Computational Elucidation of Electronic Structure and Noncovalent Interactions in NHC-Supported Palladium-PEPPSI Complexes for Acceptorless Alcohol Dehydrogenation

Computational Elucidation of Electronic Structure and Noncovalent Interactions in NHC-Supported Palladium-PEPPSI Complexes for Acceptorless Alcohol Dehydrogenation | 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 Computational Elucidation of Electronic Structure and Noncovalent Interactions in NHC-Supported Palladium-PEPPSI Complexes for Acceptorless Alcohol Dehydrogenation Poonam Bhadoria, Manoj Kumar Gangwar, Vivek Kumar Yadav This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9096875/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract A systematic density functional theory (DFT) investigation was conducted to elucidate the structural stability, electronic properties, and noncovalent interactions of NHC-supported Pd-PEPPSI complexes (cata-1 to cata-5) relevant to acceptorless alcohol dehydrogenation. All geometries were optimized at the M06-2X-D3/def2-TZVPP level, and frequency analyses confirmed true minima without imaginary modes. Thermodynamic evaluation revealed subtle stability differences among the complexes, with cata-2 exhibiting the most favorable Gibbs free energy. Frontier molecular orbital analysis showed closely comparable HOMO energies (-7.09 to -7.01 eV) and HOMO–LUMO gaps (6.29 to 6.35 eV), indicating high kinetic stability with slight variations in electronic softness and reactivity. Differences in dipole moment and electrophilicity index demonstrate that ligand substitution effectively modulates polarization and charge distribution around the Pd center. Charge analyses using Hirshfeld, electrostatic potential (ESP), and natural population analysis (NPA) consistently confirm the electrophilic character of palladium and highlight substituent-dependent electronic redistribution within the coordination sphere. Atoms-in-molecules (AIM) topology reveals weak closed-shell N···H and I···H interactions (ρ BCP ≈ 0.003-0.011 a.u.) that contribute to structural stabilization without covalent character. Vibrational analysis further confirms the integrity of the square-planar Pd coordination environment, with characteristic Pd-I stretching modes near ~120 cm -1 . Overall, the results establish clear structure–property relationships, demonstrating that ligand architecture fine-tunes electronic distribution, polarization, and intermolecular stabilization while preserving structural robustness, thereby providing fundamental computational insights for the rational design of palladium catalysts for sustainable dehydrogenation processes. Density Functional Theory (DFT) Pd-PEPPSI complexes N-Heterocyclic Carbene (NHC) Electronic structure analysis Acceptorless alcohol dehydrogenation Figures Figure 1 Figure 2 Introduction Palladium-based catalysts have emerged as highly versatile systems in homogeneous catalysis, particularly in cross-coupling, C-H activation, and transfer hydrogenation reactions[ 1 – 4 ]. Among these, palladium–PEPPSI (Pyridine-Enhanced Precatalyst Preparation, Stabilization, and Initiation) complexes supported by N-heterocyclic carbene (NHC) ligands have attracted sustained attention due to their remarkable thermal stability, air tolerance, and tunable steric–electronic properties[ 5 – 7 ]. Experimentally, PEPPSI-type complexes have demonstrated high efficiency in Suzuki–Miyaura, Heck, and Buchwald–Hartwig reactions [ 8 – 10 ], as well as in acceptorless alcohol dehydrogenation (AAD), a transformation of growing importance for sustainable hydrogen production and green oxidation chemistry[ 11 – 13 ]. The strong σ-donating nature of NHC ligands stabilizes low-coordinate Pd centers, enhances metal–ligand covalency, and promotes catalytic robustness under mild conditions [ 6 , 14 ]. However, despite extensive experimental reports on their catalytic activity, a detailed molecular-level understanding of how ligand substitution modulates electronic structure, charge distribution, and intrinsic stability remains incomplete [ 15 ]. From a computational perspective, density functional theory (DFT) has proven to be a powerful framework for elucidating structure–reactivity relationships of transition-metal complexes [ 16 – 18 ]. Numerous theoretical studies have investigated palladium-catalyzed cross-coupling and dehydrogenation mechanisms, revealing key insights into oxidative addition, migratory insertion, β-hydride elimination, and reductive elimination pathways [ 19 – 21 ]. In particular, DFT analyses have clarified how ligand electronics influence frontier molecular orbital (FMO) alignment, metal-centered electrophilicity, and activation barriers [ 22 – 24 ]. Computational descriptors such as HOMO–LUMO gap, global electrophilicity index, chemical hardness, and charge transfer characteristics have been successfully employed to rationalize catalytic trends across related Pd systems[ 25 – 27 ]. Furthermore, energy decomposition and charge population analyses, such as Natural Population Analysis (NPA), Hirshfeld charges, and electrostatic potential (ESP) mapping, provide quantitative measures of electron donation and back-donation between metal centers and supporting ligands [ 28 – 30 ]. Recent theoretical investigations emphasize the importance of noncovalent interactions and subtle intramolecular contacts in stabilizing organometallic frameworks [ 31 – 33 ]. Quantum Theory of Atoms in Molecules (QTAIM) and topological analyses have revealed that weak interactions such as C-H···X (X = halogen, heteroatom) or N···H contacts can significantly influence conformational stability, orbital localization, and electronic polarization [ 34 – 36 ]. In square-planar Pd(II) complexes, such interactions often modulate the spatial distribution of electron density without substantially altering the coordination geometry [ 37 ]. Vibrational frequency analysis further serves as a diagnostic tool for verifying structural stability and identifying characteristic metal-ligand stretching modes, particularly Pd-halide and Pd-carbene vibrations [ 38 , 39 ]. Acceptorless alcohol dehydrogenation has gained considerable interest as an atom-economical route for hydrogen generation and carbonyl compound synthesis without sacrificial oxidants [ 11 , 40 ]. While experimental studies report high turnover numbers and excellent selectivity for NHC-supported Pd catalysts [ 12 , 13 ], theoretical understanding of the intrinsic electronic factors governing their activity is still evolving[ 21 , 24 ]. In this context, systematic computational analysis of ligand-modified Pd-PEPPSI frameworks can provide valuable insights into how electronic redistribution, polarization effects, and frontier orbital characteristics correlate with thermodynamic stability and potential catalytic performance [ 15 , 23 ]. The present study therefore aims to deliver a comprehensive first-principles investigation of a series of NHC-supported Pd-PEPPSI complexes with varying ligand substitution patterns. Using dispersion-corrected DFT methods [ 17 , 18 ], we examine optimized geometries, thermodynamic stability, frontier orbital distributions, global reactivity descriptors, charge population characteristics, and topological features of electron density. By integrating FMO analysis, electrophilicity metrics[ 25 ], electrostatic potential mapping[ 29 ], and QTAIM evaluation [ 34 ], this work establishes clear structure–electronic property relationships within the catalyst series. The findings provide a molecular-level understanding of how subtle ligand modifications tune electronic softness, polarization, and noncovalent stabilization while preserving the square-planar Pd coordination environment [ 37 ]. Such insights are essential for the rational design of next-generation palladium catalysts for sustainable hydrogen production and green dehydrogenation chemistry. Results and discussion All quantum-chemical calculations were performed using the Gaussian16 suite of programs [ 41 ]. Geometry optimizations for all five NHC-supported Pd-PEPPSI catalysts (Cata-1 to Cata-5) were carried out at the M06-2X-D3/def2-TZVPP level of theory. The M06-2X functional is well recognized for its reliable treatment of thermochemistry and transition-metal systems[ 42 ], while Grimme’s D3 dispersion correction accounts for long-range noncovalent interactions critical in organometallic complexes [ 43 ]. The def2-TZVPP basis set provides balanced triple-ζ accuracy for main-group and transition-metal elements [ 44 ]. The optimized structures correspond to true minima on the potential energy surface, as confirmed by vibrational frequency analyses at the same level, which yielded no imaginary frequencies. Vibrational modes were visualized using GaussView6 [ 45 ]. Charge analyses, frontier molecular orbital (FMO) global reactivity parameters, thermodynamic properties, and atoms-in-molecules (AIM) analyses were also computed at the same theoretical level. Geometry Optimization: All five NHC-supported Pd-PEPPSI catalysts were fully optimized without symmetry constraints (Fig. 1 ). The square-planar coordination geometry observed around Pd is consistent with established structural features of Pd(II) PEPPSI-type complexes [ 5 , 6 ]. Subtle differences in ligand orientation arise from steric and electronic substituent effects, which are known to influence catalytic reactivity in NHC-supported systems [ 7 , 15 ]. Thermodynamic parameters (ΔG, ΔH, ΔS, Cp) were computed from frequency calculations using standard statistical thermodynamics formalism implemented in Gaussian [ 41 ]. The relative Gibbs free energy trends indicate minimal enthalpy–entropy compensation. Similar thermodynamic analyses have been used extensively to compare organometallic catalyst stability [ 19 ]. To assess the relative stabilities of the catalysts, thermodynamic quantities including Gibbs free energy (ΔG), enthalpy (ΔH), entropy (ΔS), and heat capacity (Cp) were computed (Table 1 ). The ΔG and ΔH values follow a similar trend, indicating minimal enthalpy–entropy compensation. Among the series, cata-2 exhibits the lowest (most negative) Gibbs free energy (-11.25 × 10⁵ kcal mol⁻¹), suggesting it is the most thermodynamically stable complex. This is followed closely by cata-3 and cata-1, while cata-4 and cata-5 display comparatively less favorable stabilization. The entropy values increase in the order cata-5 < cata-4 < cata-1 < cata-3 < cata-2, indicating greater conformational flexibility in catalysts with bulkier ligand frameworks. Correspondingly, the computed heat capacities show the same trend, supporting the observation that structural flexibility and heavier substituents contribute to enhanced vibrational degrees of freedom. These results reveal that structural variations among the ligands significantly influence the thermodynamic stability of the Pd-PEPPSI complexes, with cata-2 being the most stable and cata-5 the least stabilized under identical computational conditions. Table 1 Thermodynamic parameters of NHC-Supported Palladium-PEPPSI Catalysts at M062X-D3/def2-TZVPP level of theory Thermodynamic Parameters (in) cata-1 cata-2 cata-3 cata-4 cata-5 GibbsFree Energy (∆G) (× 10 5 ) kcal/mol -10.76 -11.25 -11.0 -10.29 -10.04 Enthalpy(∆H) (× 10 5 ) kcal/mol -10.76 -11.25 -11.0 -10.29 -10.04 Entropy (∆S) (cal/mol-kelvin) 188.09 197.78 194.06 179.47 174.55 Heat Capacity (cal/mol-kelvin) 92.08 103.74 96.89 88.47 83.65 Charge analysis and FMO analysis: To gain deeper insight into the electronic structure and metal–ligand interactions of the five NHC-supported Pd-PEPPSI catalysts (cata-1 to cata-5), atomic charge analyses were carried out using Hirshfeld charges, electrostatic potential (ESP/ Merz–Kollman) charges, and Natural Population Analysis (NPA) at the M06-2X-D3/def2-TZVPP level of theory. Using more than one population analysis scheme is essential because atomic charges are not directly observable quantities and different theoretical models often yield varying numerical values. Evaluating multiple charge descriptors provides a more robust and chemically meaningful interpretation of electron distribution, catalytic activity, and ligand effects. Hirshfeld Charges are derived from electron density partitioning based on stockholder partitioning and typically provide moderate charge separation. These values are often less sensitive to the basis set but may underestimate charge transfer in strongly polarized systems. ESP/MK Charges are fitted to reproduce the electrostatic potential surrounding the molecule and are generally more sensitive to electronic polarization. These charges are particularly relevant for reactivity descriptors and modeling electrostatic interactions with substrates or solvents. While NPA Charges are based on Natural Bond Orbital (NBO) theory and reflect the occupancy of localized orbitals, providing the most chemically intuitive description. They typically yield the largest charge separation, making them suitable for evaluating metal center electron richness, ligand donation, and bonding character. Across all charge methods, the positive charge on Pd remains consistent, confirming its electrophilic nature and role as the catalytic center. Hirshfeld and NPA values show only small variation among catalysts (Pd ≈ + 0.16 a.u. in Hirshfeld and + 0.09–0.10 a.u. in NPA), whereas ESP charges reveal more pronounced polarization, particularly in cata-2 and cata-5 (Pd ≈ + 0.45–0.68 a.u.). This suggests stronger ligand polarization effects in these complexes, which may influence substrate activation. The coordinated iodides (I2 and I3) consistently exhibit substantial negative charge, indicating their strong electron-donating role and reinforcing their function as stabilizing spectators rather than active sites in substrate binding. The NHC ligand nitrogens (N5–N8) display varying charge polarity depending on the substitution pattern. In all catalysts, NPA charges predict the strongest electron donation from these atoms (values up to -0.43 a.u.), consistent with the well-known electron-rich carbene character. ESP values show significant variation among catalysts, indicating that substituent effects modulate local electrostatic potential, which could influence catalytic turnover and intermediate stabilization. Carbon centers of the ligand backbone show relatively small but systematic shifts in charge depending on ligand substituents. Catalysts cata-3, cata-4, and cata-5, which contain more electron-withdrawing substituents, display higher electrophilicity in ESP and NPA schemes, suggesting enhanced substrate activation capability. The combined charge analyses demonstrate that ligand modification significantly alters the local electronic environment around palladium and associated donor atoms. Among the charge models applied, NPA offers the most chemically intuitive depiction of bonding, whereas ESP charges provide insight into electrostatic reactivity control. Together, these results help establish how structural modifications influence catalytic behavior in acceptorless alcohol dehydrogenation. The Hirshfeld (HF), ESP[MK], and Natural population charge (NPC) charge values [a.u.] on each atom of cata-1 to cata-5 catalysts are shown in the supplementary information (Table ST1(a), ST1(b) and ST1(c)). To gain insight into the electronic structure and potential catalytic behavior of the NHC-supported Pd-PEPPSI complexes, a detailed frontier molecular orbital (FMO) analysis complemented by global reactivity descriptors was performed at the M06-2X-D3/def2-TZVPP level of theory, as shown in Table 2 . All five catalysts exhibit comparable HOMO energies in the range of − 7.09 to − 7.01 eV, suggesting a similar tendency toward electron donation across the series. Catalyst 1 displays the lowest HOMO energy (− 7.09 eV), indicating slightly higher ionization resistance and stronger metal–ligand orbital stabilization, whereas catalysts 4 and 5 possess the highest HOMO values (− 7.01 eV), implying relatively enhanced donor ability, which may facilitate substrate activation during oxidative addition or hydride transfer steps. Similarly, the LUMO energies span from − 0.77 to − 0.68 eV, with catalyst 3 exhibiting the lowest value (− 0.77 eV), consistent with a greater electron-accepting capacity and potentially improved stabilization of reaction intermediates involving back-donation or hydride abstraction. The narrow range of HOMO–LUMO gaps (6.29–6.35 eV) across the complexes indicates an overall comparable kinetic stability; however, the slightly smaller gap observed for catalyst 4 (6.29 eV) suggests increased electronic softness, aligning with possible enhanced reactivity in catalytic dehydrogenation pathways. The computed dipole moments show a more prominent variation, with catalysts 4 (3.35 D) and 5 (3.33 D) exhibiting the highest polarity, which may influence solvation behavior, substrate alignment, and transition-state stabilization under experimental conditions. The calculated chemical hardness values (− 3.93 to − 3.84 eV) and electronegativity trends mirror the observed orbital energies, further supporting the relative softness and improved electron-exchange capability of catalysts 4 and 5 compared to the others. The electrophilicity index (ω) varies marginally (− 1.30 to − 1.26 eV), suggesting that all complexes maintain similar electrophilic character, although catalyst 5 is predicted to be slightly more electrophilic, potentially correlating with enhanced interaction strength toward alcohol substrates during acceptorless dehydrogenation. Collectively, the FMO profiles and global descriptors indicate subtle yet meaningful variations in electron distribution and reactivity trends, supporting the experimentally observed catalytic behavior and providing a theoretical basis for structure–activity relationships within the catalyst series. Table 2 Computed energy (eV) parameters of NHC-Supported Palladium-PEPPSI catalysts at M062X-D3/def2-TZVPP level of theory Energy Parameters cata-1 cata-2 cata-3 cata-4 cata-5 E HOMO (IP) [eV] -7.09 -7.08 -7.08 -7.01 -7.01 E LUMO (EA) [eV] -0.77 -0.73 -0.77 -0.71 -0.68 HOMO-LUMO gap [eV] 6.31 6.35 6.30 6.29 6.33 Dipole moment(D) 2.27 2.15 2.48 3.35 3.33 Hardness(η) -3.93 -3.90 -3.92 -3.86 -3.84 Chemical potential(µ) -3.16 -3.17 -3.15 -3.15 -3.16 Electronegativity(χ) -3.93 -3.90 -3.92 -3.86 -3.84 Electrophilicity index(ω) -1.27 -1.29 -1.26 -1.28 -1.30 AIM analysis: To probe the network of non-covalent contacts that shape the three-dimensional arrangements of the NHC-supported Pd-PEPPSI complexes, we carried out an atoms-in-molecules (AIM) topology analysis at the M06-2X-D3/def2-TZVPP level. Electron density ρ(r) and its Laplacian ∇²ρ(r) were mapped and bond critical points (BCPs, (3, − 1) points) were located for the short interatomic contacts observed in the optimized structures, as shown in Fig. 2 . The AIM descriptors, the electron density at the BCP (ρBCP), the kinetic (GBCP) and potential (VBCP) energy densities, their sum (HBCP = GBCP + VBCP), and the Laplacian ∇²ρBCP, provide a compact, quantitative view of the interaction type and strength. In the AIM framework, values of ρBCP well below ∼0.20 a.u. indicate closed-shell interactions (ionic, van der Waals, hydrogen bonds, etc.), while the sign of HBCP together with the Laplacian are commonly used to assess the degree of covalence: negative HBCP (and usually ∇²ρ 0 is characteristic of weak, closed-shell interactions. Estimated interaction energies (E int ) at the BCPs were also provided to give an approximate sense of the energetic importance of each contact, as given in Table 3 . The AIM data show that all identified BCPs correspond to weak, closed-shell interactions rather than covalent bonds. Electron densities at the BCPs are small (typically in the 0.0035–0.0111 a.u. window) and far below the ∼0.20 a.u. threshold for shared covalent bonding. The Laplacian values are uniformly positive for these contacts (examples: cata-1 ρBCP(N6–H24) = 0.01055 a.u., ∇²ρ = 0.04126 a.u.; cata-3 ρBCP(N6–H32) = 0.01110 a.u., ∇²ρ = 0.04256 a.u.), and the total energy densities HBCP are small but positive in all cases (HBCP values in the range ≈ + 0.00047 to + 0.00167 a.u.). According to the Rozas–Cremer–Kraka criteria, the combination ∇²ρ > 0 and H > 0 places these contacts in the category of weak, primarily electrostatic hydrogen-bonding/closed-shell interactions rather than medium or strongly covalent H-bonds. This classification is also reflected in the modest interaction energies: the strongest identified contacts are on the order of − 1.6 to − 1.7 kcal·mol⁻¹ (for example, cata-3 N6–H32, E int ≈ − 1.73 kcal·mol⁻¹; cata-1 N6–H24, E int ≈ − 1.61 kcal·mol⁻¹), while many I···H halogen-type contacts cluster around − 1.4 to − 1.5 kcal·mol⁻¹ and a few are nearly negligible ( ≈ − 0.05 to − 0.4 kcal·mol⁻¹). In essence, the AIM metrics consistently indicate multiple weak, stabilizing contacts (mostly I···H and N···H motifs) that help hold particular ligand conformations but do not approach covalent bond character. Comparing across the catalyst series, N-centered contacts (N···H) tend to be marginally stronger than the majority of I···H contacts, as seen by slightly larger ρBCP and more negative Eint for the top N···H entries (e.g., cata-3 and cata-1). Several iodide-hydrogen BCPs are recurrent in every complex (typical ρBCP ≈ 0.0097–0.0099 a.u., HBCP ≈ + 0.00081 a.u., Eint ≈ − 1.3 to − 1.4 kcal·mol⁻¹), indicating that the iodide ligands form a network of weak electrostatic contacts with proximal C–H and N–H groups; these I···H contacts likely act as conformational anchors that influence the shape of the catalytic pocket. A number of very small BCPs (ρBCP ≈ 0.0035–0.0055 a.u., E int ≈ − 0.05 to − 0.5 kcal·mol⁻¹) denote marginal interactions that will have minimal energetic consequence but still contribute to the overall packing and internal orientation of substituents. Correlation of the AIM analysis with the FMO and global descriptor results provides a consistent and complementary interpretation. The FMO results showed relatively similar HOMO–LUMO profiles across the series with small variations in orbital energies and dipole moments; catalysts with slightly higher polarity (cata-4 and cata-5) showed marginally increased dipole moments and a small trend toward electronic softness. The presence of the weak intramolecular H-bonding network revealed by AIM provides a structural rationale for these electronic subtleties: modest N···H and I···H contacts restrict local geometry and can tune the electrostatic environment around the Pd center and the ligand π-framework, thereby modulating the electrostatic potential that determines ESP-fitted charges and the distribution of frontier orbitals. In other words, the weak closed-shell interactions do not create new covalent pathways but they influence orbital energies and spatial localization by slightly rigidifying the ligand scaffold and altering local polarization. This is consistent with the charge analyses (Hirshfeld/ESP/NPA) in which catalysts with stronger local polarization showed larger ESP charges at metal-adjacent sites; AIM confirms those polarization patterns arise in part from recurring iodide-hydrogen and N-H contacts. Functionally, these weak intramolecular interactions are expected to stabilize particular conformers and to affect substrate approach orientation rather than to play a direct mechanistic role in bond-making/breaking steps of acceptorless dehydrogenation. Catalysts that possess the relatively stronger N···H BCPs (cata-3, cata-1) may be slightly more conformationally biased, whereas complexes dominated by many moderate I···H contacts (all complexes) will present an electrostatically shaped pocket that could influence transition-state stabilization via long-range electrostatic effects. Taken together, the AIM results therefore support a model in which a constellation of weak, closed-shell interactions tunes the local electronic and geometric environment of the Pd center, complementing the trends observed in the FMO and charge analyses and providing a microscopic basis for subtle differences in catalytic behavior across the series. Table 3 Topological parameters for bonds of interacting atoms in NHC-Supported Palladium-PEPPSI Catalysts: electron density (ρBCP), kinetic electron energy density (GBCP), potential electron energy density (VBCP), total electron energy density (HBCP), Laplacian of electron density (∇ 2 BCP), estimated interaction energy (E int ) at bond critical point (BCP) cata-1 Critical Point number ρBCP [a.u.] G BCP [a.u.] V BCP [a.u.] H BCP [a.u.] ∇ 2 ρBCP [a.u.] E int [kcal/mol] 72[N6----H24] 0.01055 0.00864 -0.00697 0.00167 0.04126 -1.61 75[I2----H34] 0.00977 0.00615 -0.00533 0.00081 0.02789 -1.43 89[I3----H24] 0.00364 0.00194 -0.00144 0.00050 0.00983 -0.07 102[I3----H42] 0.00980 0.00613 -0.00531 0.00081 0.02780 -1.44 104[I3----H26] 0.00477 0.00263 -0.00200 0.00062 0.01304 -0.32 cata-2 57[I3----H28] 0.00455 0.00250 -0.00190 0.00059 0.01241 -0.27 61[I3----H44] 0.00974 0.00610 -0.00528 0.00081 0.02768 -1.43 63[I3----H33] 0.00675 0.00384 -0.00315 0.00069 0.01814 -0.76 73[I3----H30] 0.00453 0.00246 -0.00188 0.00057 0.01214 -0.26 104[I2----H52] 0.00971 0.00608 -0.00527 0.00081 0.02762 -1.42 111[I2----H13] 0.00520 0.00307 -0.00241 0.00065 0.01489 -0.41 cata-3 60[I2—H13] 0.00549 0.00320 -0.00250 0.00069 0.01557 -0.48 79[N6----H32] 0.01110 0.00899 -0.00735 0.00164 0.04256 -1.73 81[I2----H42] 0.00990 0.00624 -0.00542 0.00081 0.02824 -1.46 96[I3----H32] 0.00356 0.00188 -0.00140 0.00047 0.00943 -0.05 99[I3----H49] 0.00682 0.00366 -0.00301 0.00065 0.01728 -0.78 111[I3----H34] 0.00977 0.00613 -0.00531 0.00081 0.02782 -1.43 113[I3----H30] 0.00491 0.00269 -0.00206 0.00062 0.01329 -0.35 cata-4 48[I3----H38] 0.00955 0.00605 -0.00524 0.00081 0.02747 -1.38 53[I3----H36] 0.00606 0.00323 -0.00260 0.00062 0.01542 -0.60 58[I3----H12] 0.00611 0.00351 -0.00284 0.00067 0.01676 -0.62 105[I2----H31] 0.00868 0.00496 -0.00423 0.00073 0.02280 -1.19 107[I2----H46] 0.00917 0.00614 -0.00532 0.00081 0.02786 -1.30 cata-5 45[I3----H35] 0.00967 0.00607 -0.00525 0.00081 0.02755 -1.41 95[I2----H32] 0.00693 0.00395 -0.00325 0.00070 0.01865 -0.80 99[I2----H43] 0.00965 0.00608 -0.00526 0.00081 0.02760 -1.41 ##number after atoms represent label of that atom (Fig. 1 ). Vibrational Mode analysis: Vibrational frequency calculations performed at the M06-2X-D3/def2-TZVPP level provided insight into the key IR-active modes associated with the NHC-supported Pd-PEPPSI catalysts (Table 4 ). All five catalysts displayed characteristic low-frequency bands in the range of 120–450 cm⁻¹, corresponding primarily to metal-ligand motions, including Pd–I stretching (~ 120 cm⁻¹) and ring-bending modes of pyridine, benzene, and triazole units. These features confirm structural integrity around the metal center and support the formation of stable coordination frameworks. Mid-frequency signals between 600–1200 cm⁻¹ correspond to ring deformation, C–O–C bending, and C–H in-plane bending, with minor variations among catalysts reflecting substituent influence and ligand-specific rigidity. Notably, triazole and pyridine deformation bands appear consistently across all structures, indicating conserved ligand vibrational behavior despite structural modification. Higher frequency regions between 1400–1700 cm⁻¹ are dominated by stretching modes such as N = N, C–N, and aromatic C–C vibrations, suggesting strong electronic coupling across the ligand backbone. The spectral proximity of these modes across the catalyst series implies that electronic variation induced by substituent changes does not significantly distort the global bonding framework. Finally, the high-frequency region (3000–3245 cm⁻¹) exhibits aliphatic and aromatic C–H stretching, including symmetric and asymmetric stretching of CH₂/CH₃ groups, along with pyridine and benzene C–H stretching and breathing modes. These well-resolved peaks confirm the preservation of aromaticity and ligand integrity, while subtle shifts across the catalysts mirror trends observed in frontier orbital analysis and AIM results, suggesting a relationship between substituent-induced steric environments and vibrational perturbations. Thus, across FMO, global reactivity descriptors, AIM analysis, and vibrational mode characterization, a coherent structure–property relationship emerges for the NHC-supported Pd-PEPPSI catalysts. The relatively narrow HOMO–LUMO gaps and comparable chemical hardness values indicate similar intrinsic reactivity profiles, while variations in dipole moments and electrophilicity reflect substituent-induced polarization. AIM analysis confirms the presence of multiple weak to medium-strength noncovalent interactions, including hydrogen bonding and weak halogen contacts, which contribute to conformational stabilization and may facilitate substrate approach in catalytic pathways. Vibrational spectroscopy further supports the structural robustness of the catalytic framework and demonstrates that ligand substitution fine-tunes electronic distribution without disrupting core bonding patterns. Together, these results suggest that subtle modifications in ligand architecture modulate catalyst activation, stability, and potential reactivity in a predictable manner. Table 4 Calculated IR vibrational frequencies of NHC-Supported Palladium-PEPPSI Catalysts (cata 1–5) at M062X-D3/def2-TZVPP level of theory Calculated wave numbers [cm − 1 ] Tentative assignment of vibrations [##] cata-1 cata-2 cata-3 cata-4 cata-5 121 120 120 120 121 Pd-I stretching 129, 1096 129, 1098 - 134 140 Methyl bending 402 401 402 402 402 Pyridine C-C-C bending 419 418 419 - - Benzene C-C bending - - - 428 429 Hexane C-C-C bending 449 448 449 449 448 Pyridine ring bending 450 437 460 498 499 C-O-C bending 497 474 500 - - Benzene ring bending 619 704 621, 725 728 748 Triazole ring deformation 636, 1022 634, 1022 636, 1022 - - Benzene ring deformation 649, 666, 1054, 1062 648, 666, 1054, 1062 649, 666, 1054, 1062 648, 666, 1054, 1062 649, 666, 1054, 1062 Pyridine ring deformation 718, 732, 880, 1014, 1040 725, 728, 883, 1015, 1038 718, 733, 882, 1015, 1040 - - Benzene C-H bending 721, 785, 908, 1048 721, 784, 907, 1033, 1048 721, 785, 908, 1048 721, 785, 907, 992, 1049 722, 785, 908, 995, 1048 Pyridine C-H bending 992 867 991 - - C-O-C stretching 1020, 1026 1047 1020, 1027 1044 1044 CH2 wagging 1146 1142 1149 1147 1143 Triazole ring deformation 1182 1185 1182 - - Benzene C-H bending + C-O-C bending + CH2 bending 1416 1416 1415 1417 1419 N = N stretch + C-N stretch + CH3 bending 1498 1498 1497 1498 1498 Pyridine in-plane C-H bending, 1498 1502 1498 - - Benzene in-plane C-H bending, 1503, 1512 1503, 1510 1503, 1512 1414, 1501, 1512 1410, 1501, 1510 CH2 scissoring 1539 1542 1531 1528 1537 C-N stretching 1601, 1655, 1677, 1684 1607, 1655, 1679, 1683 1597, 1655, 1678, 1684 1598, 1656, 1684 1603, 1656, 1684 C-C stretching 3032, 3105 3042, 3115 3106, 3134 3118 3119 C-H stretching 3055, 3083 3083 3030, 3053, 3082 3057, 3077, 3110 3057, 3064, 3117 CH2 symmetric stretching 3085 3068, 3075, 3085 3074, 3070 3086 CH3 stretching 3130, 3133 3123, 3138 3129, 3141 3128, 3128 CH2 asymmetric stretching 3163, 3202 3143, 3153, 3166 3152, 3157, 3173 3144, 3135 3135 CH3 asymmetric stretching 3188, 3205, 3210, 3219 3181, 3202, 3212, 3188, 3206, 3211, 3220 - - Benzene C-H stretching 3213, 3223, 3227, 3239 3213, 3224, 3227, 3241 3213, 3223, 3227 3212, 3225, 3240 3212, 3225, 3238 Pyridine C-H stretching 3229 3223 3230 - - Benzene breathing vibration 3244 3245 3243 3244 3243 Pyridine breathing vibration Conclusion In this work, a comprehensive first-principles investigation was carried out to elucidate the structural stability, electronic characteristics, and intramolecular interactions of NHC-supported Pd-PEPPSI complexes. Geometry optimization and vibrational frequency analyses confirmed that all complexes are true minima on the potential energy surface and retain a robust square-planar coordination environment around the Pd(II) center. Thermodynamic evaluation revealed subtle variations in Gibbs free energy across the catalyst series, highlighting the influence of ligand substitution on intrinsic stability. Frontier molecular orbital analysis demonstrated closely spaced HOMO energy levels and comparable HOMO–LUMO gaps, indicating high kinetic stability while revealing slight differences in electronic softness and reactivity. The modulation of orbital distribution around the palladium center suggests that ligand architecture effectively tunes donor–acceptor interactions without disrupting structural integrity. Global reactivity descriptors, including electrophilicity and chemical hardness, further support the role of ligand substitution in regulating electronic polarization and charge-transfer capability. Charge population analyses (Hirshfeld, NPA, and ESP mapping) consistently confirm the electrophilic character of the Pd center and reveal substituent-dependent redistribution of electron density within the coordination sphere. Topological analysis based on QTAIM identified weak closed-shell interactions, such as N···H and I···H contacts, which contribute to conformational stabilization without introducing covalent character. These subtle noncovalent interactions enhance structural rigidity and electronic balance within the complexes. Overall, the theoretical findings establish clear structure–property relationships in NHC-supported Pd-PEPPSI systems. Ligand modification systematically influences thermodynamic stability, electronic distribution, and intermolecular stabilization while preserving the fundamental coordination geometry. These insights provide a solid computational foundation for understanding electronic tuning strategies and support the rational design of palladium-based catalysts for efficient and sustainable dehydrogenation processes. Declarations Conflicts of Interest: The authors declare no conflict of interest. Funding: No funding to report. Author Contribution P.B., M.K.G., and V.K.Y. wrote the main manuscript text and prepared all the figures. All authors reviewed the manuscript. Acknowledgments: VKY acknowledge the National Supercomputing Mission (NSM) for providing computing resources for PARAM Kamrupa at IIT Guwahati, which C-DAC implements and is supported by the Ministry of Electronics and Information Technology (MeitY) and the Department of Science and Technology (DST), Government of India and also thanks the University of Allahabad for providing a research facility. Data Availability Statement: The data have been cited and listed in the bibliography. References Miyaura, N.; Suzuki, A. Palladium-Catalyzed Cross-Coupling Reactions of Organoboron Compounds. Chem. Rev. 1995, 95 , 2457–2483. https://doi.org/10.1021/cr00039a007 Hartwig, J. F. Carbon–Heteroatom Bond Formation Catalysed by Organometallic Complexes. Nature 2008, 455 , 314–322. https://doi.org/10.1038/nature07369 Crabtree, R. H. Alkane C–H Activation and Functionalization with Homogeneous Transition Metal Catalysts: A Century of Progress—A New Millennium in Prospect. J. Chem. 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Rev. 2013, 42 , 6723–6753. https://doi.org/10.1039/C3CS60027K Kozuch, S.; Shaik, S. How to Conceptualize Catalytic Cycles. Acc. Chem. Res. 2011, 44 , 101–110. https://doi.org/10.1021/ar1000956 Additional Declarations No competing interests reported. Supplementary Files manuscriptSI11March26.docx Cite Share Download PDF Status: Posted 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-9096875","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":609309552,"identity":"da770240-5d7a-425b-b4c0-2ce9aee817b9","order_by":0,"name":"Poonam Bhadoria","email":"","orcid":"","institution":"Jiwaji University","correspondingAuthor":false,"prefix":"","firstName":"Poonam","middleName":"","lastName":"Bhadoria","suffix":""},{"id":609309565,"identity":"075a826d-09a6-4593-811d-c593678f0795","order_by":1,"name":"Manoj Kumar Gangwar","email":"","orcid":"","institution":"University of Allahabad (UoA)","correspondingAuthor":false,"prefix":"","firstName":"Manoj","middleName":"Kumar","lastName":"Gangwar","suffix":""},{"id":609309569,"identity":"fc584c4c-983a-430c-baf8-0c2c4fbc519f","order_by":2,"name":"Vivek Kumar Yadav","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6klEQVRIiWNgGAWjYDACHgiWY2BnbpBgYJCAiCYQocWYgZmRRC2JDRAtRACDM2cMP7ypOZze38zYeJt3h0ViA/vhBwwPd+DRcrbHWHLOscO5Mw4zNlvznpFIbOBJM2BIPINbi2Q/j4E0D1tabsNhxjZp3jYJYwaGHKA72/BqMf7N8y8tXR6uhf8Nfi38vD1mQJU2CQZQLXIMEgRs4ec5VmY5t8/GcCPQL5ZzgVrYJJ4ZHMCnhY0nefONN98k5OWONx+88batjoefP/nhw594tDAwcBigGQLEB/BpYGBgf4BffhSMglEwCkYBAI4yR6XIo3qQAAAAAElFTkSuQmCC","orcid":"","institution":"University of Allahabad (UoA)","correspondingAuthor":true,"prefix":"","firstName":"Vivek","middleName":"Kumar","lastName":"Yadav","suffix":""}],"badges":[],"createdAt":"2026-03-11 17:08:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9096875/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9096875/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105904045,"identity":"9877e8da-e338-40ae-af10-ba51944a1e80","added_by":"auto","created_at":"2026-04-01 10:02:37","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":332782,"visible":true,"origin":"","legend":"\u003cp\u003eOptimized structures of all NHC-Supported Palladium-PEPPSI catalysts [cata 1-5] at M062X-D3/def2-TZVPP level of theory (numbers on atoms represent the label of that atom in the optimized geometry)\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-9096875/v1/15eff3fe8ac55fd9606c7a66.png"},{"id":105759732,"identity":"98adc52b-49c2-4ba1-baae-275ba07b854d","added_by":"auto","created_at":"2026-03-30 17:41:11","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":362038,"visible":true,"origin":"","legend":"\u003cp\u003eTopological basin surfaces with Bond critical points (3,-1) of NHC-Supported Palladium-PEPPSI catalysts (cata 1-5) at M062X-D3/def2-TZVPP level\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-9096875/v1/9e77f2c8a5dffa220af447e5.png"},{"id":106961394,"identity":"a8925308-e8dc-4907-900a-adfe79d3d4c8","added_by":"auto","created_at":"2026-04-15 09:25:25","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1683088,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9096875/v1/dac21cf2-df74-46c1-b042-ce1c9f10f13f.pdf"},{"id":105904273,"identity":"5822488e-99aa-44a3-b050-2a8684916864","added_by":"auto","created_at":"2026-04-01 10:07:00","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":27434,"visible":true,"origin":"","legend":"","description":"","filename":"manuscriptSI11March26.docx","url":"https://assets-eu.researchsquare.com/files/rs-9096875/v1/f0bebaa24c89b39191fdee07.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Computational Elucidation of Electronic Structure and Noncovalent Interactions in NHC-Supported Palladium-PEPPSI Complexes for Acceptorless Alcohol Dehydrogenation","fulltext":[{"header":"Introduction","content":"\u003cp\u003ePalladium-based catalysts have emerged as highly versatile systems in homogeneous catalysis, particularly in cross-coupling, C-H activation, and transfer hydrogenation reactions[\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Among these, palladium\u0026ndash;PEPPSI (Pyridine-Enhanced Precatalyst Preparation, Stabilization, and Initiation) complexes supported by N-heterocyclic carbene (NHC) ligands have attracted sustained attention due to their remarkable thermal stability, air tolerance, and tunable steric\u0026ndash;electronic properties[\u003cspan additionalcitationids=\"CR6\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Experimentally, PEPPSI-type complexes have demonstrated high efficiency in Suzuki\u0026ndash;Miyaura, Heck, and Buchwald\u0026ndash;Hartwig reactions [\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], as well as in acceptorless alcohol dehydrogenation (AAD), a transformation of growing importance for sustainable hydrogen production and green oxidation chemistry[\u003cspan additionalcitationids=\"CR12\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. The strong σ-donating nature of NHC ligands stabilizes low-coordinate Pd centers, enhances metal\u0026ndash;ligand covalency, and promotes catalytic robustness under mild conditions [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. However, despite extensive experimental reports on their catalytic activity, a detailed molecular-level understanding of how ligand substitution modulates electronic structure, charge distribution, and intrinsic stability remains incomplete [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFrom a computational perspective, density functional theory (DFT) has proven to be a powerful framework for elucidating structure\u0026ndash;reactivity relationships of transition-metal complexes [\u003cspan additionalcitationids=\"CR17\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Numerous theoretical studies have investigated palladium-catalyzed cross-coupling and dehydrogenation mechanisms, revealing key insights into oxidative addition, migratory insertion, β-hydride elimination, and reductive elimination pathways [\u003cspan additionalcitationids=\"CR20\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. In particular, DFT analyses have clarified how ligand electronics influence frontier molecular orbital (FMO) alignment, metal-centered electrophilicity, and activation barriers [\u003cspan additionalcitationids=\"CR23\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Computational descriptors such as HOMO\u0026ndash;LUMO gap, global electrophilicity index, chemical hardness, and charge transfer characteristics have been successfully employed to rationalize catalytic trends across related Pd systems[\u003cspan additionalcitationids=\"CR26\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Furthermore, energy decomposition and charge population analyses, such as Natural Population Analysis (NPA), Hirshfeld charges, and electrostatic potential (ESP) mapping, provide quantitative measures of electron donation and back-donation between metal centers and supporting ligands [\u003cspan additionalcitationids=\"CR29\" citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eRecent theoretical investigations emphasize the importance of noncovalent interactions and subtle intramolecular contacts in stabilizing organometallic frameworks [\u003cspan additionalcitationids=\"CR32\" citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. Quantum Theory of Atoms in Molecules (QTAIM) and topological analyses have revealed that weak interactions such as C-H\u0026middot;\u0026middot;\u0026middot;X (X\u0026thinsp;=\u0026thinsp;halogen, heteroatom) or N\u0026middot;\u0026middot;\u0026middot;H contacts can significantly influence conformational stability, orbital localization, and electronic polarization [\u003cspan additionalcitationids=\"CR35\" citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. In square-planar Pd(II) complexes, such interactions often modulate the spatial distribution of electron density without substantially altering the coordination geometry [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Vibrational frequency analysis further serves as a diagnostic tool for verifying structural stability and identifying characteristic metal-ligand stretching modes, particularly Pd-halide and Pd-carbene vibrations [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAcceptorless alcohol dehydrogenation has gained considerable interest as an atom-economical route for hydrogen generation and carbonyl compound synthesis without sacrificial oxidants [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. While experimental studies report high turnover numbers and excellent selectivity for NHC-supported Pd catalysts [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], theoretical understanding of the intrinsic electronic factors governing their activity is still evolving[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. In this context, systematic computational analysis of ligand-modified Pd-PEPPSI frameworks can provide valuable insights into how electronic redistribution, polarization effects, and frontier orbital characteristics correlate with thermodynamic stability and potential catalytic performance [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe present study therefore aims to deliver a comprehensive first-principles investigation of a series of NHC-supported Pd-PEPPSI complexes with varying ligand substitution patterns. Using dispersion-corrected DFT methods [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], we examine optimized geometries, thermodynamic stability, frontier orbital distributions, global reactivity descriptors, charge population characteristics, and topological features of electron density. By integrating FMO analysis, electrophilicity metrics[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], electrostatic potential mapping[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], and QTAIM evaluation [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e], this work establishes clear structure\u0026ndash;electronic property relationships within the catalyst series. The findings provide a molecular-level understanding of how subtle ligand modifications tune electronic softness, polarization, and noncovalent stabilization while preserving the square-planar Pd coordination environment [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Such insights are essential for the rational design of next-generation palladium catalysts for sustainable hydrogen production and green dehydrogenation chemistry.\u003c/p\u003e"},{"header":"Results and discussion","content":"\u003cp\u003eAll quantum-chemical calculations were performed using the Gaussian16 suite of programs [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. Geometry optimizations for all five NHC-supported Pd-PEPPSI catalysts (Cata-1 to Cata-5) were carried out at the M06-2X-D3/def2-TZVPP level of theory. The M06-2X functional is well recognized for its reliable treatment of thermochemistry and transition-metal systems[\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e], while Grimme\u0026rsquo;s D3 dispersion correction accounts for long-range noncovalent interactions critical in organometallic complexes [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. The def2-TZVPP basis set provides balanced triple-ζ accuracy for main-group and transition-metal elements [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. The optimized structures correspond to true minima on the potential energy surface, as confirmed by vibrational frequency analyses at the same level, which yielded no imaginary frequencies. Vibrational modes were visualized using GaussView6 [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. Charge analyses, frontier molecular orbital (FMO) global reactivity parameters, thermodynamic properties, and atoms-in-molecules (AIM) analyses were also computed at the same theoretical level.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eGeometry Optimization:\u003c/h2\u003e \u003cp\u003eAll five NHC-supported Pd-PEPPSI catalysts were fully optimized without symmetry constraints (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The square-planar coordination geometry observed around Pd is consistent with established structural features of Pd(II) PEPPSI-type complexes [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Subtle differences in ligand orientation arise from steric and electronic substituent effects, which are known to influence catalytic reactivity in NHC-supported systems [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Thermodynamic parameters (ΔG, ΔH, ΔS, Cp) were computed from frequency calculations using standard statistical thermodynamics formalism implemented in Gaussian [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. The relative Gibbs free energy trends indicate minimal enthalpy\u0026ndash;entropy compensation. Similar thermodynamic analyses have been used extensively to compare organometallic catalyst stability [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo assess the relative stabilities of the catalysts, thermodynamic quantities including Gibbs free energy (ΔG), enthalpy (ΔH), entropy (ΔS), and heat capacity (Cp) were computed (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The ΔG and ΔH values follow a similar trend, indicating minimal enthalpy\u0026ndash;entropy compensation. Among the series, cata-2 exhibits the lowest (most negative) Gibbs free energy (-11.25 \u0026times; 10⁵ kcal mol⁻\u0026sup1;), suggesting it is the most thermodynamically stable complex. This is followed closely by cata-3 and cata-1, while cata-4 and cata-5 display comparatively less favorable stabilization. The entropy values increase in the order cata-5\u0026thinsp;\u0026lt;\u0026thinsp;cata-4\u0026thinsp;\u0026lt;\u0026thinsp;cata-1\u0026thinsp;\u0026lt;\u0026thinsp;cata-3\u0026thinsp;\u0026lt;\u0026thinsp;cata-2, indicating greater conformational flexibility in catalysts with bulkier ligand frameworks. Correspondingly, the computed heat capacities show the same trend, supporting the observation that structural flexibility and heavier substituents contribute to enhanced vibrational degrees of freedom.\u003c/p\u003e \u003cp\u003eThese results reveal that structural variations among the ligands significantly influence the thermodynamic stability of the Pd-PEPPSI complexes, with cata-2 being the most stable and cata-5 the least stabilized under identical computational conditions.\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\u003eThermodynamic parameters of NHC-Supported Palladium-PEPPSI Catalysts at M062X-D3/def2-TZVPP level of theory\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThermodynamic Parameters (in)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecata-1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ecata-2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ecata-3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ecata-4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ecata-5\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGibbsFree Energy (∆G) (\u0026times; 10\u003csup\u003e5\u003c/sup\u003e) kcal/mol\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-10.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-11.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-11.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-10.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-10.04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnthalpy(∆H) (\u0026times; 10\u003csup\u003e5\u003c/sup\u003e) kcal/mol\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-10.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-11.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-11.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-10.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-10.04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEntropy (∆S) (cal/mol-kelvin)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e188.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e197.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e194.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e179.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e174.55\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHeat Capacity (cal/mol-kelvin)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e92.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e103.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e96.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e88.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e83.65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eCharge analysis and FMO analysis:\u003c/h3\u003e\n\u003cp\u003eTo gain deeper insight into the electronic structure and metal\u0026ndash;ligand interactions of the five NHC-supported Pd-PEPPSI catalysts (cata-1 to cata-5), atomic charge analyses were carried out using Hirshfeld charges, electrostatic potential (ESP/ Merz\u0026ndash;Kollman) charges, and Natural Population Analysis (NPA) at the M06-2X-D3/def2-TZVPP level of theory. Using more than one population analysis scheme is essential because atomic charges are not directly observable quantities and different theoretical models often yield varying numerical values. Evaluating multiple charge descriptors provides a more robust and chemically meaningful interpretation of electron distribution, catalytic activity, and ligand effects. Hirshfeld Charges are derived from electron density partitioning based on stockholder partitioning and typically provide moderate charge separation. These values are often less sensitive to the basis set but may underestimate charge transfer in strongly polarized systems. ESP/MK Charges are fitted to reproduce the electrostatic potential surrounding the molecule and are generally more sensitive to electronic polarization. These charges are particularly relevant for reactivity descriptors and modeling electrostatic interactions with substrates or solvents. While NPA Charges are based on Natural Bond Orbital (NBO) theory and reflect the occupancy of localized orbitals, providing the most chemically intuitive description. They typically yield the largest charge separation, making them suitable for evaluating metal center electron richness, ligand donation, and bonding character.\u003c/p\u003e \u003cp\u003eAcross all charge methods, the positive charge on Pd remains consistent, confirming its electrophilic nature and role as the catalytic center. Hirshfeld and NPA values show only small variation among catalysts (Pd\u0026thinsp;\u0026asymp;\u0026thinsp;+\u0026thinsp;0.16 a.u. in Hirshfeld and +\u0026thinsp;0.09\u0026ndash;0.10 a.u. in NPA), whereas ESP charges reveal more pronounced polarization, particularly in cata-2 and cata-5 (Pd\u0026thinsp;\u0026asymp;\u0026thinsp;+\u0026thinsp;0.45\u0026ndash;0.68 a.u.). This suggests stronger ligand polarization effects in these complexes, which may influence substrate activation. The coordinated iodides (I2 and I3) consistently exhibit substantial negative charge, indicating their strong electron-donating role and reinforcing their function as stabilizing spectators rather than active sites in substrate binding.\u003c/p\u003e \u003cp\u003eThe NHC ligand nitrogens (N5\u0026ndash;N8) display varying charge polarity depending on the substitution pattern. In all catalysts, NPA charges predict the strongest electron donation from these atoms (values up to -0.43 a.u.), consistent with the well-known electron-rich carbene character. ESP values show significant variation among catalysts, indicating that substituent effects modulate local electrostatic potential, which could influence catalytic turnover and intermediate stabilization. Carbon centers of the ligand backbone show relatively small but systematic shifts in charge depending on ligand substituents. Catalysts cata-3, cata-4, and cata-5, which contain more electron-withdrawing substituents, display higher electrophilicity in ESP and NPA schemes, suggesting enhanced substrate activation capability.\u003c/p\u003e \u003cp\u003eThe combined charge analyses demonstrate that ligand modification significantly alters the local electronic environment around palladium and associated donor atoms. Among the charge models applied, NPA offers the most chemically intuitive depiction of bonding, whereas ESP charges provide insight into electrostatic reactivity control. Together, these results help establish how structural modifications influence catalytic behavior in acceptorless alcohol dehydrogenation. The Hirshfeld (HF), ESP[MK], and Natural population charge (NPC) charge values [a.u.] on each atom of cata-1 to cata-5 catalysts are shown in the supplementary information (Table ST1(a), ST1(b) and ST1(c)).\u003c/p\u003e \u003cp\u003eTo gain insight into the electronic structure and potential catalytic behavior of the NHC-supported Pd-PEPPSI complexes, a detailed frontier molecular orbital (FMO) analysis complemented by global reactivity descriptors was performed at the M06-2X-D3/def2-TZVPP level of theory, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. All five catalysts exhibit comparable HOMO energies in the range of \u0026minus;\u0026thinsp;7.09 to \u0026minus;\u0026thinsp;7.01 eV, suggesting a similar tendency toward electron donation across the series. Catalyst 1 displays the lowest HOMO energy (\u0026minus;\u0026thinsp;7.09 eV), indicating slightly higher ionization resistance and stronger metal\u0026ndash;ligand orbital stabilization, whereas catalysts 4 and 5 possess the highest HOMO values (\u0026minus;\u0026thinsp;7.01 eV), implying relatively enhanced donor ability, which may facilitate substrate activation during oxidative addition or hydride transfer steps. Similarly, the LUMO energies span from \u0026minus;\u0026thinsp;0.77 to \u0026minus;\u0026thinsp;0.68 eV, with catalyst 3 exhibiting the lowest value (\u0026minus;\u0026thinsp;0.77 eV), consistent with a greater electron-accepting capacity and potentially improved stabilization of reaction intermediates involving back-donation or hydride abstraction. The narrow range of HOMO\u0026ndash;LUMO gaps (6.29\u0026ndash;6.35 eV) across the complexes indicates an overall comparable kinetic stability; however, the slightly smaller gap observed for catalyst 4 (6.29 eV) suggests increased electronic softness, aligning with possible enhanced reactivity in catalytic dehydrogenation pathways.\u003c/p\u003e \u003cp\u003eThe computed dipole moments show a more prominent variation, with catalysts 4 (3.35 D) and 5 (3.33 D) exhibiting the highest polarity, which may influence solvation behavior, substrate alignment, and transition-state stabilization under experimental conditions. The calculated chemical hardness values (\u0026minus;\u0026thinsp;3.93 to \u0026minus;\u0026thinsp;3.84 eV) and electronegativity trends mirror the observed orbital energies, further supporting the relative softness and improved electron-exchange capability of catalysts 4 and 5 compared to the others. The electrophilicity index (ω) varies marginally (\u0026minus;\u0026thinsp;1.30 to \u0026minus;\u0026thinsp;1.26 eV), suggesting that all complexes maintain similar electrophilic character, although catalyst 5 is predicted to be slightly more electrophilic, potentially correlating with enhanced interaction strength toward alcohol substrates during acceptorless dehydrogenation. Collectively, the FMO profiles and global descriptors indicate subtle yet meaningful variations in electron distribution and reactivity trends, supporting the experimentally observed catalytic behavior and providing a theoretical basis for structure\u0026ndash;activity relationships within the catalyst series.\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\u003eComputed energy (eV) parameters of NHC-Supported Palladium-PEPPSI catalysts at M062X-D3/def2-TZVPP level of theory\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnergy Parameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecata-1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ecata-2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ecata-3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ecata-4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ecata-5\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eE\u003csub\u003e\u003cb\u003eHOMO\u003c/b\u003e\u003c/sub\u003e (IP) [eV]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-7.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-7.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-7.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-7.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-7.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eE\u003csub\u003e\u003cb\u003eLUMO\u003c/b\u003e\u003c/sub\u003e (EA) [eV]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-0.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-0.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-0.68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHOMO-LUMO gap [eV]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6.33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDipole moment(D)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3.33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHardness(η)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-3.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-3.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-3.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-3.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-3.84\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eChemical potential(\u0026micro;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-3.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-3.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-3.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-3.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-3.16\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElectronegativity(χ)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-3.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-3.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-3.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-3.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-3.84\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElectrophilicity index(ω)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-1.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-1.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-1.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-1.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-1.30\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\u003eAIM analysis:\u003c/h3\u003e\n\u003cp\u003eTo probe the network of non-covalent contacts that shape the three-dimensional arrangements of the NHC-supported Pd-PEPPSI complexes, we carried out an atoms-in-molecules (AIM) topology analysis at the M06-2X-D3/def2-TZVPP level. Electron density ρ(r) and its Laplacian \u0026nabla;\u0026sup2;ρ(r) were mapped and bond critical points (BCPs, (3, \u0026minus;\u0026thinsp;1) points) were located for the short interatomic contacts observed in the optimized structures, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The AIM descriptors, the electron density at the BCP (ρBCP), the kinetic (GBCP) and potential (VBCP) energy densities, their sum (HBCP\u0026thinsp;=\u0026thinsp;GBCP\u0026thinsp;+\u0026thinsp;VBCP), and the Laplacian \u0026nabla;\u0026sup2;ρBCP, provide a compact, quantitative view of the interaction type and strength. In the AIM framework, values of ρBCP well below \u0026sim;0.20 a.u. indicate closed-shell interactions (ionic, van der Waals, hydrogen bonds, etc.), while the sign of HBCP together with the Laplacian are commonly used to assess the degree of covalence: negative HBCP (and usually \u0026nabla;\u0026sup2;ρ\u0026thinsp;\u0026lt;\u0026thinsp;0) points toward shared-electron (partially covalent) character, whereas positive HBCP with \u0026nabla;\u0026sup2;ρ\u0026thinsp;\u0026gt;\u0026thinsp;0 is characteristic of weak, closed-shell interactions. Estimated interaction energies (E\u003csub\u003eint\u003c/sub\u003e) at the BCPs were also provided to give an approximate sense of the energetic importance of each contact, as given in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe AIM data show that all identified BCPs correspond to weak, closed-shell interactions rather than covalent bonds. Electron densities at the BCPs are small (typically in the 0.0035\u0026ndash;0.0111 a.u. window) and far below the \u0026sim;0.20 a.u. threshold for shared covalent bonding. The Laplacian values are uniformly positive for these contacts (examples: cata-1 ρBCP(N6\u0026ndash;H24)\u0026thinsp;=\u0026thinsp;0.01055 a.u., \u0026nabla;\u0026sup2;ρ\u0026thinsp;=\u0026thinsp;0.04126 a.u.; cata-3 ρBCP(N6\u0026ndash;H32)\u0026thinsp;=\u0026thinsp;0.01110 a.u., \u0026nabla;\u0026sup2;ρ\u0026thinsp;=\u0026thinsp;0.04256 a.u.), and the total energy densities HBCP are small but positive in all cases (HBCP values in the range\u0026thinsp;\u0026asymp;\u0026thinsp;+\u0026thinsp;0.00047 to +\u0026thinsp;0.00167 a.u.). According to the Rozas\u0026ndash;Cremer\u0026ndash;Kraka criteria, the combination \u0026nabla;\u0026sup2;ρ\u0026thinsp;\u0026gt;\u0026thinsp;0 and H\u0026thinsp;\u0026gt;\u0026thinsp;0 places these contacts in the category of weak, primarily electrostatic hydrogen-bonding/closed-shell interactions rather than medium or strongly covalent H-bonds. This classification is also reflected in the modest interaction energies: the strongest identified contacts are on the order of \u0026minus;\u0026thinsp;1.6 to \u0026minus;\u0026thinsp;1.7 kcal\u0026middot;mol⁻\u0026sup1; (for example, cata-3 N6\u0026ndash;H32, E\u003csub\u003eint\u003c/sub\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;\u0026minus;\u0026thinsp;1.73 kcal\u0026middot;mol⁻\u0026sup1;; cata-1 N6\u0026ndash;H24, E\u003csub\u003eint\u003c/sub\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;\u0026minus;\u0026thinsp;1.61 kcal\u0026middot;mol⁻\u0026sup1;), while many I\u0026middot;\u0026middot;\u0026middot;H halogen-type contacts cluster around \u0026minus;\u0026thinsp;1.4 to \u0026minus;\u0026thinsp;1.5 kcal\u0026middot;mol⁻\u0026sup1; and a few are nearly negligible (\u0026thinsp;\u0026asymp;\u0026thinsp;\u0026minus;\u0026thinsp;0.05 to \u0026minus;\u0026thinsp;0.4 kcal\u0026middot;mol⁻\u0026sup1;). In essence, the AIM metrics consistently indicate multiple weak, stabilizing contacts (mostly I\u0026middot;\u0026middot;\u0026middot;H and N\u0026middot;\u0026middot;\u0026middot;H motifs) that help hold particular ligand conformations but do not approach covalent bond character.\u003c/p\u003e \u003cp\u003eComparing across the catalyst series, N-centered contacts (N\u0026middot;\u0026middot;\u0026middot;H) tend to be marginally stronger than the majority of I\u0026middot;\u0026middot;\u0026middot;H contacts, as seen by slightly larger ρBCP and more negative Eint for the top N\u0026middot;\u0026middot;\u0026middot;H entries (e.g., cata-3 and cata-1). Several iodide-hydrogen BCPs are recurrent in every complex (typical ρBCP\u0026thinsp;\u0026asymp;\u0026thinsp;0.0097\u0026ndash;0.0099 a.u., HBCP\u0026thinsp;\u0026asymp;\u0026thinsp;+\u0026thinsp;0.00081 a.u., Eint\u0026thinsp;\u0026asymp;\u0026thinsp;\u0026minus;\u0026thinsp;1.3 to \u0026minus;\u0026thinsp;1.4 kcal\u0026middot;mol⁻\u0026sup1;), indicating that the iodide ligands form a network of weak electrostatic contacts with proximal C\u0026ndash;H and N\u0026ndash;H groups; these I\u0026middot;\u0026middot;\u0026middot;H contacts likely act as conformational anchors that influence the shape of the catalytic pocket. A number of very small BCPs (ρBCP\u0026thinsp;\u0026asymp;\u0026thinsp;0.0035\u0026ndash;0.0055 a.u., E\u003csub\u003eint\u003c/sub\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;\u0026minus;\u0026thinsp;0.05 to \u0026minus;\u0026thinsp;0.5 kcal\u0026middot;mol⁻\u0026sup1;) denote marginal interactions that will have minimal energetic consequence but still contribute to the overall packing and internal orientation of substituents.\u003c/p\u003e \u003cp\u003eCorrelation of the AIM analysis with the FMO and global descriptor results provides a consistent and complementary interpretation. The FMO results showed relatively similar HOMO\u0026ndash;LUMO profiles across the series with small variations in orbital energies and dipole moments; catalysts with slightly higher polarity (cata-4 and cata-5) showed marginally increased dipole moments and a small trend toward electronic softness. The presence of the weak intramolecular H-bonding network revealed by AIM provides a structural rationale for these electronic subtleties: modest N\u0026middot;\u0026middot;\u0026middot;H and I\u0026middot;\u0026middot;\u0026middot;H contacts restrict local geometry and can tune the electrostatic environment around the Pd center and the ligand π-framework, thereby modulating the electrostatic potential that determines ESP-fitted charges and the distribution of frontier orbitals. In other words, the weak closed-shell interactions do not create new covalent pathways but they influence orbital energies and spatial localization by slightly rigidifying the ligand scaffold and altering local polarization. This is consistent with the charge analyses (Hirshfeld/ESP/NPA) in which catalysts with stronger local polarization showed larger ESP charges at metal-adjacent sites; AIM confirms those polarization patterns arise in part from recurring iodide-hydrogen and N-H contacts.\u003c/p\u003e \u003cp\u003eFunctionally, these weak intramolecular interactions are expected to stabilize particular conformers and to affect substrate approach orientation rather than to play a direct mechanistic role in bond-making/breaking steps of acceptorless dehydrogenation. Catalysts that possess the relatively stronger N\u0026middot;\u0026middot;\u0026middot;H BCPs (cata-3, cata-1) may be slightly more conformationally biased, whereas complexes dominated by many moderate I\u0026middot;\u0026middot;\u0026middot;H contacts (all complexes) will present an electrostatically shaped pocket that could influence transition-state stabilization via long-range electrostatic effects. Taken together, the AIM results therefore support a model in which a constellation of weak, closed-shell interactions tunes the local electronic and geometric environment of the Pd center, complementing the trends observed in the FMO and charge analyses and providing a microscopic basis for subtle differences in catalytic behavior across the series.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTopological parameters for bonds of interacting atoms in NHC-Supported Palladium-PEPPSI Catalysts: electron density (ρBCP), kinetic electron energy density (GBCP), potential electron energy density (VBCP), total electron energy density (HBCP), Laplacian of electron density (\u0026nabla;\u003csup\u003e2\u003c/sup\u003e BCP), estimated interaction energy (E\u003csub\u003eint\u003c/sub\u003e) at bond critical point (BCP)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\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 \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003ecata-1\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCritical Point number\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eρBCP [a.u.]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eG\u003csub\u003eBCP\u003c/sub\u003e [a.u.]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eV\u003csub\u003eBCP\u003c/sub\u003e [a.u.]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eH\u003csub\u003eBCP\u003c/sub\u003e [a.u.]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026nabla;\u003csup\u003e2\u003c/sup\u003eρBCP [a.u.]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eE\u003csub\u003eint\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e[kcal/mol]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e72[N6----H24]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.01055\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00864\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00697\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00167\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.04126\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.61\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e75[I2----H34]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00977\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00615\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00533\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00081\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.02789\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.43\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e89[I3----H24]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00364\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00194\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00144\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00050\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.00983\u003c/p\u003e \u003c/td\u003e 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\u003cp\u003e0.00477\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00263\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.01304\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.32\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003ecata-2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e57[I3----H28]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00455\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e 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align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00453\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00246\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00188\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00057\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.01214\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e104[I2----H52]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00971\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00608\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00527\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00081\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.02762\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e111[I2----H13]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00520\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00307\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00241\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00065\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.01489\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.41\u003c/p\u003e \u003c/td\u003e 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colname=\"c4\"\u003e \u003cp\u003e-0.00542\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00081\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.02824\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.46\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e96[I3----H32]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00356\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00188\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00047\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.00943\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e99[I3----H49]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00682\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00366\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00301\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00065\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.01728\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.78\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e111[I3----H34]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00977\u003c/p\u003e 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\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.01329\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003ecata-4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e48[I3----H38]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00955\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00605\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00524\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00081\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.02747\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.38\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e53[I3----H36]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00606\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00323\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00260\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.01542\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e58[I3----H12]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00611\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00351\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00284\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00067\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.01676\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.62\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e105[I2----H31]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00868\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00496\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00423\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.02280\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.19\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e107[I2----H46]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00917\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00614\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00532\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00081\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.02786\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003ecata-5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e45[I3----H35]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00967\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00607\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00525\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00081\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.02755\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.41\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e95[I2----H32]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00693\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00395\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00325\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00070\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.01865\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e99[I2----H43]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00965\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00608\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.00526\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00081\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.02760\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.41\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##number after atoms represent label of that atom (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\n\u003ch3\u003eVibrational Mode analysis:\u003c/h3\u003e\n\u003cp\u003eVibrational frequency calculations performed at the M06-2X-D3/def2-TZVPP level provided insight into the key IR-active modes associated with the NHC-supported Pd-PEPPSI catalysts (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). All five catalysts displayed characteristic low-frequency bands in the range of 120\u0026ndash;450 cm⁻\u0026sup1;, corresponding primarily to metal-ligand motions, including Pd\u0026ndash;I stretching (~\u0026thinsp;120 cm⁻\u0026sup1;) and ring-bending modes of pyridine, benzene, and triazole units. These features confirm structural integrity around the metal center and support the formation of stable coordination frameworks. Mid-frequency signals between 600\u0026ndash;1200 cm⁻\u0026sup1; correspond to ring deformation, C\u0026ndash;O\u0026ndash;C bending, and C\u0026ndash;H in-plane bending, with minor variations among catalysts reflecting substituent influence and ligand-specific rigidity. Notably, triazole and pyridine deformation bands appear consistently across all structures, indicating conserved ligand vibrational behavior despite structural modification.\u003c/p\u003e \u003cp\u003eHigher frequency regions between 1400\u0026ndash;1700 cm⁻\u0026sup1; are dominated by stretching modes such as N\u0026thinsp;=\u0026thinsp;N, C\u0026ndash;N, and aromatic C\u0026ndash;C vibrations, suggesting strong electronic coupling across the ligand backbone. The spectral proximity of these modes across the catalyst series implies that electronic variation induced by substituent changes does not significantly distort the global bonding framework. Finally, the high-frequency region (3000\u0026ndash;3245 cm⁻\u0026sup1;) exhibits aliphatic and aromatic C\u0026ndash;H stretching, including symmetric and asymmetric stretching of CH₂/CH₃ groups, along with pyridine and benzene C\u0026ndash;H stretching and breathing modes. These well-resolved peaks confirm the preservation of aromaticity and ligand integrity, while subtle shifts across the catalysts mirror trends observed in frontier orbital analysis and AIM results, suggesting a relationship between substituent-induced steric environments and vibrational perturbations.\u003c/p\u003e \u003cp\u003eThus, across FMO, global reactivity descriptors, AIM analysis, and vibrational mode characterization, a coherent structure\u0026ndash;property relationship emerges for the NHC-supported Pd-PEPPSI catalysts. The relatively narrow HOMO\u0026ndash;LUMO gaps and comparable chemical hardness values indicate similar intrinsic reactivity profiles, while variations in dipole moments and electrophilicity reflect substituent-induced polarization. AIM analysis confirms the presence of multiple weak to medium-strength noncovalent interactions, including hydrogen bonding and weak halogen contacts, which contribute to conformational stabilization and may facilitate substrate approach in catalytic pathways. Vibrational spectroscopy further supports the structural robustness of the catalytic framework and demonstrates that ligand substitution fine-tunes electronic distribution without disrupting core bonding patterns. Together, these results suggest that subtle modifications in ligand architecture modulate catalyst activation, stability, and potential reactivity in a predictable manner.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCalculated IR vibrational frequencies of NHC-Supported Palladium-PEPPSI Catalysts (cata 1\u0026ndash;5) at M062X-D3/def2-TZVPP level of theory\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\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 \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e \u003cp\u003eCalculated wave numbers [cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTentative assignment of vibrations\u003csup\u003e[##]\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ecata-1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecata-2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ecata-3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ecata-4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ecata-5\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e121\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e121\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePd-I stretching\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e129, 1096\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e129, 1098\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e134\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMethyl bending\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e402\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e401\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e402\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e402\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e402\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePyridine C-C-C bending\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e419\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e418\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e419\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eBenzene C-C bending\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e428\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e429\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHexane C-C-C bending\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e449\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e448\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e449\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e449\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e448\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePyridine ring bending\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e437\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e460\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e498\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e499\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC-O-C bending\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e497\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e474\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eBenzene ring bending\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e619\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e704\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e621, 725\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e728\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e748\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eTriazole ring deformation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e636, 1022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e634, 1022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e636, 1022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eBenzene ring deformation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e649, 666, 1054, 1062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e648, 666, 1054, 1062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e649, 666, 1054, 1062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e648, 666, 1054, 1062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e649, 666, 1054, 1062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePyridine ring deformation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e718, 732, 880, 1014, 1040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e725, 728, 883, 1015, 1038\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e718, 733, 882, 1015, 1040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eBenzene C-H bending\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e721, 785, 908, 1048\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e721, 784, 907, 1033, 1048\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e721, 785, 908, 1048\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e721, 785, 907, 992, 1049\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e722, 785, 908, 995, 1048\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePyridine C-H bending\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e992\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e867\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e991\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC-O-C stretching\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1020, 1026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1047\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1020, 1027\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1044\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1044\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCH2 wagging\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1142\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1149\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1147\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1143\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eTriazole ring deformation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1182\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1185\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1182\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eBenzene C-H bending\u0026thinsp;+\u0026thinsp;C-O-C bending\u0026thinsp;+\u0026thinsp;CH2 bending\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1416\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1416\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1415\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1417\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1419\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eN\u0026thinsp;=\u0026thinsp;N stretch\u0026thinsp;+\u0026thinsp;C-N stretch\u0026thinsp;+\u0026thinsp;CH3 bending\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1498\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1498\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1497\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1498\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1498\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePyridine in-plane C-H bending,\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1498\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1502\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1498\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eBenzene in-plane C-H bending,\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1503, 1512\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1503, 1510\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1503, 1512\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1414, 1501, 1512\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1410, 1501, 1510\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCH2 scissoring\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1539\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1542\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1531\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1528\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1537\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC-N stretching\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1601, 1655, 1677, 1684\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1607, 1655, 1679, 1683\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1597, 1655, 1678, 1684\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1598, 1656, 1684\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1603, 1656, 1684\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC-C stretching\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3032, 3105\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3042, 3115\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3106, 3134\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3118\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3119\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC-H stretching\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3055, 3083\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3083\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3030, 3053, 3082\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3057, 3077, 3110\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3057, 3064, 3117\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCH2 symmetric stretching\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3085\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3068, 3075, 3085\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3074,\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3070\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3086\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCH3 stretching\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3130, 3133\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3123, 3138\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3129, 3141\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3128,\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCH2 asymmetric stretching\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3163, 3202\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3143, 3153, 3166\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3152, 3157, 3173\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3144, 3135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCH3 asymmetric stretching\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3188, 3205, 3210, 3219\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3181, 3202, 3212,\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3188, 3206, 3211, 3220\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eBenzene C-H stretching\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3213, 3223, 3227, 3239\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3213, 3224, 3227, 3241\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3213, 3223, 3227\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3212, 3225, 3240\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3212, 3225, 3238\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePyridine C-H stretching\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3229\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3223\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3230\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eBenzene breathing vibration\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3244\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3245\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3243\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3244\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3243\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePyridine breathing vibration\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eIn this work, a comprehensive first-principles investigation was carried out to elucidate the structural stability, electronic characteristics, and intramolecular interactions of NHC-supported Pd-PEPPSI complexes. Geometry optimization and vibrational frequency analyses confirmed that all complexes are true minima on the potential energy surface and retain a robust square-planar coordination environment around the Pd(II) center. Thermodynamic evaluation revealed subtle variations in Gibbs free energy across the catalyst series, highlighting the influence of ligand substitution on intrinsic stability.\u003c/p\u003e \u003cp\u003eFrontier molecular orbital analysis demonstrated closely spaced HOMO energy levels and comparable HOMO\u0026ndash;LUMO gaps, indicating high kinetic stability while revealing slight differences in electronic softness and reactivity. The modulation of orbital distribution around the palladium center suggests that ligand architecture effectively tunes donor\u0026ndash;acceptor interactions without disrupting structural integrity. Global reactivity descriptors, including electrophilicity and chemical hardness, further support the role of ligand substitution in regulating electronic polarization and charge-transfer capability.\u003c/p\u003e \u003cp\u003eCharge population analyses (Hirshfeld, NPA, and ESP mapping) consistently confirm the electrophilic character of the Pd center and reveal substituent-dependent redistribution of electron density within the coordination sphere. Topological analysis based on QTAIM identified weak closed-shell interactions, such as N\u0026middot;\u0026middot;\u0026middot;H and I\u0026middot;\u0026middot;\u0026middot;H contacts, which contribute to conformational stabilization without introducing covalent character. These subtle noncovalent interactions enhance structural rigidity and electronic balance within the complexes.\u003c/p\u003e \u003cp\u003eOverall, the theoretical findings establish clear structure\u0026ndash;property relationships in NHC-supported Pd-PEPPSI systems. Ligand modification systematically influences thermodynamic stability, electronic distribution, and intermolecular stabilization while preserving the fundamental coordination geometry. These insights provide a solid computational foundation for understanding electronic tuning strategies and support the rational design of palladium-based catalysts for efficient and sustainable dehydrogenation processes.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eConflicts of Interest:\u003c/h2\u003e \u003cp\u003eThe authors declare no conflict of interest.\u003c/p\u003e \u003ch2\u003eFunding:\u003c/h2\u003e \u003cp\u003eNo funding to report.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eP.B., M.K.G., and V.K.Y. wrote the main manuscript text and prepared all the figures. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgments:\u003c/h2\u003e \u003cp\u003eVKY acknowledge the National Supercomputing Mission (NSM) for providing computing resources for PARAM Kamrupa at IIT Guwahati, which C-DAC implements and is supported by the Ministry of Electronics and Information Technology (MeitY) and the Department of Science and Technology (DST), Government of India and also thanks the University of Allahabad for providing a research facility.\u003c/p\u003e\u003ch2\u003eData Availability Statement:\u003c/h2\u003e \u003cp\u003eThe data have been cited and listed in the bibliography.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eMiyaura, N.; Suzuki, A. Palladium-Catalyzed Cross-Coupling Reactions of Organoboron Compounds. \u003cem\u003eChem. Rev.\u003c/em\u003e 1995, \u003cem\u003e95\u003c/em\u003e, 2457\u0026ndash;2483. https://doi.org/10.1021/cr00039a007\u003c/li\u003e\n\u003cli\u003eHartwig, J. F. 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Res.\u003c/em\u003e 2011, \u003cem\u003e44\u003c/em\u003e, 101\u0026ndash;110. https://doi.org/10.1021/ar1000956\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Density Functional Theory (DFT), Pd-PEPPSI complexes, N-Heterocyclic Carbene (NHC), Electronic structure analysis, Acceptorless alcohol dehydrogenation","lastPublishedDoi":"10.21203/rs.3.rs-9096875/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9096875/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA systematic density functional theory (DFT) investigation was conducted to elucidate the structural stability, electronic properties, and noncovalent interactions of NHC-supported Pd-PEPPSI complexes (cata-1 to cata-5) relevant to acceptorless alcohol dehydrogenation. All geometries were optimized at the M06-2X-D3/def2-TZVPP level, and frequency analyses confirmed true minima without imaginary modes. Thermodynamic evaluation revealed subtle stability differences among the complexes, with cata-2 exhibiting the most favorable Gibbs free energy. Frontier molecular orbital analysis showed closely comparable HOMO energies (-7.09 to -7.01 eV) and HOMO–LUMO gaps (6.29 to 6.35 eV), indicating high kinetic stability with slight variations in electronic softness and reactivity. Differences in dipole moment and electrophilicity index demonstrate that ligand substitution effectively modulates polarization and charge distribution around the Pd center. Charge analyses using Hirshfeld, electrostatic potential (ESP), and natural population analysis (NPA) consistently confirm the electrophilic character of palladium and highlight substituent-dependent electronic redistribution within the coordination sphere. Atoms-in-molecules (AIM) topology reveals weak closed-shell N···H and I···H interactions (ρ\u003csup\u003eBCP\u003c/sup\u003e ≈ 0.003-0.011 a.u.) that contribute to structural stabilization without covalent character. Vibrational analysis further confirms the integrity of the square-planar Pd coordination environment, with characteristic Pd-I stretching modes near ~120 cm\u003csup\u003e-1\u003c/sup\u003e. Overall, the results establish clear structure–property relationships, demonstrating that ligand architecture fine-tunes electronic distribution, polarization, and intermolecular stabilization while preserving structural robustness, thereby providing fundamental computational insights for the rational design of palladium catalysts for sustainable dehydrogenation processes.\u003c/p\u003e","manuscriptTitle":"Computational Elucidation of Electronic Structure and Noncovalent Interactions in NHC-Supported Palladium-PEPPSI Complexes for Acceptorless Alcohol Dehydrogenation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-30 17:41:01","doi":"10.21203/rs.3.rs-9096875/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"55653f58-60d3-4901-91ea-965bb1056949","owner":[],"postedDate":"March 30th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-14T12:26:21+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-30 17:41:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9096875","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9096875","identity":"rs-9096875","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}