covalent interactions on FT-IR spectrum and properties of 4-methylbenzylammonium nitrate. A DFT and molecular docking study. Heliyon 1;7(10). https://doi.org/10.1016/j.heliyon.2021.e08204 Mohsen-Nia M, Ebrahimabadi AH, Niknahad B (2012) Partition coefficient n-octanol/water of propranolol and atenolol at different temperatures: experimental and theoretical studies. J Chem Ther­modyn 54:393–397. https://doi.org/10.1016/j.jct.2012.05.021 Medimagh M, Issaoui N, Gatfaoui S, Brandán SA, Al-Dossary O, Marouani H, Wojcik MJ (2021) Impact of non-covalent interactions on FT-IR spectrum and properties of 4-methylbenzylammonium nitrate. A DFT and molecular docking study. Heliyon 1;7(10). https://doi.org/10.1016/j.heliyon.2021.e08204 Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 16 Dec, 2025 Reviewers invited by journal 14 Sep, 2025 Editor assigned by journal 11 Sep, 2025 First submitted to journal 09 Sep, 2025 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. 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11:27:18","extension":"html","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":114461,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7575992/v1/10a16a03b0033fd237e7b8bf.html"},{"id":91852311,"identity":"99691085-d27f-4c33-a897-21f4f2fc2407","added_by":"auto","created_at":"2025-09-22 11:27:18","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":612157,"visible":true,"origin":"","legend":"\u003cp\u003eFrontier molecular orbital (HOMO and LUMO) of neutral (A) DDOAB, PPL, ATL and, MPL (B) PPL-DDOAB, ATL-DDOAB and MPL-DDOAB complexes\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7575992/v1/95a6aeaea9e0518b5d586bb9.png"},{"id":91852312,"identity":"83832b6a-595e-4de7-b052-30dde29cd38f","added_by":"auto","created_at":"2025-09-22 11:27:18","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":359780,"visible":true,"origin":"","legend":"\u003cp\u003eCombined visualization of non-covalent interaction (NCI) isosurfaces and the corresponding reduced density gradient (RDG) scatter plots for DDOAB, PPL, ATL, and MPL systems. The isosurfaces highlight regions of weak non-covalent interactions: blue represents hydrogen bonding, green indicates van der Waals forces, and red denotes steric repulsion.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7575992/v1/e50aa4cee59d3d985e9e5b69.png"},{"id":91852316,"identity":"7cb8b6bc-1c97-49a0-8d34-5e021a45f923","added_by":"auto","created_at":"2025-09-22 11:27:18","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":305868,"visible":true,"origin":"","legend":"\u003cp\u003eNCI isosurface and corresponding RDG scatter plots showing visualization and characterisation of weak interactions in drug- DDOAB complex.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7575992/v1/4f599d8af5c9dcfaa17a8915.png"},{"id":91856009,"identity":"fbc32a34-5853-422e-a7a6-9129994ddb5d","added_by":"auto","created_at":"2025-09-22 11:59:20","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1686739,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7575992/v1/0739f7a1-c364-4ee3-a326-c8fbc049c444.pdf"}],"financialInterests":"","formattedTitle":"Selective Stabilization of β-Blockers within Cationic Vesicles: A DFT Study of Propranolol, Atenolol, and Metoprolol","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eMicelles and vesicles, the two predominant self-assembled surfactant structures, differ fundamentally in their morphology and molecular organization. These structural distinctions strongly influence how drug molecules partition within the system, associate with the surfactant assembly, and ultimately manifest their interactions. Vesicles are structurally and functionally closer to biological membranes than micelles because they consist of a lipid bilayer arranged tail-to-tail, creating two aqueous compartments that mimic the inside and outside of a cell, whereas micelles have only a single layer with no compartmentalization. This bilayer organization in vesicles allows them to exhibit lamellar phases, gel-to-fluid transitions, and membrane-like permeability, as well as to support processes such as fusion, transport, and insertion of proteins or lipids, making them highly suitable as model membranes [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Vesicles are thus better model systems for biological membranes than micelles. Furthermore, the larger size and bilayer curvature of vesicles allow for cooperative binding effects and more complex interaction patterns, making them superior platforms for probing drug\u0026ndash;membrane interactions relevant to drug delivery and pharmacokinetics [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Vesicles prepared from the natural phospholipids surfactants are widely employed both as model membranes and as drug delivery vehicles [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. However, vesicles formed from the synthetic cationic surfactants such as dimethyldioctadecylammonium bromide (DDOAB) are particularly notable for their biocompatibility, permeability, surface potential, and close resemblance to natural membranes [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. While such systems have been extensively explored in experimental studies, theoretical investigations remain comparatively limited [\u003cspan additionalcitationids=\"CR10 CR11\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. The interaction of a drug with a membrane is governed by several factors, the most critical being its molecular shape, size, pKa, and hydrophobicity [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. A clear understanding of drug\u0026ndash;vesicle interactions is crucial for improving the efficacy and stability of many pharmaceutical formulations.\u003c/p\u003e\u003cp\u003eβ-blockers rank among the most effective therapeutic agents for managing heart failure, certain types of arrhythmias, hypertension, and myocardial infarction [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Propranolol (PPL), atenolol (ATL), and metoprolol (MPL) are widely used non-selective β-blockers in the treatment of cardiovascular disorders [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Notably, propranolol has been shown to exert membrane-stabilizing effects, indicating that its interaction with membranes [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] may be a significant factor in understanding its toxicity, particularly under overdose conditions [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Given these pharmacological properties, numerous studies have explored the interaction of β-blockers with lipid membranes using a variety of experimental techniques. Krill et al. [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] investigated several β-blocker drugs, including propranolol, oxprenolol, nadolol, and metoprolol, and reported that these compounds alter the thermotropic phase behaviour of dimyristoylphosphatidylcholine (DMPC) bilayers in a manner dependent on their lipophilicity. Likewise, the interactions of β-blockers such as propranolol, oxprenolol, and acebutolol with palmitoyloleoylphosphatidylcholine (POPC) membranes have been examined using time-dependent fluorescence shift (TDFS) and generalized polarization (GP) measurements [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. This study demonstrated that increasing β-blocker concentrations lead to a rigidification of the lipid bilayers at both the glycerol backbone and headgroup regions, with propranolol producing the most pronounced effect.\u003c/p\u003e\u003cp\u003eExperimental techniques such as calorimetry, spectroscopy, and microscopy have greatly advanced our understanding of key parameters in drug\u0026ndash;membrane systems, including partitioning, drug release, and membrane fluidity [\u003cspan additionalcitationids=\"CR22\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. However, these methods often fall short in providing detailed insights into the electronic aspects of drug\u0026ndash;surfactant interactions such as charge transfer, frontier orbital overlap, specific interaction types, and the stability of drug\u0026ndash;membrane complexes. To bridge this gap, computational approaches like Density Functional Theory (DFT) offer valuable tools for probing the electronic nature of molecular interactions as they provide atomic-level insight into the nature and strength of non-covalent forces, including hydrogen bonding, electrostatic, π\u0026ndash;π, and van der Waals interactions. DFT enables accurate evaluation of binding and interaction energies, charge distribution, and electron density changes, thereby clarifying the molecular basis of drug localization and stabilization within the environment of organised medium [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Moreover, theoretical predictions of vibrational, electronic, and NMR parameters can be directly correlated with experimental spectra, facilitating interpretation of spectral shifts upon complex formation [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] By isolating specific interaction modes in a controlled virtual environment, DFT helps overcome limitations of experimental techniques in complex multicomponent systems. Therefore, the aim of this study is to elucidate the nature of interactions between PPL, ATL, and MPL with DDOAB vesicles at the DFT level, providing insights into orbital contributions, stabilization energies, and non-covalent interaction patterns that can aid in the rational design of more effective drug delivery systems.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"2. Computational methods","content":"\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eThe theoretical computations were carried out using the DFT approach[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. All structural optimization and calculations for PPL, MPL, ATL and their complexes with DDOAB in gas phase were carried out using Gaussian 09 software package [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Additionally, the B3LYP functional, which combines Becke\u0026rsquo;s three parameters exchange and the Lee -Yang-Parr correlation functionals[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] has been used for the study along with the 6-31G (D, P) basic set, implemented in Gaussian 09 software within the framework of Density functional theory (DFT). The B3LYP functional is widely recognized as a reliable choice in drug design, owing to its proven ability to accurately predict the structural, electronic, and magnetic properties of drug molecules. It is often regarded as a \u0026ldquo;workhorse\u0026rdquo; functional in quantum chemistry, offering an effective balance between computational accuracy and cost [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Furthermore, non-covalent interaction (NCI) and reduced density gradient (RDG) analyses were carried out using Multiwfn, gnuplot, IrfanView, and VMD software[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] to visualize and evaluate weak interactions, including hydrogen bonding, van der Waals forces, and steric effects.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"3. Results and Discussion","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e3.1. Optimised structures and their energies\u003c/h2\u003e\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eThe molecular geometries of the individual β-blocker drug molecules propranolol (PPL), atenolol (ATL), and metoprolol (MTL) as well as the vesicle-forming double-tailed surfactant dioctadecyldimethylammonium bromide (DDOAB) were optimized using density functional theory (DFT). The optimisation energies are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Subsequently, the corresponding drug\u0026ndash;surfactant complexes (PPL\u0026ndash;DDOAB, ATL\u0026ndash;DDOAB, and MTL\u0026ndash;DDOAB) were also optimized, and their optimisation energies are also presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. In all cases, the energies of the drug\u0026ndash;DDOAB complexes were significantly lower than the energies of the individual drug and surfactant molecules, clearly indicating the spontaneous formation of more stable supramolecular assemblies. The total electronic energies of the PPL\u0026ndash;DDOAB, ATL\u0026ndash;DDOAB, and MTL\u0026ndash;DDOAB complexes were found to be -62.45 x 10\u003csup\u003e5\u003c/sup\u003e kJ/mol, -63.87 x 10\u003csup\u003e5\u003c/sup\u003e kJ/mol, and \u0026minus;\u0026thinsp;63.48 x 10\u003csup\u003e5\u003c/sup\u003e kJ/mol, respectively, suggesting that propranolol interacts more favorably with the vesicular surfactant, resulting in the most stable complex. This observation is consistent with the intrinsic hydrophobic character of propranolol, which enhances its affinity toward the hydrophobic microenvironment provided by the DDOAB vesicle. Previous studies have likewise demonstrated that propranolol exhibits stronger interactions with single-chain cationic surfactants as the alkyl chain length increases, primarily due to enhanced hydrophobic interactions between the surfactant tail and the hydrophobic naphthalene moiety of propranolol [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eTo gain deeper insight into complex stability, interaction (stabilization) energies (Table \u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) were calculated as the difference between the total energy of the complex and the sum of the energies of the individual drug and surfactant molecules. The calculated stabilization energies for all three drug\u0026ndash;DDOAB systems were negative, confirming that their association is thermodynamically favourable. A negative interaction energy signifies stabilizing complexation, while a positive value would indicate negligible binding. Among the systems studied, the interaction energies follow the order DDOAB\u0026ndash;PPL (\u0026minus;\u0026thinsp;0.59 eV)\u0026thinsp;\u0026gt;\u0026thinsp;DDOAB\u0026ndash;ATL (\u0026minus;\u0026thinsp;0.73 eV)\u0026thinsp;\u0026gt;\u0026thinsp;DDOAB\u0026ndash;MTL (\u0026minus;\u0026thinsp;0.77 eV), indicating that propranolol exhibits the strongest affinity toward DDOAB, followed by atenolol and metoprolol. The stronger stabilization of the PPL\u0026ndash;DDOAB complex can be attributed to the high hydrophobicity of propranolol, which facilitates deeper accommodation within the nonpolar microenvironment of the DDOAB bilayer. In addition to van der Waals stabilization, hydrophobic interactions and possible cation\u0026ndash;π interactions between the aromatic naphthalene ring of PPL and the positively charged surfactant headgroup further enhance the binding affinity. In comparison, atenolol and metoprolol, with higher polarity and hydrogen-bond donor/acceptor functionalities, results in relatively weaker overall stabilization compared to propranolol. These results are in line with previous reports that highlight the preferential association of propranolol with cationic surfactant assemblies owing to its amphiphilic character and favorable partitioning into hydrophobic domains [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e\u003c/div\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\u003eThe energy of the individual molecules, complexes, and the stabilization energy.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\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=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSystem\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eEnergy in kJ/mol\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003estabilizing energy (kJ/mol)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDDOAB\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-40.72 x 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePPL\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-21.72 x 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eATL\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-23.15 x 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMPL\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-22.76 x 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDDOAB-PPL\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-62.45 x 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-57.23\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDDOAB-ATL\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-63.87 x 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-70.88\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDDOAB-MPL\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-63.48 x 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-74.51\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Frontier Molecular Orbitals (FMOs) and HOMO\u0026ndash;LUMO Gap Analysis\u003c/h2\u003e\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eFrontier Molecular Orbital (FMO) theory provides valuable insights into molecular reactivity by analyzing the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. The HOMO energy reflects a molecule\u0026rsquo;s electron-donating ability (ionization potential), while the LUMO energy relates to its electron-accepting capacity (electron affinity) [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. The energy gap (ΔE\u0026thinsp;=\u0026thinsp;E\u003csub\u003eLUMO\u003c/sub\u003e \u0026minus; E\u003csub\u003eHOMO\u003c/sub\u003e) is a key descriptor of stability and reactivity: larger ΔE values correspond to harder, less polarizable molecules, whereas smaller ΔE values indicate more reactive systems with enhanced potential for charge transfer [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eFor the individual β-blockers, clear differences were observed. PPL exhibited the smallest HOMO\u0026ndash;LUMO gap, with its HOMO localized on the naphthalene ring, hydroxyl substituent, and secondary amine, and its LUMO spread across the naphthalene\u0026ndash;OH region. In contrast, atenolol ATL and MPL showed larger gaps, with HOMOs delocalized over their aromatic ring and hydroxyl groups, and in ATL additionally extending onto the acetamide moiety. Their LUMOs were primarily localized around the aromatic rings. These distinct orbital distributions likely contribute to the differences in their respective energy gaps. Notably, the smaller energy gap in PPL may indicate a more reactive geometry, as minimal ΔE values are often associated with enhanced chemical reactivity and potential for interaction [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. The surfactant DDOAB exhibits a higher ΔE value (\u0026minus;\u0026thinsp;6.152 eV) compared to the individual drug molecules PPL, ATL, and MPL. This difference can be attributed to the spatial distribution of the frontier molecular orbitals in DDOAB, where the HOMO is predominantly localized along the hydrocarbon alkyl chain, approximately five carbon atoms away from the head group, while the LUMO is concentrated over the head group containing the quaternary ammonium unit. A similar trend was observed in investigation involving single chain quaternary ammonium surfactants of varying alkyl chain lengths in the presence of PPL [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe calculated HOMO\u0026ndash;LUMO gaps for the complexes were: PPL\u0026ndash;DDOAB (4.67 eV)\u0026thinsp;\u0026lt;\u0026thinsp;ATL\u0026ndash;DDOAB (5.46 eV)\u0026thinsp;\u0026lt;\u0026thinsp;MPL\u0026ndash;DDOAB (6.01 eV). This order indicates that the PPL\u0026ndash;DDOAB complex requires the least energy for electronic excitation and is therefore the most chemically reactive and polarizable. ATL\u0026ndash;DDOAB exhibits moderate reactivity, while MPL\u0026ndash;DDOAB has the largest gap, implying greater kinetic stability but weaker charge-transfer potential.\u003c/p\u003e\u003cp\u003eThe results indicate that the PPL\u0026ndash;DDOAB complex exhibits pronounced intramolecular charge transfer and greater thermodynamic stability, arising from its reduced ΔE and aromatic-rich electronic framework, which stem from electron redistribution induced by the perturbation of HOMO and LUMO energy levels during complex formation [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. The resulting change in electron distribution alters the HOMO\u0026ndash;LUMO gap (ΔE), which directly influences chemical reactivity, polarizability, and stability [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. Thus, the FMO analysis underscores the importance of drug structure in dictating electronic behavior upon complexation with vesicle-forming surfactants, with direct implications for drug delivery performance.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Quantum Molecular Descriptors (QMDs)\u003c/h2\u003e\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eQuantum molecular descriptors (QMDs) derived from frontier orbital energies offer quantitative measures of global stability and reactivity. Based on Koopmans\u0026rsquo; theorem [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e], key descriptors such as chemical potential (\u0026micro;), electronegativity (χ), chemical hardness (η), softness (S), and electrophilicity index (ω) can be obtained from E\u003csub\u003eHOMO\u003c/sub\u003e and E\u003csub\u003eLUMO\u003c/sub\u003e values using equations (1)\u0026ndash;(5).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\mu\\:=\\frac{\\left({E}_{HOMO}+{E}_{LUMO}\\right)}{2}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(1\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}\\eta\\:=\\frac{\\left({E}_{LUMO}+{E}_{HOMO}\\right)}{2}\\:\\left(2\\right)\\end{array}$$ \u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}S=\\frac{1}{2{\\eta\\:}}\\:\\left(3\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}\\chi\\:=\\:\\frac{-\\left({E}_{LUMO}+{E}_{HOMO}\\right)}{2}\\:\\left(4\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}\\omega\\:=\\:\\frac{{{\\mu\\:}}^{2}}{2{\\eta\\:}}\\:\\left(5\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eThese parameters complement the HOMO\u0026ndash;LUMO gap (ΔE) analysis by providing a more detailed picture of how electronic properties change upon complexation. Generally, higher hardness (η) and lower softness (S) correspond to chemically stable systems, while lower hardness and higher softness signify greater reactivity and polarizability. The electrophilicity index (ω) reflects the ability of a system to stabilize additional electronic charge. The calculated QMD values for the individual molecules and their DDOAB complexes are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eThe E\u003csub\u003eHOMO\u003c/sub\u003e, E\u003csub\u003eLUMO\u003c/sub\u003e, Chemical potential (\u0026micro;), Electronegativity (χ), Chemical hardness (η) values in eV, and Chemical softness (s) value in (ev\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) from optimised structure in gas phase.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"8\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSystem\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDDOAB\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePPL\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eATL\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMPL\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003ePPL/\u003c/p\u003e\u003cp\u003eDDOAB\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eATL/\u003c/p\u003e\u003cp\u003eDDOAB\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003eMPL/\u003c/p\u003e\u003cp\u003eDDOAB\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eE\u003c/b\u003e\u003csub\u003e\u003cb\u003eHOMO\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e8.781\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e5.523\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e5.774\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e5.632\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e7.670\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e8.005\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e8.432\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eE\u003c/b\u003e\u003csub\u003e\u003cb\u003eLUMO\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2.628\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.878\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.157\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.144\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e2.998\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e2.546\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e2.421\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eChemical potential (\u0026micro;)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e-5.704\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-3.201\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-2.966\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-2.744\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e-5.334\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e-5.276\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e-5.427\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eElectronegativity (χ)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5.704\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e3.201\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.966\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2.744\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e5.334\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e5.276\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e5.427\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eChemical hardness (η)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e3.076\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.322\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.808\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2.888\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e2.336\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e2.729\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e3.005\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eChemical softness (s)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.163\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.215\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.178\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.173\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.214\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.183\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.166\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eElectrophilicity index (ω)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5.290\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.206\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.566\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.303\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e6.091\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e5.099\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e4.899\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eFor isolated molecules, DDOAB displayed relatively high hardness (3.08 eV) and low softness (0.163 eV⁻\u0026sup1;), indicating strong resistance to electronic deformation. Among the drugs, propranolol (PPL) had the lowest hardness (2.32 eV) and highest softness (0.215 eV⁻\u0026sup1;), consistent with its smaller ΔE and higher chemical reactivity compared to atenolol (ATL, η\u0026thinsp;=\u0026thinsp;2.81 eV) and metoprolol (MPL, η\u0026thinsp;=\u0026thinsp;2.89 eV). Upon complexation with DDOAB, the hardness of the surfactant decreased in all cases, reflecting enhanced electronic delocalization at the drug\u0026ndash;surfactant interface. The softness and electrophilicity values increased correspondingly, pointing to greater reactivity. The reduction in hardness was most pronounced for PPL\u0026ndash;DDOAB (η\u0026thinsp;=\u0026thinsp;2.34 eV), followed by ATL\u0026ndash;DDOAB (2.73 eV) and MPL\u0026ndash;DDOAB (3.01 eV). The higher softness and electrophilicity index (ω\u0026thinsp;=\u0026thinsp;6.09) of PPL\u0026ndash;DDOAB further reinforce its status as the most reactive complex, whereas MPL\u0026ndash;DDOAB remains the hardest and least polarizable, suggesting stronger kinetic stability but weaker charge-transfer potential.\u003c/p\u003e\u003cp\u003eThe observed QMD trends align closely with the HOMO\u0026ndash;LUMO analysis. The PPL\u0026ndash;DDOAB complex, with the smallest energy gap, also exhibits the lowest hardness and highest softness, highlighting its enhanced susceptibility to electronic perturbation and greater potential for intramolecular charge transfer. Conversely, MPL\u0026ndash;DDOAB, with the largest ΔE, shows the highest hardness and lowest softness, implying reduced reactivity. ATL\u0026ndash;DDOAB occupies an intermediate position between the two. Taken together, QMD analysis corroborates the FMO results and confirms that complexation with DDOAB significantly alters the electronic properties of the drugs, with PPL\u0026ndash;DDOAB emerging as the most reactive and polarizable system. This enhanced softness and electrophilicity may facilitate stronger binding and electron delocalization within the vesicle environment, offering mechanistic insights into its superior stabilization and potential in drug delivery applications.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e3.4 Non-Covalent Interactions (NCI) and Reduced Density Gradient (RDG) Analysis\u003c/h2\u003e\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eNon-covalent interactions are key determinants of drug\u0026ndash;surfactant complex stability [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. To visualize and characterize these forces, NCI and RDG analyses were performed. The RDG method highlights weak interactions by plotting the reduced density gradient against the product of the electron density (ρ) and the second eigenvalue of the Hessian matrix (λ₂) [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. Negative λ₂ρ values denote attractive interactions such as hydrogen bonding, values near zero indicate van der Waals interactions, and positive values correspond to steric repulsions. In the isosurface maps, these appear as blue (hydrogen bonding), green (van der Waals), and red (steric) regions.\u003c/p\u003e\u003cp\u003eFor the isolated drug molecules, distinct interaction patterns were observed. Propranolol (PPL) showed mainly van der Waals contacts around the aromatic naphthalene core, with negligible hydrogen bonding. Atenolol (ATL), owing to its amide side chain, exhibited prominent blue isosurfaces and sharp negative λ₂ρ spikes, consistent with strong hydrogen bonding. Metoprolol (MPL) displayed both hydrogen bonding and dispersion features, but weaker than ATL. These inherent differences reflect the polarity gradient among the drugs and precondition their interaction behavior with the cationic surfactant.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eUpon complexation with DDOAB, additional van der Waals regions appeared at the drug\u0026ndash;surfactant interface in all cases, indicating hydrophobic contacts between the DDOAB tails and drug aromatic groups. The PPL\u0026ndash;DDOAB complex was dominated by green isosurfaces, signifying stabilization primarily through van der Waals forces, consistent with its lipophilic character and deep bilayer penetration. In contrast, the ATL\u0026ndash;DDOAB complex exhibited strong hydrogen-bonding signatures at the amide and hydroxyl groups near the surfactant headgroup, along with steric patches at the interface. MPL\u0026ndash;DDOAB showed intermediate behavior, with mixed hydrogen bonding and dispersion forces.\u003c/p\u003e\u003cp\u003eOverall, the strength of non-covalent interactions follows the order ATL\u0026ndash;DDOAB\u0026thinsp;\u0026gt;\u0026thinsp;MPL\u0026ndash;DDOAB\u0026thinsp;\u0026gt;\u0026thinsp;PPL\u0026ndash;DDOAB. This hierarchy aligns with the polarity of the drugs [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]: ATL (most hydrophilic) engages strongly through hydrogen bonding, MPL shows balanced contributions, while PPL (most lipophilic) stabilizes mainly via hydrophobic dispersion. From a drug delivery standpoint, this suggests that PPL localizes deeply within the vesicle core, enhancing encapsulation; ATL remains near the surface through hydrogen bonding, which may affect release kinetics; and MPL adopts an intermediate interfacial position. These non-covalent interactions are fundamental to drug delivery mechanisms, as they play a key role in facilitating the controlled and efficient release of the drug at the target site [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. Thus, NCI and RDG analyses provide molecular-level insights into how drug polarity and structure dictate binding strength and localization within vesicle-forming DDOAB assemblies\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eThe current investigation provides a thorough theoretical understanding of the interactions between the cationic DDOAB and β- blocker drugs -PPL, ATL, and MPL by utilizing frontier molecular orbital theory (FMO) analysis, quantum molecular descriptors (QMDs), and non-covalent interaction (NCI) analysis. The comparative HOMO-LUMO energy levels indicated that the energy gaps (ΔE) of the drugs decreased upon interacting with DDOAB, indicating that the intramolecular charge transfer and reactivity profiles were altered. Among the complexes, PPL-DDOAB exhibited the smallest gap, which suggest that it has the lowest energy for excitation and highest chemical stability. Additionally, the QMD results corroborate these findings, as the chemical hardness of DDOAB was diminished during complexation, particularly in PPL-DDOAB system. This suggests that the drug surfactant interaction was successful, as evident by the increased reactivity.\u003c/p\u003e\u003cp\u003eIn addition, the NCI analysis offered quantitative and visuals evidence of non-covalent forces that regulate the interactions between the drug and DDOAB. From RDG scatter plots, the presence and strength of hydrogen bonding in the drug-surfactant complexes, particularly in ATL-DDOAB and MPL-DDOAB were confirmed by notable shifts in sign λ2(ρ) values. As evident by more prominent shifts and distinct NCI features, ATL-DDOAB exhibited the strongest non-covalent interactions among all systems studied.\u003c/p\u003e\u003cp\u003eIn summary, these results underscore the importance of non-covalent interactions, particularly hydrogen bonding and van der Waals forces, in regulating the binding behaviour of β- blockers with DDPOAB. These interactions not only affect the physiochemical properties of the complexes but also have the potential to affect their behaviour in drug delivery systems.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eOn behalf of all authors, the corresponding author states that there is no conflict of interest.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors would like to thank TMA Pai University Research Fund for providing minor grant for carrying out the research work.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u0026nbsp;\u003c/strong\u003eNot Applicable\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eKordzadeh A, Amjad-Iranagh S, Zarif M, Modarress H (2019) Adsorption and encapsulation of the drug doxorubicin on covalent functionalized carbon nanotubes: A scrutinized study by using molecular dynamics simulation and quantum mechanics calculation. 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International Journal of Pharmaceutics 23;292(1-2):179-85.https://doi.org/10.1016/j.ijpharm.2004.11.037\u003c/li\u003e\n\u003cli\u003eNatsheh H, Touitou E (2020) Phospholipid vesicles for dermal/transdermal and nasal administration of active molecules: The effect of surfactants and alcohols on the fluidity of their lipid bilayers and penetration enhancement properties. Molecules 27;25(13):2959. https://doi.org/10.3390/molecules25132959\u003c/li\u003e\n\u003cli\u003eDan N (2018) Vesicle-based drug carriers: Liposomes, polymersomes, and niosomes. InDesign and Development of New Nanocarriers pp. 1-55 https://doi.org/10.1016/B978-0-12-813627-0.00001-6\u003c/li\u003e\n\u003cli\u003eAlves FR, Zaniquelli ME, Loh W, Castanheira EM, Oliveira ME, Feitosa E (2007 Dec) Vesicle\u0026ndash;micelle transition in aqueous mixtures of the cationic dioctadecyldimethylammonium and octadecyltrimethylammonium bromide surfactants. 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Heliyon 1;7(10). https://doi.org/10.1016/j.heliyon.2021.e08204\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"chemical-papers","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"chpa","sideBox":"Learn more about [Chemical Papers](http://link.springer.com/journal/11696)","snPcode":"11696","submissionUrl":"https://www.editorialmanager.com/CHPA/default.aspx","title":"Chemical Papers","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"β- blockers, vesicle, DFT, HOMO-LUMO, non-covalent","lastPublishedDoi":"10.21203/rs.3.rs-7575992/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7575992/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTheoretical investigation on the interaction between a cationic, double tailed vesicle-forming surfactant dioctadecyldimethylammonium bromide (DDOAB) and three non-selective β-blocker drugs: propranolol (PPL), atenolol (ATL), and metoprolol (MPL), have been carried out using Density Functional Theory (DFT). The primary aim is to elucidate the molecular mechanisms governing drug-surfactant complex formation, stability, and electronic behaviour in gas phase, thereby providing foundational insights into their potential relevance in drug delivery systems. PPL-DDOAB system exhibited the most stable complex, followed by ATL-DDOAB and MPL-DDOAB, based on relative stabilization energies. Frontier Molecular Orbital (FMO) analysis revealed significant changes in the HOMO\u0026ndash;LUMO energy levels upon complex formation. The energy gap (ΔE) decreased for all drug-surfactant complexes compared to the isolated drugs, indicating enhanced electronic interaction and altered reactivity. Notably, the PPL-DDOAB complex showed the lowest energy gap (4.67 eV), suggesting improved electron mobility and the highest charge transfer potential among the studied systems. Quantum molecular descriptors (QMDs), calculated from HOMO and LUMO energies, further supported these findings. The chemical hardness (η) of DDOAB decreased upon complexation, with the lowest value in the PPL-DDOAB complex, implying increased reactivity and stabilization. Electrophilicity (ω) and softness values (S) also varied among the complexes, highlighting subtle differences in chemical behaviour. Non-Covalent Interaction (NCI) analysis, combined with Reduced Density Gradient (RDG) plots, visually and quantitatively identified van der Waals forces, steric repulsions, and hydrogen bonding as the main contributors to complex stabilization. Overall, the findings underscore the critical role of non-covalent interactions in the formation and stability of drug-surfactant complexes. These insights are vital for the rational design of vesicle-based drug delivery systems, where optimized molecular interactions can significantly influence drug loading, release, and bioavailability.\u003c/p\u003e","manuscriptTitle":"Selective Stabilization of β-Blockers within Cationic Vesicles: A DFT Study of Propranolol, Atenolol, and Metoprolol","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-22 11:27:13","doi":"10.21203/rs.3.rs-7575992/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2025-12-17T03:21:09+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-09-14T20:49:31+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-12T03:58:18+00:00","index":"","fulltext":""},{"type":"submitted","content":"Chemical Papers","date":"2025-09-09T12:55:22+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"chemical-papers","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"chpa","sideBox":"Learn more about [Chemical Papers](http://link.springer.com/journal/11696)","snPcode":"11696","submissionUrl":"https://www.editorialmanager.com/CHPA/default.aspx","title":"Chemical Papers","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"038d3b39-5b8a-44b6-8f41-af3ca6908002","owner":[],"postedDate":"September 22nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-09-22T11:27:14+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-22 11:27:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7575992","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7575992","identity":"rs-7575992","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}