Local Mode Theory Research Articles

Exploring Jahn-Teller distortions: a local vibrational mode perspective

The characterization of normal mode (CNM) procedure coupled with an adiabatic connection scheme (ACS) between local and normal vibrational modes, both being a part of the Local Vibrational Mode theory developed in our group, can identify spectral changes as structural fingerprints that monitor symmetry alterations, such as those caused by Jahn-Teller (JT) distortions. Employing the PBE0/Def2-TZVP level of theory, we investigated in this proof-of-concept study the hexaaquachromium cation case, [Cr(OH2)6]3+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[\ ext {Cr}{(\ ext {OH}_{2})}_{6}]^{3+}$$\\end{document}/[Cr(OH2)6]2+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[\ ext {Cr}(\ ext {OH}_{2})_{6}]^{2+}$$\\end{document}, as a commonly known example for a JT distortion, followed by the more difficult ferrous and ferric hexacyanide anion case, [Fe(CN)6]4-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[\ ext {Fe}{(\ ext {CN})}_{6}]^{4-}$$\\end{document}/[Fe(CN)6]3-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[\ ext {Fe}{(\ ext {CN})}_{6}]^{3-}$$\\end{document}. We found that in both cases CNM of the characteristic normal vibrational modes reflects delocalization consistent with high symmetry and ACS confirms symmetry breaking, as evidenced by the separation of axial and equatorial group frequencies. As underlined by the Cremer-Kraka criterion for covalent bonding, from [Cr(OH2)6]3+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[\ ext {Cr}{(\ ext {OH}_{2})}_{6}]^{3+}$$\\end{document} to [Cr(OH2)6]2+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[\ ext {Cr}{(\ ext {OH}_{2})}_{6}]^{2+}$$\\end{document} there is an increase in axial covalency whereas the equatorial bonds shift toward electrostatic character. From [Fe(CN)6]4-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[\ ext {Fe}{(\ ext {CN})}_{6}]^{4-}$$\\end{document} to [Fe(CN)6]3-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[\ ext {Fe}{(\ ext {CN})}_{6}]^{3-}$$\\end{document} we observed an increase in covalency without altering the bond nature. Distinct π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi $$\\end{document} back-donation disparity could be confirmed by comparison with the isolated CN-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {CN}^{-}$$\\end{document} system. In summary, our study positions the CNM/ACS protocol as a robust tool for investigating less-explored JT distortions, paving the way for future applications.Graphical abstractThe adiabatic connection scheme relates local to normal modes, with symmetry breaking giving rise to axial and equatorial group local frequencies

Metal-ring interactions in group 2 ansa-metallocenes: assessed with the local vibrational mode theory.

Ansa-metallocenes, a vital class of organometallic compounds, have attracted significant attention due to their diverse structural motifs and their pivotal roles in catalysis and materials science. We investigated 37 distinct group 2 ansa-metallocenes at the B3LYP-D3/def2-TZVP level of theory. Utilizing local mode force constants derived from our local vibrational mode theory, including a special force constant directly targeting the metal-ring interaction, we could unveil latent structural differences between solvated and non-solvated metallocenophanes and the influence of the solvent on complex stability and structure. We could quantify the intrinsic strength of the metal-cyclopentadienyl (M-Cp) bonds and the influence of the bridging motifs on the stiffness of the Cp-M-Cp angles, another determinant of complex stability. LMA was complemented by the analysis of electronic density, utilizing the quantum theory of atoms in molecules (QTAIM), which confirmed both the impact of solvent coordination on the strength of the M-Cp bond(s) and the influence of the bridging motif on the Cp-M-Cp angles. The specific effect of the ansa-motif on the M-Cp interaction was further elucidated by a comparison with linear/bent metallocene structures. In summary, our results identify the local mode analysis as an efficient tool for unraveling the intricate molecular properties of ansa-metallocenes and their unique structural features.

Iron-histidine bonding in bishistidyl hemoproteins-A local vibrational mode study.

We investigated the intrinsic strength of distal and proximal FeN bonds for both ferric and ferrous oxidation states of bishistidyl hemoproteins from bacteria, animals, human, and plants, including two cytoglobins, ten hemoglobins, two myoglobins, six neuroglobins, and six phytoglobins. As a qualified measure of bond strength, we used local vibrational force constants k (FeN) based on local mode theory developed in our group. All calculations were performed with a hybrid QM/MM ansatz. Starting geometries were taken from available x-ray structures. k (FeN) values were correlated with FeN bond lengths and covalent bond character. We also investigated the stiffness of the axial NFeN bond angle. Our results highlight that protein effects are sensitively reflected in k (FeN), allowing one to compare trends in diverse protein groups. Moreover, k (NFeN) is a perfect tool to monitor changes in the axial heme framework caused by different protein environments as well as different Fe oxidation states.

Optimization design of mode-selective ring core photonic lantern based on coupled local mode theory

In this paper, optical field transmission characteristics of a mode-selective ring core photonic lantern (MSRCPL) are theoretically analyzed and its optimization design is also investigated. This MSRCPL is based on a tapered fiber bundle of coreless fiber and glass capillary with low refractive index. Mode evolution characteristics in the taper region and mode coupling characteristics at the splicing point are analyzed. The coupled local mode theory (CLMT) is used to optimize the structure of a 3-port MSRCPL and a 5-port MSRCPL. The impact of taper length, taper shape, taper waist, and geometric arrangement on mode selectivity are calculated. Calculation results indicate that the mode selectivities of the optimized 3-port and 5-port MSRCPL are higher than 23 dB and 18 dB, respectively.

Quantum Mechanical Assessment of Protein-Ligand Hydrogen Bond Strength Patterns: Insights from Semiempirical Tight-Binding and Local Vibrational Mode Theory.

Hydrogen bonds (HB)s are the most abundant motifs in biological systems. They play a key role in determining protein-ligand binding affinity and selectivity. We designed two pharmaceutically beneficial HB databases, database A including ca. 12,000 protein-ligand complexes with ca. 22,000 HBs and their geometries, and database B including ca. 400 protein-ligand complexes with ca. 2200 HBs, their geometries, and bond strengths determined via our local vibrational mode analysis. We identified seven major HB patterns, which can be utilized as a de novo QSAR model to predict the binding affinity for a specific protein-ligand complex. Glycine was reported as the most abundant amino acid residue in both donor and acceptor profiles, and N-H⋯O was the most frequent HB type found in database A. HBs were preferred to be in the linear range, and linear HBs were identified as the strongest. HBs with HB angles in the range of 100-110°, typically forming intramolecular five-membered ring structures, showed good hydrophobic properties and membrane permeability. Utilizing database B, we found a generalized Badger's relationship for more than 2200 protein-ligand HBs. In addition, the strength and occurrence maps between each amino acid residue and ligand functional groups open an attractive possibility for a novel drug-design approach and for determining drug selectivity and affinity, and they can also serve as an important tool for the hit-to-lead process.

Theoretical analysis of mode evolution in a tapered double clad fiber based on the coupled local mode theory

Mode characteristics of a tapered double clad fiber should be analyzed based on three-layer waveguide model, so it is more complicated than that of a single clad fiber. In this paper, a method based on coupled local mode theory is introduced to calculate the mode evolution process in a tapered double clad fiber. Mode field characteristics of double clad fiber are calculated analytically with weak guidance approximation, and the expression of mode coupling coefficient is derived. Based on this, the local mode characteristics and mode coupling characteristics in a tapered double clad fiber are analyzed. The mode evolution characteristics of tapered double clad fibers with different parameters are simulated. As an example, the structure optimization process of a tapered double clad fiber is introduced. High efficiency coupling with a six-mode single clad fiber is realized, and the theoretical transmission loss is less than 0.3 dB.

On the nature of inter-anion coinage bonds.

To explore the binding energy profiles and elucidate the bonding nature in counter-intuitive anion⋯anion coinage bonds (CiBs), thirty-one complexes were constructed, and the inter-anion CiBs were studied theoretically. The metastability was evidenced by the characteristic potential wells in six cases, demonstrating that anions [Au(CN)4]-, [Ag(CN)2]- and [AuO]- are appropriate building blocks for CiBs. The kinetic stability was further supported by ab initio molecular dynamics (AIMD) simulations and the analyses based on the local vibrational mode and quantum theory of atoms in molecules (QTAIM) methods. The anion⋯anion CiBs in the dimers of [AuCl4]- and [Au(CN)4]- previously observed in condensed phases were confirmed to be thoroughly repulsive under vacuum, but turned attractive in the crystal environment which was simulated using the solvation model based on density (SMD). However, the intrinsic strength of the inter-anion bonding is barely variated by the environment, as it is the combination of the inter-anion interaction and the environment effect that stabilizes the anion pairs. The block-localized wavefunction (BLW) method and its corresponding energy decomposition (BLW-ED) approach were further employed aiming at a chemically meaningful explanation for these counterintuitive phenomena. By inspecting the profiles of energy components, we identified the vital distinction between inter-anion CiBs and conventional non-covalent interactions lying in the electrostatic interaction, which variates nonmonotonically in the inter-anion complexes. The electrostatic interaction also dominates the depth of potential wells, which is commonly used to evaluate the kinetic stability, while Pauli exchange repulsion is the most repulsive factor preventing the formation of anion adducts. The importance of the Pauli exchange repulsion was further highlighted by comparing cases with and without metastability, in which the absence of a potential well is solely caused by the enhancement of the Pauli exchange repulsion.

Dihydrogen Bonding—Seen through the Eyes of Vibrational Spectroscopy

In this work, we analyzed five groups of different dihydrogen bonding interactions and hydrogen clusters with an H3+ kernel utilizing the local vibrational mode theory, developed by our group, complemented with the Quantum Theory of Atoms-in-Molecules analysis to assess the strength and nature of the dihydrogen bonds in these systems. We could show that the intrinsic strength of the dihydrogen bonds investigated is primarily related to the protonic bond as opposed to the hydridic bond; thus, this should be the region of focus when designing dihydrogen bonded complexes with a particular strength. We could also show that the popular discussion of the blue/red shifts of dihydrogen bonding based on the normal mode frequencies is hampered from mode-mode coupling and that a blue/red shift discussion based on local mode frequencies is more meaningful. Based on the bond analysis of the H3+(H2)n systems, we conclude that the bond strength in these crystal-like structures makes them interesting for potential hydrogen storage applications.

Weak and strong π interactions between two monomers—assessed with local vibrational mode theory

We introduce in this work a unique parameter for the quantitative assessment of the intrinsic strength of the π interaction between two monomers forming a complex. The new parameter is a local intermonomer stretching force constant, based on the local mode theory, originally developed by Konkoli and Cremer, and derived from the set of nine possible intermonomer normal vibrational modes. The new local force constant was applied to a diverse set of more than 70 molecular complexes, which was divided into four groups. Group 1 includes atoms, ions, and small molecules interacting with benzene and substituted benzenes. Group 2 includes transition metal hydrides and oxides interacting with benzene while Group 3 involves ferrocenes, chromocenes, and titanium sandwich compounds. Group 4 presents an extension to oxygen π–hole interactions in comparison with in-plane hydrogen bonding. We found that the strength of the π interactions in these diverse molecular complexes can vary from weak interactions with predominantly electrostatic character, found, e.g., for argon–benzene complexes, to strong interactions with a substantial covalent nature, found, e.g., for ferrocenes; all being seamlessly described and compared with the new intermonomer local mode force constant, which also outperforms other descriptors such as an averaged force constant or a force constant guided by the electron density bond paths. We hope that our findings will inspire the community to apply the new parameter also to other intermonomer π interactions, enriching in this way the broad field of organometallic chemistry with a new efficient assessment tool.

The Local Vibrational Mode Theory and Its Place in the Vibrational Spectroscopy Arena

This Feature Article starts highlighting some recent experimental and theoretical advances in the field of IR and Raman spectroscopy, giving a taste of the breadth and dynamics of this striving field. The local mode theory is then reviewed, showing how local vibrational modes are derived from fundamental normal modes. New features are introduced that add to current theoretical efforts: (i) a unique measure of bond strength based on local mode force constants ranging from bonding in single molecules in different environments to bonding in periodic systems and crystals and (ii) a new way to interpret vibrational spectra by pinpointing and probing interactions between particular bond stretching contributions to the normal modes. All of this represents a means to work around the very nature of normal modes, namely that the vibrational motions in polyatomic molecules are delocalized. Three current focus points of the local mode analysis are reported, demonstrating how the local mode analysis extracts important information hidden in vibrational spectroscopy data supporting current experiments: (i) metal-ligand bonding in heme proteins, such as myoglobin and neuroglobin; (ii) disentanglement of DNA normal modes; and (iii) hydrogen bonding in water clusters and ice. Finally, the use of the local mode analysis by other research groups is summarized. Our vision is that in the future local mode analysis will be routinely applied by the community and that this Feature Article serves as an incubator for future collaborations between experiment and theory.

Featuring a new computational protocol for the estimation of intensity and overall quantum yield in lanthanide chelates with applications to Eu(III) mercapto-triazole Schiff base ligands

Computational studies on luminescent properties of lanthanides chelates are important for the pre-synthetic design of new luminescent materials. However, the development of suited computational methods and protocols is still in its infancy. Here we present a new computational protocol for a systematic description and analysis of luminescent properties of Ln(III) chelates. The new methodologies herein presented are divided in three major categories: (1) Utilization of local vibrational mode theory for obtaining local Ln–ligand force constants; (2) Calculation of ligand effective polarizabilities through complex localized molecular orbitals; and (3) Extended formulation of excited state donor–acceptor RL distances accounting for excited molecular orbitals weights. The protocol was applied to understand the underlying photophysical processes in two Eu(III) complexes with mercapto-triazole Schiff bases as main ligands, utilizing time-dependent density functional theory (ωB97X-D/MWB52(Eu)/Def2-TZVP). The introduction of local force constants into lanthanide spectroscopy led to a unique explanation of the inverse relationship between the Ln–ligand strength and ligand effective polarizability. This new protocol will contribute to a better understanding of Ln–ligand bond properties, to more accurate results in terms of Judd–Ofelt intensity parameters and overall quantum yield, and will bridge the current gap between available theoretical results and experimental data.

Bonding in nitrile photo-dissociating ruthenium drug candidates-A local vibrational mode study.

In this work, we investigated bonding features of 15 ruthenium(II) nitrile complexes of the type [Ru(tpy)(L)-(CH3CN)]n+, containing the tridentate tpy ligand (tpy = 2,2':6',2″-terpyridine) and various bidentate ancillary ligands L; 12 compounds originally synthesized by Loftus et al. [J. Phys. Chem. C 123, 10291-10299 (2019)] and three new complexes. We utilized local vibrational force constants derived from the local mode theory as a quantitative measure of bond strength complemented with the topological analysis of the electron density and the natural bond orbital analysis. Loftus et al. suggested that nitrile dissociation occurs after light induced singlet-triplet transition of the original complexes and they used as a measure of nitrile release efficiency quantum yields for ligand exchange in water. They observed larger quantum yields for complexes with smaller singlet-triplet energy gaps. The major goal of this work was to assess how the Ru-NC and Ru-L bond strengths in these 15 compounds relate to and explain the experimental data of Loftus et al., particularly focusing on the question whether there is a direct correlation between Ru-NC bond strength and measured quantum yield. Our study provides the interesting result that the compounds with the highest quantum yields also have the strongest Ru-NC bonds suggesting that breaking the Ru-NC bond is not the driving force for the delivery process rather than the change of the metal framework as revealed by first results of a unified reaction valley approach investigation of the mechanism. Compounds with the highest quantum yield show larger electronic structure changes upon singlet-triplet excitation, i.e., larger changes in bond strength, covalency, and difference between the singlet and triplet HOMOs, with exception of the compound 12. In summary, this work provides new insights into the interplay of local properties and experimental quantum yields forming in synergy a useful tool for fine tuning of existing and future design of new nitrile releasing ruthenium compounds. We hope that this work will bring theoretical and experimental studies closer together and serves as an incubator for future collaboration between computational chemists and their experimental colleagues.

Theoretical insights into the linear relationship between [formula omitted] values and vibrational frequencies

A linear relationship between pKa values and vibrational frequencies has been derived in this work for hydrogen halides based on a statistical thermodynamic ansatz and successfully tested for a set of 24 aliphatic carboxylic acids, with predicted pKa values differing from measured values by less than 0.3 pKa units. Our work opens the door to reliably predicting pKa values for families of compounds often difficult to measure and paves the way for a natural extension of the derived relationship referring to local vibrational mode theory to treat systems with more delocalized A-H stretching vibrations, such as nitroacetic acid.

Theoretical analysis of mode evolution in an adiabatically tapered multimode fiber by coupled local mode theory

Analyzing the mode evolution characteristics of light in a tapered multimode fiber is an important research topic for multimode fibers. In this paper, an analytical method based on coupled local mode theory is introduced, which can analyze adiabatically tapered multimode fiber with different taper parameters. Compared with traditional beam propagation methods, the coupled local mode theory can greatly improve the calculation efficiency and directly reflect the mode evolution process. Therefore, it has important application prospects in the optimal design of tapered fibers. Based on the coupled local mode theory, the multimode fibers with different taper shapes are simulated, and the optimal design of tapered fibers is carried out from the perspective of fundamental mode conservation ability. In theory, the proportion of LP01 mode in output energy can account for more than 99.9%.

LModeA-nano: A PyMOL Plugin for Calculating Bond Strength in Solids, Surfaces, and Molecules via Local Vibrational Mode Analysis.

The analysis of chemical bonding in crystal structures and surfaces is an important research topic in theoretical chemistry. In this work, we present a PyMOL plugin, named LModeA-nano, as implementation of the local vibrational mode theory for periodic systems (Tao et al. J. Chem. Theory Comput. 2019, 15, 1761) assessing bond strength in terms of local stretching force constants in extended systems of one, two, and three dimensions. LModeA-nano can also analyze chemical bonds in isolated molecular systems thus enabling a head-to-head comparison of bond strength across systems with different dimensions in periodicity (0-3D). The new code is interfaced to the output generated by various solid-state modeling packages including VASP, CP2K, Quantum ESPRESSO, CASTEP, and CRYSTAL. LModeA-nano is cross-platform, open-source and freely available on GitHub: https://github.com/smutao/LModeA-nano.

Analysis of spectator chemical bonds in SN2@C and @Si reaction mechanisms in the gas phase

In this work, Cl−+AR3Cl reactions (with A = C and Si, and R = H, Me, Et, Cl, and F) were investigated to evaluate the A–R spectator bond properties at the ω-B97X-D/SPK-TZP level of theory, applying the Quantum Theory of Atoms in Molecules, the Overlap Model, and Local Vibrational Mode theory. The different chemical bond analyses converge to the conclusion (in line with current literature) that the steric hindrance experienced by Cl− in SN2@C reactions can be viewed as a consequence of the greater covalent nature of CR bonds that concentrate density in bond region more efficiently than SiR.

Adiabatic guided wave optics - a toolbox of generalized design and optimization methods.

Starting from the fully vectorial coupled local-mode theory, a general design rule for adiabatic waveguide design is derived. The design rule guarantees adiabaticity and puts an upper limit on the transmission loss of any guided wave transformation. The rule is applicable to any waveguide geometry, admits multi-dimensional optimization, and accounts for radiative loss to guided and radiation modes. Moreover, the design technique is enhanced with further optimization procedures that eliminate coupling between particular pairs of modes. The utility of this toolbox of design rules and methods is illustrated through the design of a 2×2 coupler and a bilayer waveguide transition. These design procedures can be used to optimize single-mode and multimode photonic devices by varying one or more waveguide parameters.

Mode-Selective Transmission Line—Part II: Excitation Scheme and Experimental Verification

In Part I of this two-part work, we have presented the theoretical foundation and physical mechanism of the mode-selective transmission line (MSTL). This part is devoted to its excitation scheme, practical transition design, and experimental verification. The MSTL excitation is first explained by comparison with a conductor-backed coplanar waveguide (CBCPW). To produce the specific mode excitation, an ultrabroadband transition between CBCPW and MSTL is proposed. It has a tapered structure operating as a tapered-mode coupler, which supports smooth evolution from the fixed CPW mode of CBCPW to the frequency-dependent dominant mode of MSTL. This modal evolution along the transition is analytically treated based on a local normal mode theory. Couplings between the local normal modes are negligible as a result of gradual tapering, thereby effectively suppressing higher order modes in MSTL and sustaining a mode purity over an ultrabroad frequency range. For experimental demonstration purposes, back-to-back CBCPW-to-MSTL transition circuits are physically realized. The measured results are in agreement with the prediction, showing a return loss of 15 dB from 3 to 109 GHz; the single transition introduces a relatively low insertion loss of 1.84 dB at 100 GHz. The propagation characteristics of MSTL are also extracted from the measured S-parameters, which provides an excellent validation of the proposed structure.

Equilibrium Geometries, Adiabatic Excitation Energies and Intrinsic C=C/C–H Bond Strengths of Ethylene in Lowest Singlet Excited States Described by TDDFT

Seventeen singlet excited states of ethylene have been calculated via time-dependent density functional theory (TDDFT) with the CAM-B3LYP functional and the geometries of 11 excited states were optimized successfully. The local vibrational mode theory was employed to examine the intrinsic C=C/C–H bond strengths and their change upon excitation. The natural transition orbital (NTO) analysis was used to further analyze the C=C/C–H bond strength change in excited states versus the ground state. For the first time, three excited states including πy′ → 3s, πy′ → 3py and πy′ → 3pz were identified with stronger C=C ethylene double bonds than in the ground state.

Local Vibrational Mode Analysis of π–Hole Interactions between Aryl Donors and Small Molecule Acceptors

11 aryl–lone pair and three aryl–anion π –hole interactions are investigated, along with the argon–benzene dimer and water dimer as reference compounds, utilizing the local vibrational mode theory, originally introduced by Konkoli and Cremer, to quantify the strength of the π –hole interaction in terms of a new local vibrational mode stretching force constant between the two engaged monomers, which can be conveniently used to compare different π –hole systems. Several factors have emerged which influence strength of the π –hole interactions, including aryl substituent effects, the chemical nature of atoms composing the aryl rings/ π –hole acceptors, and secondary bonding interactions between donors/acceptors. Substituent effects indirectly affect the π –hole interaction strength, where electronegative aryl-substituents moderately increase π –hole interaction strength. N-aryl members significantly increase π –hole interaction strength, and anion acceptors bind more strongly with the π –hole compared to charge neutral acceptors (lone–pair donors). Secondary bonding interactions between the acceptor and the atoms in the aryl ring can increase π –hole interaction strength, while hydrogen bonding between the π –hole acceptor/donor can significantly increase or decrease strength of the π –hole interaction depending on the directionality of hydrogen bond donation. Work is in progress expanding this research on aryl π –hole interactions to a large number of systems, including halides, CO, and OCH3− as acceptors, in order to derive a general design protocol for new members of this interesting class of compounds.