Energy decomposition analysis in an adiabatic picture

Completely Multipolar Model as a General Framework for Many-Body Interactions as Illustrated for Water

We introduce a general framework for many-body force fields, the Completely Multipolar Model (CMM), that utilizes multipolar electrical moments modulated by exponential decay of electron density as a common functional form for all terms of an energy decomposition analysis of intermolecular interactions. With this common functional form, the CMM model establishes well-formulated damped tensors that reach the correct asymptotes at both long- and short-range while formally ensuring no short-range catastrophes. CMM describes the separable EDA terms of dispersion, exchange polarization, and Pauli repulsion with short-ranged anisotropy, polarization as intramolecular charge fluctuations and induced dipoles, while charge transfer describes explicit movement of charge between molecules, and naturally describes many-body charge transfer by coupling into the polarization equations. We also utilize a new one-body potential that accounts for intramolecular polarization by including an electric field-dependent correction to the Morse potential to ensure that CMM reproduces all physically relevant monomer properties including the dipole moment, molecular polarizability, and dipole and polarizability derivatives. The quality of CMM is illustrated through agreement of individual terms of the EDA and excellent extrapolation to energies and geometries of an extensive validation set of water cluster data.

Solvent Effect on Dative and Ionic Bond Strengths: A Unified Theory from Potential Analysis and Valence-Bond Computations

Solvent molecules interact with a solute through various intermolecular forces. Here we employed a potential energy surface (PES) analysis to interpret the solvent-induced variations in the strengths of dative (Me3NBH3) and ionic (LiCl) bonds, which possess both ionic and covalent (neutral) characteristics. The change of a bond is driven by the gradient (force) of the solvent-solute interaction energy with respect to the focused bond length. Positive force shortens the bond length and increases the bond force constant, leading to a blue-shift of the bond stretching vibrational frequency upon solvation. Conversely, negative force elongates the bond, resulting in a reduced bond force constant and red-shift of the stretching vibrational frequency. The different responses of Me3NBH3 and LiCl to solvation are studied with valence bond (VB) theory, as Me3NBH3 and LiCl are dominated by the neutral covalent VB structure and the ionic VB structure, respectively. The dipole moment of an ionic VB structure increases along the increasing bond distance, while the dipole moment of a neutral covalent VB structure increases with the decreasing bond distance. The roles of the dominating VB structures are further examined by the geometry optimizations and frequency calculations with the block-localized wavefunction (BLW) method.

Kohn-Sham fragment energy decomposition analysis

We introduce the concept of Kohn-Sham fragment localized molecular orbitals (KS-FLMOs), which are Kohn-Sham molecular orbitals (MOs) localized in specific fragments constituting a generic molecular system. In detail, we minimize the local electronic energies of various fragments, while maximizing the repulsion between them, resulting in the effective localization of the MOs. We use the developed KS-FLMOs to propose a novel energy decomposition analysis, which we name Kohn-Sham fragment energy decomposition analysis, which allows for rationalizing the main non-covalent interactions occurring in interacting systems both in vacuo and in solution, providing physical insights into non-covalent interactions. The method is validated against state-of-the-art energy decomposition analysis techniques and with high-level calculations.

Conformational Preference of Lithium Polysulfide Clusters Li2Sx (x = 4-8) in Lithium-Sulfur Batteries

Structures are of fundamental importance for diverse studies of lithium polysulfide clusters, which govern the performance of lithium-sulfur batteries. The ring-like geometries were regarded as the most stable structures, but their physical origin remains elusive. In this work, we systematically explored the minimal structures of Li2Sx (x = 4-8) clusters to uncover the driving force for their conformational preferences. All low-lying isomers were generated by performing global searches using the ABCluster program, and the ionic nature of the Li···S interactions was evidenced with the energy decomposition analysis based on the block-localized wave function (BLW-ED) approach and further confirmed with the quantum theory of atoms in molecule (QTAIM). By analysis of the contributions of various energy components to the relative stability with the references of the lowest-lying isomers, the controlling factor for isomer preferences was found to be the polarization interaction. Notably, although the electrostatic interaction dominates the binding energies, it contributes favorably to the relative stabilities of most isomers. The Li+···Li+ distance is identified as the key geometrical parameter that correlates with the strength of the polarization of the Sx2- fragment imposed by the Li+ cations. Further BLW-ED analyses reveal that the cooperativity of the Li+ cations primarily determines the relative strength of the polarization.

The iron group transition-metal (Fe, Ru, Os) coordination of Se-doped graphitic carbon (Se@g-C3N4) nanostructures for the smart therapeutic delivery of zidovudine (ZVD) as an antiretroviral drug: a theoretical calculation perspective

This study employed density functional theory (DFT) computational techniques at the ωB97XD/def2svp level of theory to comprehensively explore the electronic behavior of Fe-group transition metal (Fe, Ru, Os) coordination of Se-doped graphitic carbon (Se@g-C3N4) nanosystems in the smart delivery of zidovudine (ZVD), an antiretroviral drug. The HOMO-LUMO results of the interactions show a general reduction in energy gap values across all complexes in the following order: ZVD_Se@C3N4 < ZVD_Ru_Se@C3N4 < ZVD_Fe_Se@C3N4 < ZVD_Os_Se@C3N4. ZVD_Se@C3N4 exhibits the smallest post-interaction band gap of 3.783 eV, while ZVD_Os_Se@C3N4 presents the highest energy band gap of 5.438 eV. Results from the corrected adsorption energy (BSSE) revealed that Os_Se@C3N4 and Ru_Se@C3N4 demonstrated more negative adsorption energies of -2.67 and -2.701 eV, respectively, pointing to a more favorable interaction between ZVD and these systems, thus potentially enhancing the drug delivery efficiency. The investigation into the drug release mechanism from the adsorbents involved a comprehensive examination of the dipole moment and the influence of pH, shedding light on the controlled release of ZVD. Additionally, investigating the energy decomposition analysis (EDA) revealed that ZVD_Ru_Se@C3N4 and ZVD_Fe_Se@C3N4 exhibited the same total energy of -787.7 kJ mol-1. This intriguing similarity in their total energy levels suggested that their stability was governed by factors beyond reactivity, possibly due to intricate orbital interactions. Furthermore, analyzing the bond dissociation energies showed that all systems exhibited negative enthalpy values, indicating that these systems were exothermic at both surface and interaction levels, thus suggesting that these processes emitted heat, contributing to the surrounding thermal energy.

Computational Studies of Rubber Ozonation Explain the Effectiveness of 6PPD as an Antidegradant and the Mechanism of Its Quinone Formation

The discovery that the commercial rubber antidegradant 6PPD reacts with ozone (O₃) to produce a highly toxic quinone (6PPDQ) spurred a significant research effort into nontoxic alternatives. This work has been hampered by lack of a detailed understanding of the mechanism of protection that 6PPD affords rubber compounds against ozone. Herein, we report high-level density functional theory studies into early steps of rubber and PPD (p-phenylenediamine) ozonation, identifying key steps that contribute to the antiozonant activity of PPDs. In this, we establish that our density functional theory approach can achieve chemical accuracy for many ozonation reactions, which are notoriously difficult to model. Using adiabatic energy decomposition analysis, we examine and dispel the notion that one-electron charge transfer initiates ozonation in these systems, as is sometimes argued. Instead, we find direct interaction between O₃ and the PPD aromatic ring is kinetically accessible and that this motif is more significant than interactions with PPD nitrogens. The former pathway results in a hydroxylated PPD intermediate, which reacts further with O₃ to afford 6PPD hydroquinone and, ultimately, 6PPDQ. This mechanism directly links the toxicity of 6PPDQ to the antiozonant function of 6PPD. These results have significant implications for development of alternative antiozonants, which are discussed.

Force Decomposition Analysis: A Method to Decompose Intermolecular Forces into Physically Relevant Component Contributions

Computational quantum chemistry can be more than just numerical experiments when methods are specifically adapted to investigate chemical concepts. One important example is the development of energy decomposition analysis (EDA) to reveal the physical driving forces behind intermolecular interactions. In EDA, typically the interaction energy from a good-quality density functional theory (DFT) calculation is decomposed into multiple additive components that unveil permanent and induced electrostatics, Pauli repulsion, dispersion, and charge-transfer contributions to noncovalent interactions. Herein, we formulate, implement, and investigate decomposing the forces associated with intermolecular interactions into the same components. The resulting force decomposition analysis (FDA) is potentially useful as a complement to the EDA to understand chemistry, while also providing far more information than an EDA for data analysis purposes such as training physics-based force fields. We apply the FDA based on absolutely localized molecular orbitals (ALMOs) to analyze interactions of water with sodium and chloride ions as well as in the water dimer. We also analyze the forces responsible for geometric changes in carbon dioxide upon adsorption onto (and activation by) gold and silver anions. We also investigate how the force components of an EDA-based force field for water clusters, namely MB-UCB, compare to those from force decomposition analysis.

Generalization of ETS-NOCV and ALMO-COVP Energy Decomposition Analysis to Connect Any Two Electronic States and Comparative Assessment

Energy decomposition analysis (EDA) is a useful tool for obtaining chemically meaningful insights into molecular interactions. The extended transition-state method with natural orbitals for chemical valence (ETS-NOCV) and the absolutely localized molecular orbital-based method with complementary occupied-virtual pairs (ALMO-COVP) are two successful EDA schemes. Working within ground-state generalized Kohn-Sham density functional theory (DFT), we extend these methods to perform EDA between any two electronic states that can be connected by a unitary transformation of density matrices. A direct proof that the NOCV eigenvalues are symmetric pairs is given, and we also prove that the charge and energy difference defined by ALMO are invariant under certain orbital rotations, allowing us to define COVPs. We point out that ETS is actually a 1-point quadrature to obtain the effective Fock matrix, and though it is reasonably accurate, it can be systematically further improved by adding more quadrature points. We explain why the calculated amount of transferred charge measured by ALMO-COVP is typically much smaller than that of ETS-NOCV and explain why the ALMO-COVP values should be preferred. While the two schemes are independent, ETS-NOCV and ALMO-COVP in fact give a very similar chemical picture for a variety of chemical interactions, including H-H⁺, the transition structure for the Diels-Alder reaction between ethene and butadiene, and two hydrogen-bonded complexes, H₂O···F^- and H₂O···HF.

Hydrogen Bonding versus Halogen Bonding: Spectroscopic Investigation of Gas-Phase Complexes Involving Bromide and Chloromethanes

Hydrogen bonding and halogen bonding are important non-covalent interactions that are known to occur in large molecular systems, such as in proteins and crystal structures. Although these interactions are important on a large scale, studying hydrogen and halogen bonding in small, gas-phase chemical species allows for the binding strengths to be determined and compared at a fundamental level. In this study, anion photoelectron spectra are presented for the gas-phase complexes involving bromide and the four chloromethanes, CH₃ Cl, CH₂ Cl₂ , CHCl₃ , and CCl₄ . The stabilisation energy and electron binding energy associated with each complex are determined experimentally, and the spectra are rationalised by high-level CCSD(T) calculations to determine the non-covalent interactions binding the complexes. These calculations involve nucleophilic bromide and electrophilic bromine interactions with chloromethanes, where the binding motifs, dissociation energies and vertical detachment energies are compared in terms of hydrogen bonding and halogen bonding.

Computational Investigation of Substituent Effects on the Fluorescence Wavelengths of Oxyluciferin Analogs

Oxyluciferin, which is the light emitter for firefly bioluminescence, has been subjected to extensive chemical modifications to tune its emission wavelength and quantum yield. However, the exact mechanisms for various electron-donating and withdrawing groups to perturb the photophysical properties of oxyluciferin analogs are still not fully understood. To elucidate the substituent effects on the fluorescence wavelength of oxyluciferin analogs, we applied the absolutely localized molecular orbitals (ALMO)-based frontier orbital analysis to assess various types of interactions (i.e. permanent electrostatics/exchange repulsion, polarization, occupied-occupied orbital mixing, virtual-virtual orbital mixing, and charge-transfer) between the oxyluciferin and substituent orbitals. We suggested two distinct mechanisms that can lead to red-shifted oxyluciferin emission wavelength, a design objective that can help increase the tissue penetration of bioluminescence emission. Within the first mechanism, an electron-donating group (such as an amino or dimethylamino group) can contribute its highest occupied molecular orbital (HOMO) to an out-of-phase combination with oxyluciferin's HOMO, thus raising the HOMO energy of the substituted analog and narrowing its HOMO-LUMO gap. Alternatively, an electron-withdrawing group (such as a nitro or cyano group) can participate in an in-phase virtual-virtual orbital mixing of fragment LUMOs, thus lowering the LUMO energy of the substituted analog. Such an ALMO-based frontier orbital analysis is expected to lead to intuitive principles for designing analogs of not only the oxyluciferin molecule, but also many other functional dyes.

Cycloaddition Reactivities Analyzed by Energy Decomposition Analyses and the Frontier Molecular Orbital Model

This Account describes our quest to understand and predict organic reactivity, a principal goal of physical and theoretical organic chemistry. The focus is on the development and testing of models for the prediction of cycloaddition reactivities and selectivities. We describe the involvement of the Houk group, and other groups, in the evolution of theoretical models that can achieve ever greater accuracy as well as provide practical heuristic models for understanding and prediction.Is the venerable frontier molecular orbital (FMO) model, the basis of Kenichi Fukui's 1981 Nobel Prize, still useful, or must it be replaced with more advanced models? In particular, models such as Conceptual Density Functional, the Pauli Exclusion Model, and the recent popularity of Electrostatic Potential Plots and Dispersion Energies have not only added to our understanding, but they have also created uncertainty about whether the simple FMO heuristic model has a place in 21st century discussions. This Account addresses this issue and asserts the value of the FMO model.Beginning with brief descriptions of selected models for cycloaddition reactivity starting with early donor-acceptor (nucleophile-electrophile) charge-transfer concepts, this Account reviews Fukui's frontier molecular orbital model, Salem and Klopman's orbital, electrostatic and Pauli repulsion model, the conceptual DFT model by Parr and later by Domingo and others, the recent Houk and Bickelhaupt Distortion/Interaction Activation Strain model, and the Bickelhaupt-Hamlin's Pauli-repulsion lowering model.Computations and analyses of four well-studied Diels-Alder cycloadditions, both normal and inverse electron-demand types, are presented. Most were studied earlier in our published work but are presented here with new insights from calculations with modern methods. Depending on the types of substrates (cycloaddends), the dominant factors controlling reactivity can be orbital interactions, electrostatics and polarization, or Pauli repulsion and dispersion effects, or a combination of all of these.By comparing orbital interactions, especially the frontier molecular orbital interactions, with the other factors that influence reactivity, we show why the FMO model is such a powerful─and theoretically meaningful─heuristic for understanding and predicting reactivity. We also present a method to understand Pauli repulsion effects on activation barriers, ρ(1.1). The use of a new reaction coordinate, the extent of Pauli repulsion along the reaction path, is advocated to emphasize the role of repulsive occupied orbital interactions on reactivity.Fukui's frontier molecular orbital model is effective because FMO interactions parallel all the quantities that influence reactivity. The FMO model continues to provide a practical model to understand and guide experiments.

Revisiting the Bonding Model for Gold(I) Species: The Importance of Pauli Repulsion Revealed in a Gold(I)-Cyclobutadiene Complex

Understanding the bonding of gold(I) species has been central to the development of gold(I) catalysis. Herein, we present the synthesis and characterization of the first gold(I)-cyclobutadiene complex, accompanied with bonding analysis by state-of-the-art energy decomposition analysis methods. Analysis of possible coordination modes for the new species not only confirms established characteristics of gold(I) bonding, but also suggests that Pauli repulsion is a key yet hitherto overlooked element. Additionally, we obtain a new perspective on gold(I)-bonding by comparison of the gold(I)-cyclobutadiene to congeners stabilized by p-, d-, and f-block metals. Consequently, we refine the gold(I) bonding model, with a delicate interplay of Pauli repulsion and charge transfer as the key driving force for various coordination motifs. Pauli repulsion is similarly determined as a significant interaction in AuI -alkyne species, corroborating this revised understanding of AuI bonding.

Can Brønsted Photobases Act as Lewis Photobases?

Dative bonding or Lewis acid-base chemistry underpins a large number of chemical phenomena in a variety of fields, such as catalysis, metal-ligand interactions, and surface chemistry. Developing light-controlled Lewis acid-base interactions could offer a new way of controlling and understanding such phenomena. Photoinduced proton transfer, that is, excited-state Brønsted acidity and basicity, has been extensively studied and applied. Here, in direct analogy to excited-state Brønsted basicity, we show that exciting a photobasic molecule with light generates a thermodynamic drive for the transfer of a Lewis acid from a donor to a photobasic molecule. We have used the archetypal BF₃ as our Lewis acid and our photoactive Lewis bases are a family of quinolines, which are known Brønsted photobases as well. We have constructed the experimental Förster cycle for this system and have verified it computationally to demonstrate that a significant drive (0.2-0.7 eV) exists for the transfer of BF₃ to a photoexcited quinoline. The magnitude of this drive is similar to those reported for Brønsted photobasicity in quinolines. Computational results from TDDFT and energy decomposition analysis show that the origin of such an effect is similar to the Brønsted photoactivity of these molecules, in that they follow the Hammett parameter of substituent groups. These results suggest that photobases may be capable of controlling the chemical phenomena beyond proton transfer and may open opportunities for a new handle in photocatalysis.

Dissociation of HCl in water nanoclusters: an energy decomposition analysis perspective

As known, small HCl-water nanoclusters display a particular dissociation behaviour, whereby at least four water molecules are required for the ionic dissociation of HCl. In this work, we examine how intermolecular interactions promote the ionic dissociation of such nanoclusters. To this end, a set of 45 HCl-water nanoclusters with up to four water molecules is introduced. Energy decomposition analysis based on absolutely localized molecular orbitals (ALMO-EDA) is employed in order to study the importance of frozen interaction, dispersion, polarization, and charge-transfer for the dissociation. The vertical ALMO-EDA scheme is applied to HCl-water clusters along a proton-transfer coordinate varying the amount of spectator water molecules. The corresponding ALMO-EDA results show a clear preference for the dissociated cluster only in the presence of four water molecules. Our analysis of adiabatic ALMO-EDA results reveals a push-pull mechanism for the destabilization of the HCl bond based on the synergy between forward and backward charge-transfer.

Characterization of cisplatin/membrane interactions by QM/MM energy decomposition analysis

We extend for the first time a quantum mechanical energy decomposition analysis scheme based on deformation electron densities to a hybrid electrostatic embedding quantum mechanics/molecular mechanics framework. The implemented approach is applied to characterize the interactions between cisplatin and a dioleyl-phosphatidylcholine membrane, which play a key role in the permeation mechanism of the drug inside the cells. The interaction energy decomposition into electrostatic, induction, dispersion and Pauli repulsion contributions is performed for ensembles of geometries to account for conformational sampling. It is evidenced that the electrostatic and repulsive components are predominant in both polar and non-polar regions of the bilayer.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Determinant Factors of Three-Dimensional Aromaticity in Antiaromatic Cyclophanes

Three-dimensional aromaticity arising from the close stacking of two antiaromatic π-conjugated macrocycles has recently received considerable attention. Here, a cyclophane consisting of two antiaromatic Ni(II) norcorrole units tethered with two flexible alkyl chains was synthesized. The norcorrole cyclophane showed crystal polymorphism providing three different solid-state structures. Surprisingly, one of them adopted an aligned face-to-face stacking arrangement with negligible displacement along the slipping axis. Although the exchange repulsion between two π-clouds should be maximized in this orientation, the π-π distance is remarkably close (3.258 Å). Three-dimensional aromaticity in this conformation has been supported experimentally and theoretically as evidenced by small bond length alternations as well as the presence of a diatropic ring current. An analogous cyclophane with two aromatic Ni(II) porphyrin units was prepared for comparison. The porphyrin cyclophane exhibited a slipped-stacking conformation with a larger displacement (2.9 Å) and a larger interplanar distance (3.402 Å) without noticeable change of the aromaticity of each porphyrin unit. In solution, the norcorrole cyclophane forms a twist stacking arrangement with effective interplanar orbital overlap and exists in an equilibrium between stacked and nonstacked structures. Thermodynamic parameters of the stacking process were estimated, revealing an inherently large attractive interaction operating between two norcorrole units, which has been further supported by energy decomposition analysis.

Quantifying Frustrations for Molecular Complexes with Noncovalent Interactions

Molecular systems bound together through noncovalent interactions are involved in a lot of life-essential processes such as molecular recognition, signal transduction, and allosteric regulation. While cooperation as an important effect discovered in these systems focuses on the behavior of system's entirety, we need also examine the behavior of individual parts. In this work, using the distortion energy as the descriptor, we quantify frustration as the energetic loss of individual parts due to the formation of nonadditive molecular complexes. The applicability of our approach has been illustrated by a few simple clusters. Our results show that the frustration effect is smaller than the cooperation effect, but same as cooperativity, it can be both positive and negative. The ultimate benefit of a system made of multiple parts is dictated by the balance between the cooperative behavior among parts and the sacrifice from its individuals. This conflicting yet complementary conceptual pair of cooperation and frustration provides us with a different perspective from the systems' viewpoint for molecular complexes. This new angle of appreciating molecular complexes can be applied in conformational changes, enzymatic catalysis, and many more.

Elucidating the Electronic Structure of a Delayed Fluorescence Emitter via Orbital Interactions, Excitation Energy Components, Charge-Transfer Numbers, and Vibrational Reorganization Energies

Recently, Wang and co-workers carried out frontier molecule orbital engineering in the design of m-Cz-BNCz, a thermally activated delayed fluorescence (TADF) molecule that emits pure green light at an external quantum efficiency of 27%. To further understand the underlying molecular design principles, we employed four advanced electronic structure analysis tools. First, an absolutely localized molecular orbitals (ALMO-) based analysis indicates an antibonding combination between the highest occupied molecular orbitals (HOMOs) of the donor 3,6-di-tert-butylcarbazole fragment and the acceptor BNCz fragment, which raises the HOMO energy and red-shifts the fluorescence emission wavelength. Second, excitation energy component analysis reveals that the S₁-T₁ gap is dominated by two-electron components of the excitation energies. Third, charge transfer number analysis, which is extended to use fragment-based Hirshfeld weights, indicates that the S₁ and T₁ excited states of m-Cz-BNCz (within time-dependent density functional theory) have notable charge transfer characters (27% for S₁ and 12% for T₁). This provides a balance between a small single-triplet gap and a substantial fluorescence intensity. Last, a vibrational reorganization energy analysis pinpoints the torsional motion between the BNCz and Cz moieties of m-Cz-BNCz as the source for its wider emission peak than that of p-Cz-BNCz. These four types of analyses are expected to be very valuable in the study and design of other TADF and functional dye molecules.

From Intermolecular Interaction Energies and Observable Shifts to Component Contributions and Back Again: A Tale of Variational Energy Decomposition Analysis

Quantum chemistry in the form of density functional theory (DFT) calculations is a powerful numerical experiment for predicting intermolecular interaction energies. However, no chemical insight is gained in this way beyond predictions of observables. Energy decomposition analysis (EDA) can quantitatively bridge this gap by providing values for the chemical drivers of the interactions, such as permanent electrostatics, Pauli repulsion, dispersion, and charge transfer. These energetic contributions are identified by performing DFT calculations with constraints that disable components of the interaction. This review describes the second-generation version of the absolutely localized molecular orbital EDA (ALMO-EDA-II). The effects of different physical contributions on changes in observables such as structure and vibrational frequencies upon complex formation are characterized via the adiabatic EDA. Example applications include red- versus blue-shifting hydrogen bonds; the bonding and frequency shifts of CO, N₂, and BF bound to a [Ru(II)(NH₃)₅]^{2 +} moiety; and the nature of the strongly bound complexes between pyridine and the benzene and naphthalene radical cations. Additionally, the use of ALMO-EDA-II to benchmark and guide the development of advanced force fields for molecular simulation is illustrated with the recent, very promising, MB-UCB potential.

A non-perturbative pairwise-additive analysis of charge transfer contributions to intermolecular interaction energies

A non-perturbative scheme for complete decomposition of energy and charge associated with charge transfer interaction into pairwise additive components.

Consistent inclusion of continuum solvation in energy decomposition analysis: theory and application to molecular CO2 reduction catalysts

To facilitate computational investigation of intermolecular interactions in the solution phase, we report the development of ALMO-EDA(solv), a scheme that allows the application of continuum solvent models within the framework of energy decomposition analysis (EDA) based on absolutely localized molecular orbitals (ALMOs). In this scheme, all the quantum mechanical states involved in the variational EDA procedure are computed with the presence of solvent environment so that solvation effects are incorporated in the evaluation of all its energy components. After validation on several model complexes, we employ ALMO-EDA(solv) to investigate substituent effects on two classes of complexes that are related to molecular CO2 reduction catalysis. For [FeTPP(CO2-κC)]2- (TPP = tetraphenylporphyrin), we reveal that two ortho substituents which yield most favorable CO2 binding, -N(CH3)3 + (TMA) and -OH, stabilize the complex via through-structure and through-space mechanisms, respectively. The coulombic interaction between the positively charged TMA group and activated CO2 is found to be largely attenuated by the polar solvent. Furthermore, we also provide computational support for the design strategy of utilizing bulky, flexible ligands to stabilize activated CO2 via long-range Coulomb interactions, which creates biomimetic solvent-inaccessible "pockets" in that electrostatics is unscreened. For the reactant and product complexes associated with the electron transfer from the p-terphenyl radical anion to CO2, we demonstrate that the double terminal substitution of p-terphenyl by electron-withdrawing groups considerably strengthens the binding in the product state while moderately weakens that in the reactant state, which are both dominated by the substituent tuning of the electrostatics component. These applications illustrate that this new extension of ALMO-EDA provides a valuable means to unravel the nature of intermolecular interactions and quantify their impacts on chemical reactivity in solution.

Catalysis on Pristine 2D Materials via Dispersion and Electrostatic Interactions

Shape complementarity between catalyst and transition state structure is one of the cornerstones of chemical catalysis. Likewise, noncovalent interactions play a major role in catalysis. It has been predicted computationally and recently confirmed experimentally [Kroeger, A. A.; Hooper, J. F.; Karton, A. ChemPhysChem, 2020, 21, 1675-1681] that pristine graphene can efficiently catalyze chemical processes via π-interactions and shape complementarity. Here we show that other two-dimensional materials with different electronic structures and chemical compositions (h-BN and graphane) can also catalyze chemical processes that proceed via planar transition state structures. These include the bowl-to-bowl inversions in corannulene and sumanene and the rotation about the C-C bond in substituted biphenyls. This catalytic activity is achieved through shape complementarity between planar nanomaterial and planar transition state structure, enabling disproportionate stabilization of the transition state structures over the nonplanar reactants and products. A DFT-based energy decomposition analysis shows that this catalytic activity is mainly driven by dispersion and electrostatic forces, which together outweigh the Pauli repulsion term. These findings enrich and expand the concept of catalysis by pristine 2D materials.

Probing radical-molecule interactions with a second generation energy decomposition analysis of DFT calculations using absolutely localized molecular orbitals

Intermolecular interactions between radicals and closed-shell molecules are ubiquitous in chemical processes, ranging from the benchtop to the atmosphere and extraterrestrial space. While energy decomposition analysis (EDA) schemes for closed-shell molecules can be generalized for studying radical-molecule interactions, they face challenges arising from the unique characteristics of the electronic structure of open-shell species. In this work, we introduce additional steps that are necessary for the proper treatment of radical-molecule interactions to our previously developed unrestricted Absolutely Localized Molecular Orbital (uALMO)-EDA based on density functional theory calculations. A "polarize-then-depolarize" (PtD) scheme is used to remove arbitrariness in the definition of the frozen wavefunction, rendering the ALMO-EDA results independent of the orientation of the unpaired electron obtained from isolated fragment calculations. The contribution of radical rehybridization to polarization energies is evaluated. It is also valuable to monitor the wavefunction stability of each intermediate state, as well as their associated spin density profiles, to ensure the EDA results correspond to a desired electronic state. These radical extensions are incorporated into the "vertical" and "adiabatic" variants of uALMO-EDA for studies of energy changes and property shifts upon complexation. The EDA is validated on two model complexes, H₂O˙F and FH˙OH. It is then applied to several chemically interesting radical-molecule complexes, including the sandwiched and T-shaped benzene dimer radical cation, complexes of pyridine with benzene and naphthalene radical cations, binary and ternary complexes of the hydroxyl radical with water (˙OH(H₂O) and ˙OH(H₂O)₂), and the pre-reactive complexes and transition states in the ˙OH + HCHO and ˙OH + CH₃CHO reactions. These examples suggest that this second generation uALMO-EDA is a useful tool for furthering one's understanding of both energetic and property changes associated with radical-molecule interactions.

Electronic structure calculations permit identification of the driving forces behind frequency shifts in transition metal monocarbonyls

Our direct DFT decomposition of CO frequency shifts updates the paradigm for metal carbonyl binding.

On generalized partition methods for interaction energies

The breakdown of interaction energy has always been a very important means to understand chemical bonding and it has become a seamlessly useful tool for modern supramolecular chemistry.

What Next for Quantum Mechanics in Structure-Based Drug Discovery?

There is significant potential for electronic structure methods to improve the quality of the predictions furnished by the tools of computer-aided drug design, which typically rely on empirically derived functions. In this perspective, we consider some recent examples of how quantum mechanics has been applied in predicting protein-ligand geometries, protein-ligand binding affinities and ligand strain on binding. We then outline several significant developments in quantum mechanics methodology likely to influence these approaches: in particular, we note the advent of more computationally expedient ab initio quantum mechanical methods that can provide chemical accuracy for larger molecular systems than hitherto possible. We highlight the emergence of increasingly accurate semiempirical quantum mechanical methods and the associated role of machine learning and molecular databases in their development. Indeed, the convergence of improved algorithms for solving and analyzing electronic structure, modern machine learning methods, and increasingly comprehensive benchmark data sets of molecular geometries and energies provides a context in which the potential of quantum mechanics will be increasingly realized in driving future developments and applications in structure-based drug discovery.

Observation of the Low-Frequency Spectrum of the Water Dimer as a Sensitive Test of the Water Dimer Potential and Dipole Moment Surfaces

Using the helium nanodroplet isolation setup at the ultrabright free-electron laser source FELIX in Nijmegen (BoHeNDI@FELIX), the intermolecular modes of water dimer in the frequency region from 70 to 550 cm^-1 were recorded. Observed bands were assigned to donor torsion, acceptor wag, acceptor twist, intermolecular stretch, donor torsion overtone, and in-plane and out-of-plane librational modes. This experimental data set provides a sensitive test for state-of-the-art water potentials and dipole moment surfaces. Theoretical calculations of the IR spectrum are presented using high-level quantum and approximate quasiclassical molecular dynamics approaches. These calculations use the full-dimensional ab initio WHHB potential and dipole moment surfaces. Based on the experimental data, a considerable increase of the acceptor switch and a bifurcation tunneling splitting in the librational mode is deduced, which is a consequence of the effective decrease in the tunneling barrier.

The Nature of Hydrogen Bonds: A Delineation of the Role of Different Energy Components on Hydrogen Bond Strengths and Lengths

Hydrogen bonds are a complex interplay between different energy components, and their nature is still subject of an ongoing debate. In this minireview, we therefore provide an overview of the different perspectives on hydrogen bonding. This will be done by discussing the following individual energy components: 1) electrostatic interactions, 2) charge-transfer interactions, 3) π-resonance assistance, 4) steric repulsion, 5) cooperative effects, 6) dispersion interactions and 7) secondary electrostatic interactions. We demonstrate how these energetic factors are essential in a correct description of the hydrogen bond, and discuss several examples of systems whose energetic and geometrical features are not captured by easy-to-use predictive models.

Three-dimensional aromaticity in an antiaromatic cyclophane

Understanding of interactions among molecules is essential to elucidate the binding of pharmaceuticals on receptors, the mechanism of protein folding and self-assembling of organic molecules. While interactions between two aromatic molecules have been examined extensively, little is known about the interactions between two antiaromatic molecules. Theoretical investigations have predicted that antiaromatic molecules should be stabilized when they stack with each other by attractive intermolecular interactions. Here, we report the synthesis of a cyclophane, in which two antiaromatic porphyrin moieties adopt a stacked face-to-face geometry with a distance shorter than the sum of the van der Waals radii of the atoms involved. The aromaticity in this cyclophane has been examined experimentally and theoretically. This cyclophane exhibits three-dimensional spatial current channels between the two subunits, which corroborates the existence of attractive interactions between two antiaromatic π-systems.

Little is known about interactions between two antiaromatic molecules. Here, the authors synthesised a cyclophane, in which two antiaromatic porphyrin moieties adopt a stacked face-to-face geometry with a distance shorter than the sum of the van der Waals radii of the atoms involved.

Probing Blue-Shifting Hydrogen Bonds with Adiabatic Energy Decomposition Analysis

The physical origin of blue-shifting hydrogen bonds remains a subject of debate, although many plausible explanations have been proposed. Using a molecular property decomposition analysis based on absolutely localized molecular orbitals, we investigated several representative F₃CH···Y (Y = H₂O, NH₃, Cl^-) complexes. We reveal that features of a blue-shifting H-bond already appear on the frozen surface where both polarization and charge transfer (CT) are "turned off", and that the final frequency shift observed depends on the strength of CT. Further decomposition of forces at the frozen level shows that Pauli repulsion is the only component that shortens the C-H bond in the short-range, while both permanent electrostatics and dispersion lengthen the bond. The effects of these forces from the medium to long-range are also discussed. Our analysis provides a complete picture for blue-shifting H-bonds and suggests two necessary conditions for their features to be observed at equilibrium structures: (i) stronger Pauli repulsion than the combination of electrostatic and dispersion forces; (ii) relatively weak CT that is insufficient to compensate for the blue-shifting effect of the frozen interaction.

Nine questions on energy decomposition analysis

The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the "natural selection" process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross-validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the "standard model" of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc.

Exciplex Organic Light-Emitting Diodes with Nearly 20% External Quantum Efficiency: Effect of Intermolecular Steric Hindrance between the Donor and Acceptor Pair

Exciplex emitters have emerged as an important class of thermally activated delayed fluorescence (TADF) materials for highly efficient OLEDs. A TADF exciplex emitter requires an intermolecular donor/acceptor pair. We have synthesized a bipolar donor-type material, DPSTPA, which was used to pair with known acceptor materials (2CzPN, 4CzIPN, or CzDBA). The OLEDs based on the exciplex emitters, DPSTPA/X, where X = 2CzPN and CzDBA, give green and orange-red colors with record-high external quantum efficiencies (EQEs) of 19.0 ± 0.6 and 14.6 ± 0.4%, respectively. In contrast, the exciplex pair DPSTPA/4CzIPN gave a very low photoluminescence quantum yield (PLQY) and a very low EQE value of the device. The DFT calculations indicate that the intermolecular distance between the donor and the acceptor plays a key factor for the PLQY and EQE. The observed low PLQY and the poor device performance for the DPSTPA/4CzIPN pair are probably because of the relatively long distance between the DPSTPA and 4CzIPN in the thin film caused by the four congested carbazole (Cz) groups of 4CzIPN, which effectively block the interaction of the nitrile acceptor with the triphenylamino donor of DPSTPA.

Local Energy Decomposition of Open-Shell Molecular Systems in the Domain-Based Local Pair Natural Orbital Coupled Cluster Framework

Local energy decomposition (LED) analysis decomposes the interaction energy between two fragments calculated at the domain-based local pair natural orbital CCSD(T) (DLPNO-CCSD(T)) level of theory into a series of chemically meaningful contributions and has found widespread applications in the study of noncovalent interactions. Herein, an extension of this scheme that allows for the analysis of interaction energies of open-shell molecular systems calculated at the UHF-DLPNO-CCSD(T) level is presented. The new scheme is illustrated through applications to the CH₂···X (X = He, Ne, Ar, Kr, and water) and heme···CO interactions in the low-lying singlet and triplet spin states. The results are used to discuss the mechanism that governs the change in the singlet–triplet energy gap of methylene and heme upon adduct formation.

Unraveling substituent effects on frontier orbitals of conjugated molecules using an absolutely localized molecular orbital based analysis

It is common to introduce electron-donating or electron-withdrawing substituent groups into functional conjugated molecules (such as dyes) to tune their electronic structure properties (such as frontier orbital energy levels) and photophysical properties (such as absorption and emission wavelengths). However, there lacks a generally applicable tool that can unravel the underlying interactions between orbitals from a substrate molecule and those from its substituents in modern electronic structure calculations, despite the long history of qualitative molecular orbital theory. In this work, the absolutely localized molecular orbitals (ALMO) based analysis is extended to analyze the effects of substituent groups on the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of a given system. This provides a bottom-up avenue towards quantification of effects from distinct physical origins (e.g. permanent electrostatics/Pauli repulsion, mutual polarization, inter-fragment orbital mixing). For the example case of prodan (a typical dye molecule), it is found that inter-fragment orbital mixing plays a key role in narrowing the HOMO-LUMO gap of the naphthalene core. Specifically, an out-of-phase mixing of high-lying occupied orbitals on the naphthalene core and the dimethylamino group leads to an elevated HOMO, whereas an in-phase combination of LUMOs on the naphthalene core and the propionyl group lowers the LUMO energy of the entire molecule. We expect this ALMO-based analysis to bridge the gap between concepts from qualitative orbital interaction analysis and quantitative electronic structure calculations.

Nature of halogen bonding involving π-systems, nitroxide radicals and carbenes: a highlight of the importance of charge transfer

The recently developed adiabatic absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) has proven to be useful in determining the effects of different energy components on the geometries of complexes bound by intermolecular interactions. The authors have applied it to systems such as the water dimer, water-ion complexes, metallocenes and lone-pair type halogen-bonded (XB) dimers. In this study, we have extended the second-generation ALMO-EDA method to 40 different XB complexes by benchmarking against its classical counterpart and symmetry-adapted perturbation theory (SAPT). In addition, we have examined the nature of halogen bonding involving less studied XB acceptors, namely π-systems, radicals and carbenes, using the adiabatic ALMO-EDA analyses, particularly to shed light on how each energy component affects the geometries of the XB complexes. Our results show that the second-generation ALMO-EDA predicts a higher electrostatic energy contribution in all XB complexes compared to SAPT and classical ALMO-EDA schemes. On the other hand, when comparing across different XB acceptors, all three partition schemes produced the same qualitative finding. The adiabatic ALMO-EDA analyses indicate that while the inclusion of a charge transfer contribution is important in achieving accurate XB bond lengths and interaction energies, as well as recovering the binding site specificity of XB involving benzene and naphthalene acceptors, it is sufficient to obtain the linearity of the XB complexes in the frozen approximation.

Perspective: Found in translation: Quantum chemical tools for grasping non-covalent interactions

Today's quantum chemistry methods are extremely powerful but rely upon complex quantities such as the massively multidimensional wavefunction or even the simpler electron density. Consequently, chemical insight and a chemist's intuition are often lost in this complexity leaving the results obtained difficult to rationalize. To handle this overabundance of information, computational chemists have developed tools and methodologies that assist in composing a more intuitive picture that permits better understanding of the intricacies of chemical behavior. In particular, the fundamental comprehension of phenomena governed by non-covalent interactions is not easily achieved in terms of either the total wavefunction or the total electron density, but can be accomplished using more informative quantities. This perspective provides an overview of these tools and methods that have been specifically developed or used to analyze, identify, quantify, and visualize non-covalent interactions. These include the quantitative energy decomposition analysis schemes and the more qualitative class of approaches such as the Non-covalent Interaction index, the Density Overlap Region Indicator, or quantum theory of atoms in molecules. Aside from the enhanced knowledge gained from these schemes, their strengths, limitations, as well as a roadmap for expanding their capabilities are emphasized.

Local energy decomposition analysis of hydrogen-bonded dimers within a domain-based pair natural orbital coupled cluster study

The local energy decomposition (LED) analysis allows for a decomposition of the accurate domain-based local pair natural orbital CCSD(T) [DLPNO-CCSD(T)] energy into physically meaningful contributions including geometric and electronic preparation, electrostatic interaction, interfragment exchange, dynamic charge polarization, and London dispersion terms. Herein, this technique is employed in the study of hydrogen-bonding interactions in a series of conformers of water and hydrogen fluoride dimers. Initially, DLPNO-CCSD(T) dissociation energies for the most stable conformers are computed and compared with available experimental data. Afterwards, the decay of the LED terms with the intermolecular distance (r) is discussed and results are compared with the ones obtained from the popular symmetry adapted perturbation theory (SAPT). It is found that, as expected, electrostatic contributions slowly decay for increasing r and dominate the interaction energies in the long range. London dispersion contributions decay as expected, as r-6. They significantly affect the depths of the potential wells. The interfragment exchange provides a further stabilizing contribution that decays exponentially with the intermolecular distance. This information is used to rationalize the trend of stability of various conformers of the water and hydrogen fluoride dimers.

On the Computational Characterization of Charge-Transfer Effects in Noncovalently Bound Molecular Complexes

Charge-transfer (CT) is an important binding force in the formation of intermolecular complexes, and there have been a variety of theoretical models proposed to quantify this effect. These approaches, which typically rely on a definition of a "CT-free" state based on a partition of the system, sometimes yield significantly different results for a given intermolecular complex. Two widely used definitions of the "CT-free" state, the absolutely localized molecular orbitals (ALMO) method (where only on-fragment orbital mixings are permitted) and the constrained density functional theory (CDFT) approach (where fragment electron populations are fixed), are carefully examined in this work. Natural bond orbital (NBO) and the regularized symmetry-adapted perturbation theory (SAPT) are also briefly considered. Results for the ALMO and CDFT definitions of CT are compared on a broad range of model systems, including hydrogen-bonding systems, borane complexes, metal-carbonyl complexes, and complexes formed by water and metal cations. For most of these systems, CDFT yields a much smaller equilibrium CT energy compared to that given by the ALMO-based definition. This is mainly because the CDFT population constraint does not fully inhibit CT, which means that the CDFT "CT-free" state is in fact CT-contaminated. Examples of this contamination include (i) matching forward and backward donation (e.g., formic acid dimer) and (ii) unidirectional CT without changing fragment populations. The magnitude of the latter effect is quantified in systems such as the water dimer by employing a 3-space density constraint in addition to the orbital constraint. Furthermore, by means of the adiabatic EDA, it is shown that several observable effects of CT, such as the "pyramidalization" of the planar BH₃ molecule upon the complexation with Lewis bases, already appear on the "CT-free" CDFT surface. These results reveal the essential distinctions between the ALMO and CDFT definitions of CT and suggest that the former is more consistent with accepted understanding of the role of CT in intermolecular binding.

Characterizing the interplay of Pauli repulsion, electrostatics, dispersion and charge transfer in halogen bonding with energy decomposition analysis

Variational energy decomposition analysis establishes charge-transfer as the origin of halogen bond strength differences that go against electrostatics.

Computational Chemistry: The Fate of Current Methods and Future Challenges

"Where do we go from here?" is the underlying question regarding the future (perhaps foreseeable) developments in computational chemistry. Although this young discipline has already permeated practically all of chemistry, it is likely to become even more powerful with the rapid development of computational hard- and software.