Symmetry-adapted Perturbation Theory Research Articles

Dispersion Interactions in Exciton-Localized States. Theory and Applications to π-π* and n-π* Excited States.

We address the problem of intermolecular interaction energy calculations in molecular complexes with localized excitons. Our focus is on the correct representation of the dispersion energy. We derive an extended Casimir-Polder formula for direct computation of this contribution through second order in the intermolecular interaction operator V̂. An alternative formula, accurate to infinite order in V̂, is derived within the framework of the adiabatic connection (AC) theory. We also propose a new parametrization of the VV10 nonlocal correlation density functional, so that it corrects the CASSCF energy for the dispersion contribution and can be applied to excited-state complexes. A numerical investigation is carried out for benzene, pyridine, and peptide complexes with the local exciton corresponding to the lowest π–π* or n– π* states. The extended Casimir-Polder formula is implemented in the framework of multiconfigurational symmetry-adapted perturbation theory, SAPT(MC). A SAPT(MC) analysis shows that the creation of a localized exciton affects mostly the electrostatic component of the interaction energy of investigated complexes. Nevertheless, the changes in Pauli repulsion and dispersion energies cannot be neglected. We verify the performance of several perturbation- and AC-based methods. Best results are obtained with a range-separated variant of an approximate AC approach employing extended random phase approximation and CASSCF wave functions.

The influence of a solvent environment on direct non-covalent interactions between two molecules: A symmetry-adapted perturbation theory study of polarization tuning of π–π interactions by water

High-level quantum chemical computations have provided significant insight into the fundamental physical nature of non-covalent interactions. These studies have focused primarily on gas-phase computations of small van der Waals dimers; however, these interactions frequently take place in complex chemical environments, such as proteins, solutions, or solids. To better understand how the chemical environment affects non-covalent interactions, we have undertaken a quantum chemical study of π–π interactions in an aqueous solution, as exemplified by T-shaped benzene dimers surrounded by 28 or 50 explicit water molecules. We report interaction energies (IEs) using second-order Møller–Plesset perturbation theory, and we apply the intramolecular and functional-group partitioning extensions of symmetry-adapted perturbation theory (ISAPT and F-SAPT, respectively) to analyze how the solvent molecules tune the π–π interactions of the solute. For complexes containing neutral monomers, even 50 explicit waters (constituting a first and partial second solvation shell) change total SAPT IEs between the two solute molecules by only tenths of a kcal mol−1, while significant changes of up to 3 kcal mol−1 of the electrostatic component are seen for the cationic pyridinium–benzene dimer. This difference between charged and neutral solutes is attributed to large non-additive three-body interactions within solvated ion-containing complexes. Overall, except for charged solutes, our quantum computations indicate that nearby solvent molecules cause very little “tuning” of the direct solute–solute interactions. This indicates that differences in binding energies between the gas phase and solution phase are primarily indirect effects of the competition between solute–solute and solute–solvent interactions.

A comprehensive theoretical analysis on the intermolecular hydrogen bond interactions with the Lewis bases having multiple hydrogen bonding abilities

AbstractThis work comprehensively studies the intermolecular H … O and H … N hydrogen bonding (HB) interactions between 3H‐pyrrol‐3‐one as a computationally simple model Lewis base (LB) comprising two different basic centers (sp2 hybridized O and N atoms) and hydrogen halides (Hal‐H, Hal = F, Cl, Br, and I) as common Lewis acids (LAs). In an equimolar mixture of LB and any of LAs, the formation of H … O and H … N HBs can compete with each other over the course of binary (dimer) complexation processes. Computed values of counterpoise‐corrected interaction energies (CP‐IE) together with energy decomposition analysis (EDA) through symmetry‐adapted perturbation theory (SAPT) reveal that these HBs should be classified as “weak‐to‐medium” ones which are mainly dominated with electrostatic interactions. Among many explored correlation analyses, within the binary complexes formation, the values of CP‐IE are perfectly linearly correlated with those of electron density at the bond critical points of the mentioned HBs, , leading to two different regression equations as ‐ . These equations allow that an accurate prediction of the value of CP‐IE for H … O and H … N HBs is made feasible using the value of easily and rapidly computable without an explicit (direct) calculation of the so costly CP‐IE. Such equations, also, were used to accurately and individually predict CP‐IE values in ternary (trimer) complexes where both of approximately pairwise additive H … O and H … N HBs can be formed at once. Moreover, in terms of the calculated values of cooperativity energies, these two HBs make each other weaken portraying an anticooperativity in the ternary complexes studied.

Development of the Quantum-Inspired SIBFA Many-Body Polarizable Force Field: Enabling Condensed-Phase Molecular Dynamics Simulations.

We present the extension of the Sum of Interactions Between Fragments Ab initio Computed (SIBFA) many-body polarizable force field to condensed-phase molecular dynamics (MD) simulations. The quantum-inspired SIBFA procedure is grounded on simplified integrals obtained from localized molecular orbital theory and achieves full separability of its intermolecular potential. It embodies long-range multipolar electrostatics (up to quadrupole) coupled to a short-range penetration correction (up to charge-quadrupole), exchange repulsion, many-body polarization, many-body charge transfer/delocalization, exchange dispersion, and dispersion (up to C10). This enables the reproduction of all energy contributions of ab initio symmetry-adapted perturbation theory (SAPT(DFT)) gas-phase reference computations. The SIBFA approach has been integrated within the Tinker-HP massively parallel MD package. To do so, all SIBFA energy gradients have been derived and the approach has been extended to enable periodic boundary conditions simulations using smooth particle mesh Ewald. This novel implementation also notably includes a computationally tractable simplification of the many-body charge transfer/delocalization contribution. As a proof of concept, we perform a first computational experiment defining a water model fitted on a limited set of SAPT(DFT) data. SIBFA is shown to enable a satisfactory reproduction of both gas-phase energetic contributions and condensed-phase properties highlighting the importance of its physically motivated functional form.

Electrochemical sensing of heptazine graphitic C3N4 quantum dot for chemical warfare agents; a quantum chemical approach

Despite the numerous publications describing the photocatalytic and electronic properties of heptazine-based C3N4, the systematic study on the sensing behavior of pure heptazine-C3N4 toward harmful chemical warfare agents (CWAs) is still lacking. Herein, we performed DFT calculations to investigate the adsorption behavior of C3N4 toward various harmful and toxic CWAs including formaldehyde (OCH2), thioformaldehyde (SCH2), phosgene (OCCl2), and thiophosgene (SCCl2). ωB97XD functional of DFT along with 6–31G (d, p) basis set is used for all calculations for accurate estimation of noncovalent interactions. The CWAs are physiosorbed onto the C3N4 having calculated interaction energy between −16.01 and −11.00 kcal/mol. Noncovalent interactions are further analyzed by symmetry-adapted perturbation theory (SAPT0), noncovalent interaction index (NCI), and quantum theory of atoms in molecules (QTAIM) analyses. The electronic behavior is characterized by the HOMO and LUMO energies, their energy gaps, and natural bond orbital (NBO) charge transfer. The charge transportation either donation or back donation is characterized by energy density difference (EDD) and charge decomposition analysis (CDA) analyses. The results demonstrate the trend of sensitivity of C3N4 for toxic gases is OCH2@C3N4 > SCH2@C3N4 > OCCl2@C3N4> SCCl2@C3N4. This theoretical work suggests that the C3N4 can act as a good electrochemical sensor for a variety of toxic gaseous molecules.

External Electric Field Effect on the Strength of σ-Hole Interactions: A Theoretical Perspective in Like⋯Like Carbon-Containing Complexes.

For the first time, σ-hole interactions within like⋯like carbon-containing complexes were investigated, in both the absence and presence of the external electric field (EEF). The effects of the directionality and strength of the utilized EEF were thoroughly unveiled in the (F-C-F3)2, (F-C-H3)2, and (H-C-F3)2 complexes. In the absence of the EEF, favorable interaction energies, with negative values, are denoted for the (F-C-F3)2 and (H-C-F3)2 complexes, whereas the (F-C-H3)2 complex exhibits unfavorable interactions. Remarkably, the strength of the applied EEF exhibits a prominent role in turning the repulsive forces within the latter complex into attractive ones. The symmetrical nature of the considered like⋯like carbon-containing complexes eradicated the effect of directionality of the EEF. The quantum theory of atoms in molecules (QTAIM), and the noncovalent interaction (NCI) index, ensured the occurrence of the attractive forces, and also outlined the substantial contributions of the three coplanar atoms to the total strength of the studied complexes. Symmetry-adapted perturbation theory (SAPT) results show the dispersion-driven nature of the interactions.

Conformational Landscape of the Hydrogen-Bonded 1-Phenyl-2,2,2-Trilfuoroethanol···1,4-Dioxane Complex: Dispersion Interactions and Conformational Conversion

A rotational spectrum of the hydrogen-bonded complex between 1-phenyl-2,2,2-trilfuoroethanol (PhTFE), a chiral fluoroalcohol, and 1,4-dioxane, a common solvent for organic reactions, was measured using a chirped pulse Fourier transform microwave spectrometer. Initial theoretical conformational searches were carried out using CREST, a recently developed conformational searching tool. Subsequent geometry optimization and harmonic frequency calculations at the B3LYP-D3(BJ)/def2-TZVP level of theory yielded nearly 30 binary conformers of which 13 are within an energy window of ∼5 kJ mol-1. Interestingly, while the O-H···O hydrogen bond dominates the attractive binary interactions, the complex conformational landscape is mainly controlled by subtle dispersion interactions between the phenyl and 1,4-dioxane rings. Two sets of rotational transitions were assigned in the experimental spectrum and attributed to the two most stable conformers of PhTFE···1,4-dioxane. The quantum theory of atoms in molecules (QTAIM), noncovalent interactions (NCI), and symmetry-adapted perturbation theory (SAPT) analyses were employed in order to appreciate how the phenyl ring and O-H functional groups influence the intermolecular interaction and conformational distribution of the binary complex. The main PhTFE conformation within the complex, identified experimentally, is different from that of the isolated PhTFE monomer reported previously.

Intramolecular resonance-assisted hydrogen bonds: Insights from symmetry adapted perturbation theory

The accurate description of hydrogen bonds (H-bonds) is one of the primary challenges when describing intermolecular forces. Intramolecular hydrogen bonds (IMHB) are even more challenging because of their ill-defined energy and their interplay with π-systems. In this contribution, we investigate the role of π-resonance in the enhancement of IMHBs. This is accomplished by comparing a number of π-conjugated systems to their saturated planar counterparts using intramolecular symmetry adapted perturbation theory (I-SAPT). The change in the composition of the IMHB energies (electrostatics, exchange, induction, and dispersion) due to π-conjugation is examined in detail. The biggest changes are observed in the induction and electrostatics contributions. However, electrostatics is nearly canceled by its exchange counterpart. The importance of induction term is also observed when plotting rotational potential curves for the different energy components. Once the distance between the H-bond donor and acceptor is frozen, the stabilization of IMHBs mostly occurs through the decrease in the exchange term leading to less repulsion. In any case, all results are consistent with expected trends in the resonance-assisted hydrogen bonds (RAHBs), and corroborate the fragmentation procedures used in this study. The closeness of induction contribution to the whole interaction energy and the existence of a linear correlation between the IMHB energy and the induction component show that the induction term is a good predictor of the intramolecular RAHBs stability trends.

Strongly Bound π-Hole Tetrel Bonded Complexes between H2 SiO and Substituted Pyridines. Influence of Substituents.

Ab initio calculation at the MP2/aug-cc-pVTZ level has been performed on the π-hole based N… Si tetrel bonded complexes between substituted pyridines and H2 SiO. The primary aim of the study is to find out the effect of substitution on the strength and nature of this tetrel bond, and its similarity/difference with the N… C tetrel bond. Correlation between the strength of the N… Si bond and several molecular properties of the Lewis acid (H2 SiO) and base (pyridines) are explored. The properties of the tetrel bond are analyzed using AIM, NBO, and symmetry-adapted perturbation theory calculations. The complexes are characterized with short N… Si intermolecular distances and high binding energies ranging between -142.72 and -115.37 kJ/mol. The high value of deformation energy indicates significant geometrical distortion of the monomer units. The AIM and NBO analysis reveal significant coordinate covalent bond character of the N⋅⋅⋅Si π-hole bond. Sharp differences are also noticed in the orbital interactions present in the N⋅⋅⋅Si and N⋅⋅⋅C tetrel bonds.

Radial Potential Energy Functions of Linear Halogen-Bonded Complexes YX···ClF (YX = FB, OC, SC, N2) and the Effects of Substituting X by Second-Row Analogues: Mulliken Inner and Outer Complexes

Energies of linear, halogen-bonded complexes in the isoelectronic series YX···ClF (YX = FB, OC, or N2) are calculated at several levels of theory as a function of the intermolecular distance r(X···Cl) to yield radial potential energy functions. When YX = OC, a secondary minimum is observed corresponding to lengthened and shortened distances r(ClF) and r(CCl), respectively, relative to the primary minimum, suggesting a significant contribution from the Mulliken inner complex structure [O=C–Cl]+···F–. A conventional weak, halogen-bond complex OC···ClF occurs at the primary minimum. For YX = FB, the primary minimum corresponds to the inner complex [F=B–Cl]+···F–, while the outer complex FB···ClF is at the secondary minimum. The effects on the potential energy function of systematic substitution of Y and X by second-row congeners and of reversing the order of X and Y are also investigated. Symmetry-adapted perturbation theory and natural population analyses are applied to further understand the nature of the various halogen-bond interactions.

Reassessing the Role of σ Holes in Noncovalent Interactions: It is Pauli Repulsion that Counts

A number of prototypical weak electron donor–electron acceptor complexes are investigated by the Symmetry Adapted Perturbation Theory, some of which belong to novel classes of weak bonds such as halogen and chalcogen bonds. Also included are complexes involving strong Lewis acids such as BeO and AuF. The common view in the literature is to associate these novel bonds with a variety of “holes”, σ, π, δ, or positive areas in their electrostatic potential maps. The presumption is that these positive areas of the electrostatic potential are indicative of the electrostatic nature of these noncovalent bonds. The electrostatic view extends to the explanations of the directionality of approaches between the subsystems forming these bonds. This work demonstrates that one common feature of these electrostatic potential “holes” is the local depletion of electron density of which the best detector is the first-order Pauli repulsion. The minimization of this repulsion determines the bond directionality and its relative angular rigidity. In relatively strong complexes of BeO with rare gases, where BeO shows a clear cavity in electron density—an ultimate “σ hole”—the electrostatic effect does not control the bending potential—the exchange repulsion does. In halogen bonds, the halogen atom is nonspherical, displaying an axial “σ hole” in its electrostatic potential. However, in no examined case, from rare gas acting as an electron donor to a polar donor to an anionic donor, is the electrostatic energy responsible for the directionality of the halogen bond. In fact, it is not even maximized in the direction of the σ hole in N2-ClF and NH3-ClF. Yet, in all the cases, the exchange repulsion is minimized in the direction of the σ hole. The minimized exchange repulsion associated with the subtle and less subtle depletions of the electron density occur on the nodal planes or on the intersections thereof in the highest occupied molecular orbitals of Lewis acids, provided that the systems are closed-shell. The role of nodal planes in covalent and coordinate covalent bonds is well recognized. This work points to their similarly equal importance in certain types of donor–acceptor noncovalent interactions.

Revealing Intra- and Intermolecular Interactions Determining Physico-Chemical Features of Selected Quinolone Carboxylic Acid Derivatives.

The intra- and intermolecular interactions of selected quinolone carboxylic acid derivatives were studied in monomers, dimers and crystals. The investigated compounds are well-recognized as medicines or as bases for further studies in drug design. We employed density functional theory (DFT) in its classical formulation to develop gas-phase and solvent reaction field (PCM) models describing geometric, energetic and electronic structure parameters for monomers and dimers. The electronic structure was investigated based on the atoms in molecules (AIM) and natural bond orbital (NBO) theories. Special attention was devoted to the intramolecular hydrogen bonds (HB) present in the investigated compounds. The characterization of energy components was performed using symmetry-adapted perturbation theory (SAPT). Finally, the time-evolution methods of Car–Parrinello molecular dynamics (CPMD) and path integral molecular dynamics (PIMD) were employed to describe the hydrogen bond dynamics as well as the spectroscopic signatures. The vibrational features of the O-H stretching were studied using Fourier transformation of the autocorrelation function of atomic velocity. The inclusion of quantum nuclear effects provided an accurate depiction of the bridged proton delocalization. The CPMD and PIMD simulations were carried out in the gas and crystalline phases. It was found that the polar environment enhances the strength of the intramolecular hydrogen bonds. The SAPT analysis revealed that the dispersive forces are decisive factors in the intermolecular interactions. In the electronic ground state, the proton-transfer phenomena are not favourable. The CPMD results showed generally that the bridged proton is localized at the donor side, with possible proton-sharing events in the solid-phase simulation of stronger hydrogen bridges. However, the PIMD enabled the quantitative estimation of the quantum effects inclusion—the proton position was moved towards the bridge midpoint, but no qualitative changes were detected. It was found that the interatomic distance between the donor and acceptor atoms was shortened and that the bridged proton was strongly delocalized.

Interactions between Artificial Channel Protein, Water Molecules, and Ions Based on Theoretical Approaches

Contemporary techniques of molecular modeling allow for rational design of several specific classes of artificial proteins. Transmembrane channels are among these classes. A recent successful synthesis of self-assembling, highly symmetrical 12- or 16-helix channels by David Baker’s group prompted us to study interactions between one of these proteins, TMHC6, and low-molecular-weight components of the environment: water molecules and ions. To examine protein stability in a polar environment, molecular dynamics (MD) with classical force fields of the AMBER family was employed. Further characteristics of the chosen interactions were obtained using interaction energy calculations with usage of partially polarizable GFN-FF force field of Spicher and Grimme, symmetry-adapted perturbation theory (SAPT) and atoms in molecules (AIM) approaches for models of residues from the channel entry, crucial for interactions with water molecules and ions. The comparison of the interaction energy values between the gas phase and solvent reaction field gives the quantitative estimation of the strength of the interactions. The energy decomposition via the SAPT method showed that the electrostatics forces play a dominant role in the substructure stabilization. An application of the AIM theory enabled a description of the intermolecular hydrogen bonds and other noncovalent interactions.

Sensing behaviour of monocyclic C18 and B9N9 analogues toward chemical warfare agents (CWAs); quantum chemical approach

This study describes the first demonstration of using monocyclic C18 and B9N9 as active materials for the sensing and removing of chemical warfare agents (CWAs) such as formaldehyde (Fd), phosgene (Ph), and thiophosgene (TPh). The sensitivities and adsorption capacities of both C18 and B9N9 analogues toward considered molecules are thoroughly characterized by optimized geometries, energetic stabilities, electronic behaviour, and optical properties at the M05-2X-D3/6-31++G(d,p) method of density functional theory (DFT). In the complexes, the analytes interact through the active cavity of the monocyclic (ring) systems. It is found from the BSSE corrected energies that the adsorption of analytes on B9N9 is energetically more favorable than that on C18. Based on the adsorption energies, the sensitivity of surfaces toward formaldehyde and phosgene is higher than the thiophosgene molecule. The adsorption energies of Fd@B9N9, Ph@B9N9 and Thp@B9N9 complexes are −7.47, −7.45, and −4.96 kcal mol−1, respectively which is about 2.19, 1.56, and 0.69 kcal mol−1 exothermic than Fd@C18, Ph@C18, and Thp@C18 complexes, respectively. Symmetry adapted perturbation theory (SAPT0), reduced density gradient (RDG) and quantum theory of atoms in molecule (QTAIM) results illustrate that dispersion forces play an important role in stabilizing these complexes. The variations of the electronic properties are explained based on HOMO LUMO orbitals, the density of state (DOS), NBO charge transfer, and UV-Vis analysis. The significant variations in the electronic parameters reveal that CWAs can bind more strongly with these ring systems which is more pronounced in B9N9. Therefore, these monocyclic systems may be considered a potential candidate for sensor application.

First-principles study for electrochemical sensing of neurotoxin hydrazine derivatives via h-g-C3N4 quantum dot

The density functional theory (DFT) simulations were performed to understand the sensing behavior of heptazine-based graphitic (h-g-C3N4) quantum dot towards hydrazine (Hyd), dimethylhydrazine (DHy) and phenylhydrazine (PHy). The interaction energies illustrated that the high stability of the reported complexes was due to the presence of dominant dispersion forces, which was also revealed by symmetry-adapted perturbation theory (SAPT0) analysis. The domination of dispersion forces in stabilizing the complexes was also confirmed by the two quantitative approaches i.e., noncovalent interaction index (NCI) and quantum theory of atoms in molecules (QTAIM) analysis. The observed trend of interaction stability was PHy@h-g-C3N4>Hy@h-g-C3N4>DHy@h-g-C3N4. The electronic properties of the complexes were studied by Frontier Molecular Orbital (FMO), the density of state (DOS) and NBO charge transfer analyses. According to FMO analysis, the highest molecular orbitals (HOMOs) were shifted near to the Fermi level upon complexation, resulting in the lowering of the HOMO-LUMO energy gap (Egap). A significant charge transfer was noticed which reflected the increase in conductivity. Finally, the charge density was further explained by electron density differences (EDD) and charge decomposition analysis (CDA).

First principles calculations of the adsorption of fluorouracil and nitrosourea on CTF-0; organic frameworks as drug delivery systems for cancer treatment

2D sheet like materials such graphene are superior drug delivery systems compared to the conventional macro systems due to good adsorption and reasonable bioavailability. The adsorption and bioavailability can be further improved with periodic cavity containing 2D materials which can bind with drug molecules with moderate binding energies. Therefore, we have studied for the first time the potential of 2-dimensional porous covalent triazine framework (CTF-0) for the delivery of anticancer drugs fluorouracil (FU) and nitrosourea (NU). Adsorption energy analysis shows that the drug molecules bind with CTF-0 with moderate interaction energies which is prime requirement of a good drug delivery system. However, FU@CTF-0 complex (−17.45 kcal/mol) is more stable than NU@CTF-0 (−14.83 kcal/mol), and that the dipole moment of surface increases after adsorption of drugs. The increase in dipole moment after complex formation helps to improve the solubility, which is necessary for drug delivery in biological systems. Symmetry adapted perturbation theory confirms the stability of drug-loaded complexes, where the contribution from dispersion interactions is the highest. The HOMO-LUMO energy gap (EH-L) of CTF-0 decreases from 4.5 eV to 4.1 eV and 4.0 eV after loading of FU and NU respectively. The pH in cancerous tissues is typically low, which can lead to protonation of a drug and hence aid its delivery to target cells. The nature of the attraction between the CTF-0 surface and different drugs has been evaluated on the bases of noncovalent interactions (NCI) and also the quantum theory of atoms in molecules (QTAIM). QTAIM results confirm that FU has a stronger affinity towards CTF-0 than NU. Based on all our calculated results, CTF-0 appears to be a viable candidate for the delivery of the anticancer drug FU. Previously reported surface for FU and NU drugs has much higher interaction energy which is problematic for the release of drug from the carrier in the biological system. This study provides useful information that may assist the experimental formulation of a CTF-0-based DDS for FU.

Gauging the Steric Effects of Silyl Groups with a Molecular Balance.

We present an experimental and computational study of a cyclooctatetraene (COT)-based molecular balance disubstituted with commonly used silyl groups. Such groups often serve as protecting groups and are typically considered innocent bystanders. Our motivation here is to determine the actual steric effects of such groups by employing a molecular balance. While in the unfolded 1,4-valence isomer the silyl groups are far apart (dσ-σ ≥ 5.15 Å), the folded 1,6-isomer is affected greatly by noncovalent interactions due to close σ-σ contacts (dσ-σ ≤ 2.58 Å). In order to investigate the thermodynamic equilibrium between the 1,6- and 1,4-valence isomers, we employed temperature-dependent nuclear magnetic resonance measurements. Additionally, we assessed the nature of attractive and repulsive interactions in 1,6-disilyl-COT derivatives via a combination of local energy decomposition analysis (LED) and symmetry-adapted perturbation theory (SAPT) at the DLPNO-CCSD(T)/def2-TZVP and sSAPT0/aug-cc-pVDZ levels of theory. We identified London dispersion interactions as the main contributor to the molecular stability of the folded states, whereas Pauli exchange repulsion and a resulting internal strain favor the unfolded diastereomer.

Comprehensive Basis-Set Testing of Extended Symmetry-Adapted Perturbation Theory and Assessment of Mixed-Basis Combinations to Reduce Cost.

Hybrid or "extended" symmetry-adapted perturbation theory (XSAPT) replaces traditional SAPT's treatment of dispersion with better performing alternatives while at the same time extending two-body (dimer) SAPT to a many-body treatment of polarization using a self-consistent charge embedding procedure. The present work presents a systematic study of how XSAPT interaction energies and energy components converge with respect to the choice of Gaussian basis set. Errors can be reduced in a systematic way using correlation-consistent basis sets, with aug-cc-pVTZ results converged within <0.1 kcal/mol. Similar (if slightly less systematic) behavior is obtained using Karlsruhe basis sets at much lower cost, and we introduce new versions with limited augmentation that are even more efficient. Pople-style basis sets, which are more efficient still, often afford good results if a large number of polarization functions are included. The dispersion models used in XSAPT afford much faster basis-set convergence as compared to the perturbative description of dispersion in conventional SAPT, meaning that "compromise" basis sets (such as jun-cc-pVDZ) are no longer required and benchmark-quality results can be obtained using triple-ζ basis sets. The use of diffuse functions proves to be essential, especially for the description of hydrogen bonds. The "δ(Hartree-Fock)" correction for high-order induction can be performed in double-ζ basis sets without significant loss of accuracy, leading to a mixed-basis approach that offers 4× speedup over the existing (cubic scaling) XSAPT approach.

Dispersion Interactions between Molecules in and out of Equilibrium Geometry: Visualization and Analysis.

The London dispersion interactions between systems undergoing bond breaking, twisting, or compression are not well studied due to the scarcity and the high computational cost of methods being able to describe both the dynamic correlation and the multireference character of the system. Recently developed methods based on the Generalized Valence Bond wave function, such as EERPA-GVB and SAPT(GVB) (SAPT = symmetry-adapted perturbation theory), allow one to accurately compute and analyze noncovalent interactions between multireference systems. Here, we augment this analysis by introducing a local indicator for dispersion interactions inspired by Mata and Wuttke’s Dispersion Interaction Density [J. Comput. Chem.2017, 38, 15−2327761924] applied on top of an EERPA-GVB computation. Using a few model systems, we show what insights into the nature and evolution of the dispersion interaction during bond breaking and twisting such an approach is able to offer. The new indicator can be used at a minimal cost additional to an EERPA-GVB computation and can be complemented by an energy decomposition employing the SAPT(GVB) method. We explain the physics behind the initial increase, followed by a decrease in the interaction of linear molecules upon bond stretching. Namely, the elongation of covalent bonds leads to the enhancement of attractive dispersion interactions. For even larger bond lengths, this effect is canceled by the increase of the repulsive exchange forces resulting in a suppression of the interaction and finally leading to repulsion between monomers.

The Bifurcated σ-Hole···σ-Hole Stacking Interactions.

The bifurcated σ-hole···σ-hole stacking interactions between organosulfur molecules, which are key components of organic optical and electronic materials, were investigated by using a combined method of the Cambridge Structural Database search and quantum chemical calculation. Due to the geometric constraints, the binding energy of one bifurcated σ-hole···σ-hole stacking interaction is in general smaller than the sum of the binding energies of two free monofurcated σ-hole···σ-hole stacking interactions. The bifurcated σ-hole···σ-hole stacking interactions are still of the dispersion-dominated noncovalent interactions. However, in contrast to the linear monofurcated σ-hole···σ-hole stacking interaction, the contribution of the electrostatic energy to the total attractive interaction energy increases significantly and the dispersion component of the total attractive interaction energy decreases significantly for the bifurcated σ-hole···σ-hole stacking interaction. Another important finding of this study is that the low-cost spin-component scaled zeroth-order symmetry-adapted perturbation theory performs perfectly in the study of the bifurcated σ-hole···σ-hole stacking interactions. This work will provide valuable information for the design and synthesis of novel organic optical and electronic materials.