Density-functional theory-symmetry-adapted intermolecular perturbation theory with density fitting: A new efficient method to study intermolecular interaction energies

Efficient Density-Fitted Explicitly Correlated Dispersion and Exchange Dispersion Energies

The leading-order dispersion and exchange-dispersion terms in symmetry-adapted perturbation theory (SAPT), E_disp⁽²⁰⁾ and E_exch-disp⁽²⁰⁾, suffer from slow convergence to the complete basis set limit. To alleviate this problem, explicitly correlated variants of these corrections, E_disp⁽²⁰⁾-F12 and E_exch-disp⁽²⁰⁾-F12, have been proposed recently. However, the original formalism (M., Kodrycka , J. Chem. Theory Comput. 2019, 15, 5965-5986), while highly successful in terms of improving convergence, was not competitive to conventional orbital-based SAPT in terms of computational efficiency due to the need to manipulate several kinds of two-electron integrals. In this work, we eliminate this need by decomposing all types of two-electron integrals using robust density fitting. We demonstrate that the error of the density fitting approximation is negligible when standard auxiliary bases such as aug-cc-pVXZ/MP2FIT are employed. The new implementation allowed us to study all complexes in the A24 database in basis sets up to aug-cc-pV5Z, and the E_disp⁽²⁰⁾-F12 and E_exch-disp⁽²⁰⁾-F12 values exhibit vastly improved basis set convergence over their conventional counterparts. The well-converged E_disp⁽²⁰⁾-F12 and E_exch-disp⁽²⁰⁾-F12 numbers can be substituted for conventional E_disp⁽²⁰⁾ and E_exch-disp⁽²⁰⁾ ones in a calculation of the total SAPT interaction energy at any level (SAPT0, SAPT2+3, ...). We show that the addition of F12 terms does not improve the accuracy of low-level SAPT treatments. However, when the theory errors are minimized in high-level SAPT approaches such as SAPT2+3(CCD)δMP2, the reduction of basis set incompleteness errors thanks to the F12 treatment substantially improves the accuracy of small-basis calculations.

A non-empirical intermolecular force-field for trinitrobenzene and its application in crystal structure prediction

An anisotropic atom-atom distributed intermolecular force-field (DIFF) for rigid trinitrobenzene (TNB) is developed using distributed multipole moments, dipolar polarizabilities, and dispersion coefficients derived from the charge density of the isolated molecule. The short-range parameters of the force-field are fitted to first- and second-order symmetry-adapted perturbation theory dimer interaction energy calculations using the distributed density-overlap model to guide the parameterization of the short-range anisotropy. The second-order calculations are used for fitting the damping coefficients of the long-range dispersion and polarization and also for relaxing the isotropic short-range coefficients in the final model, DIFF-srL2(rel). We assess the accuracy of the unrelaxed model, DIFF-srL2(norel), and its equivalent without short-range anisotropy, DIFF-srL0(norel), as these models are easier to derive. The model potentials are contrasted with empirical models for the repulsion-dispersion fitted to organic crystal structures with multipoles of iterated stockholder atoms (ISAs), FIT(ISA,L4), and with Gaussian Distributed Analysis (GDMA) multipoles, FIT(GDMA,L4), commonly used in modeling organic crystals. The potentials are tested for their ability to model the solid state of TNB. The non-empirical models provide more reasonable relative lattice energies of the three polymorphs of TNB and propose more sensible hypothetical structures than the empirical force-field (FIT). The DIFF-srL2(rel) model successfully has the most stable structure as one of the many structures that match the coordination sphere of form III. The neglect of the conformational flexibility of the nitro-groups is a significant approximation. This methodology provides a step toward force-fields capable of representing all phases of a molecule in molecular dynamics simulations.

Ab initio effective one-electron potential operators: Applications for charge-transfer energy in effective fragment potentials

The concept of effective one-electron potentials (EOPs) has proven to be extremely useful in efficient description of electronic structure of chemical systems, especially extended molecular aggregates such as interacting molecules in condensed phases. Here, a general method for EOP-based elimination of electron repulsion integrals is presented, that is tuned toward the fragment-based calculation methodologies such as the second generation of the effective fragment potentials (EFP2) method. Two general types of the EOP operator matrix elements are distinguished and treated either via the distributed multipole expansion or the extended density fitting (DF) schemes developed in this work. The EOP technique is then applied to reduce the high computational costs of the effective fragment charge-transfer (CT) terms being the bottleneck of EFP2 potentials. The alternative EOP-based CT energy model is proposed, derived within the framework of intermolecular perturbation theory with Hartree-Fock noninteracting reference wavefunctions, compatible with the original EFP2 formulation. It is found that the computational cost of the EFP2 total interaction energy calculation can be reduced by up to 38 times when using the EOP-based formulation of CT energy, as compared to the original EFP2 scheme, without compromising the accuracy for a wide range of weakly interacting neutral and ionic molecular fragments. The proposed model can thus be used routinely within the EFP2 framework.

Extension of an Atom-Atom Dispersion Function to Halogen Bonds and Its Use for Rational Design of Drugs and Biocatalysts

A dispersion function Das in the form of a damped atom-atom asymptotic expansion fitted to ab initio dispersion energies from symmetry-adapted perturbation theory was improved and extended to systems containing heavier halogen atoms. To illustrate its performance, the revised Das function was implemented in the multipole first-order electrostatic and second-order dispersion (MED) scoring model. The extension has allowed applications to a much larger set of biocomplexes than it was possible with the original Das. A reasonable correlation between MED and experimentally determined inhibitory activities was achieved in a number of test cases, including structures featuring nonphysically shortened intermonomer distances, which constitute a particular challenge for binding strength predictions. Since the MED model is also computationally efficient, it can be used for reliable and rapid assessment of the ligand affinity or multidimensional scanning of amino acid side-chain conformations in the process of rational design of novel drugs or biocatalysts.

Nonapproximated third-order exchange induction energy in symmetry-adapted perturbation theory

The exchange terms in symmetry-adapted perturbation theory (SAPT) are normally calculated within the so-called S² or single exchange approximation, which approximates the all-electron antisymmetrizer by interchanges of at most one electron pair between the interacting molecules. This approximation is typically very accurate at the van der Waals minimum separation and at larger intermolecular distances but begins to deteriorate at short range. Nonapproximated expressions for the second-order SAPT exchange corrections have been derived some time ago by Schäffer and Jansen [Mol. Phys. 111, 2570 (2013)]. In this work, we extend Schäffer and Jansen's formalism to derive and implement a nonapproximated expression for the third-order exchange-induction correction. Numerical tests on several representative noncovalent databases show that the S² approximation underestimates the exchange-induction contributions in both second and third orders. This underestimation is very similar in relative terms, but the larger absolute values of the third-order exchange-induction effects, and their near complete cancellation with the corresponding induction energies, make the third-order errors more severe. In the worst-case scenario of interactions involving ions, the breakdown of the S² approximation can result in a qualitatively wrong, attractive character of SAPT total energies at short range {as first observed by Lao and Herbert [J. Phys. Chem. A 116, 3042 (2012)]}. As expected, the inclusion of the full third-order exchange-induction energy in place of its S²-approximated counterpart restores the correct, repulsive short-range behavior of the SAPT potential energy curves computed through the third order.

A nuclear spin and spatial symmetry-adapted full quantum method for light particles inside carbon nanotubes: clusters of 3He, 4He, and para-H2

A new nuclear spin and spatial symmetry-adapted full quantum method for light fermionic and bosonic particles under cylindrical carbon nanotube confinement.

Many-Body Dispersion

A broad range of approaches to many-body dispersion are discussed, including empirical approaches with multiple fitted parameters, augmented density functional-based approaches, symmetry adapted perturbation theory, and a supermolecule approach based on coupled cluster theory. Differing definitions of "body" are considered, specifically atom-based vs molecule-based approaches.

The Nature of Strong Chalcogen Bonds Involving Chalcogen-Containing Heterocycles

Chalcogen bonds are σ hole interactions and have been used in recent years as an alternative to hydrogen bonds. In general, the electrostatic potential at the chalcogen atom and orbital delocalization effects are made responsible for the orientation of the chalcogen bond. Here, we were able to show by means of SAPT calculations that neither the induction (orbital delocalization effects) nor the electrostatic term is causing the spatial orientation of strong chalcogen bonds in tellurium-containing aromatics. Instead, steric interactions (Pauli repulsion) are responsible for the orientation. Against chemical intuition the dispersion energies of the examined tellurium-containing aromatics are far less important for the net attractive forces compared to the energies in the corresponding sulfur and selenium compounds. Our results underline the importance of often overlooked steric interactions (Pauli repulsion) in conformational control of σ hole interactions.

Parametrizing the Spatial Dependence of 1H NMR Chemical Shifts in π-Stacked Molecular Fragments

Most recently a renewed interest in several areas has arisen in factors governing the 1H NMR chemical shift (1H CS) of protons in aromatic systems. Therefore, it is important to describe how 1H CS values are affected by π-stacking intermolecular interactions. The parametrization of radial and angular dependences of the 1H CS is proposed, which is based on conventional gauge-independent atomic orbital (GIAO) calculations of explicit molecular fragments. Such a parametrization is exemplified for a benzene dimer with intermonomer vertical and horizontal distances which are in the range of values often found in crystals of organic compounds. Results obtained by the GIAO calculations combined with B3LYP and MP2 methods were compared, and revealed qualitatively the same trends in the 1H CS data. The parametrization was found to be quantitatively correct for the T-shaped benzene dimers, and its limitations were discussed. Parametrized 1H CS surfaces should become useful for providing additional restraints in the search of site-specific information through an analysis of structurally induced 1H CS changes.

How Much Dispersion Energy Is Included in the Multiconfigurational Interaction Energy?

We demonstrate how to quantify the amount of dispersion interaction recovered by supermolecular calculations with the multiconfigurational self-consistent field (MCSCF) wave functions. For this purpose, we present a rigorous derivation which connects the portion of dispersion interaction captured by the assumed wave function model-the residual dispersion interaction-with the size of the active space. Based on the obtained expression for the residual dispersion contribution, we propose a dispersion correction for the MCSCF that avoids correlation double counting. Numerical demonstration for model four-electron dimers in both ground and excited states described with the complete active space self-consistent field (CASSCF) reference serves as a proof-of-concept for the method. Accurate results, largely independent of the size of the active space, are obtained. For many-electron systems, routine CASSCF interaction energy calculations recover a tiny fraction of the full second-order dispersion energy. We found that the residual dispersion is non-negligible only for purely dispersion-bound complexes.

Description of Chiral Complexes within Functional-Group Symmetry-Adapted Perturbation Theory-The Case of (S/R)-Carvone with Derivatives of (-)-Menthol

Symmetry-adapted perturbation theory (SAPT) and functional-group SAPT (F-SAPT) are applied to examine differences in interaction energies of diastereoisomeric complexes of two chiral molecules of natural origin: (S/R)-carvone with (-)-menthol. The study is extended by including derivatives of menthol with its hydroxy group exchanged by another functional group, thus examining the substituent effect of the interaction and the interaction differences between diastereoisomers. The partitioning of the interaction energy into functional-group components allows one to explain this phenomenon by the mutual cancellation of attractive and repulsive interactions between functional groups. In some cases, one can identify dominant chiral interactions between groups of atoms of carvone and menthol derivatives, while in many other instances, no major interaction can be distinguished and the net chiral difference results from subtle near cancellation of several smaller terms. Our results indicate that the F-SAPT method can be faithfully utilized for such analyses.

From Molecular Aggregation to a One-Dimensional Quantum Crystal of Deuterium Inside a Carbon Nanotube of 1 nm Diameter

The quantum motion of clusters of up to four deuterium molecules under confinement in a single-wall (1 nm diameter) carbon nanotube is investigated by applying a highly accurate full quantum treatment of the most relevant nuclear degrees of freedom and an ab initio-derived potential model of the underlying dispersion-dominated intermolecular interactions. The wave functions and energies are calculated using an ad hoc-developed discrete variable representation (DVR) numerical approach in internal coordinates, with the space grid approaching a few billion grid points. We unambiguously demonstrate the formation of a solid-like pyramidal one-dimensional chain structure of molecules under the cylindrical nanotube confinement. The onset of solid-like packing is explained by analyzing the potential minima landscape. The stabilization of collective rotational motion through "rigid rotations" of four deuterium molecules provides conclusive evidence for the onset of a quantum solid-like behavior resembling that of quantum rings featuring persistent current (charged particles) or persistent flow (neutral particles).

The relative position of π-π interacting rings notably changes the nature of the substituent effect

The substituent effect in monosubstituted benzene dimers mostly follows changes on electrostatics mainly controlled by the direct interaction of the substituent and the other phenyl ring, whereas the contribution from the interacting rings is smaller. As the substituent is located further away the two contributions become of similar magnitude, so the global result is a combination of both effects. These trends are confirmed in larger systems containing a contact between phenyl rings; at closer distances the interaction of the substituent and the other ring clearly dominates over changes associated with the substituted ring, but as the substituent is located further away its contribution decreases and the contribution from the ring becomes more relevant. Care should be taken in larger systems because the observed energy change can also be affected by interactions with other regions of the molecule not directly involved in the π-π interaction.

Interaction and Reactivity of Cisplatin Physisorbed on Graphene Oxide Nano-Prototypes

The physical adsorption of cisplatin (CP) on graphene oxide (GO) and reduced graphene oxide (rGO) is investigated at the DFT level of theory by exploiting suitable molecular prototypes representing the most probable adsorbing regions of GO and rGO nano-structures. The results show that the CP binding energy is enhanced with respect to that for the interaction with pristine graphene. This is due to the preferential adsorption of the drug in correspondence of the epoxy and hydroxy groups located on GO basal plane: an energy decomposition analysis of the corresponding binding energy reveals that the most attractive contribution comes from the electrostatic attraction between the -NH3 ends of CP and the oxygen groups on (r)GO, which can be associated with hydrogen bonding effects. Moreover, it is found that the reactivity of the physically adsorbed CP is practically unaltered being the free energy variation of the first hydrolysis reaction almost matching that of its free (unadsorbed drug) counterpart. The reported results suggest that the CP physical adsorption on GO and rGO carriers is overall feasible being an exergonic process in aqueous solution. The CP adsorption could facilitate its solubility and transport in water solutions, exploiting the high hydrophilicity of the peripheral carboxylic groups located on the edge of the GO and rGO nano-structures. Moreover, the the higher affinity of CP with respect to the oxidized sites suggests a possible dependence of drug loading and release on pH conditions, which would highly facilitate its specific delivery.

SAPT codes for calculations of intermolecular interaction energies

Symmetry-adapted perturbation theory (SAPT) is a method for calculations of intermolecular (noncovalent) interaction energies. The set of SAPT codes that is described here, the current version named SAPT2020, includes virtually all variants of SAPT developed so far, among them two-body SAPT based on perturbative, coupled cluster, and density functional theory descriptions of monomers, three-body SAPT, and two-body SAPT for some classes of open-shell monomers. The properties of systems governed by noncovalent interactions can be predicted only if potential energy surfaces (force fields) are available. SAPT is the preferred approach for generating such surfaces since it is seamlessly connected to the asymptotic expansion of interaction energy. SAPT2020 includes codes for automatic development of such surfaces, enabling generation of complete dimer surfaces with a rigid monomer approximation for dimers containing about one hundred atoms. These codes can also be used to obtain surfaces including internal degrees of freedom of monomers.

Psi4 1.4: Open-source software for high-throughput quantum chemistry

PSI4 is a free and open-source ab initio electronic structure program providing implementations of Hartree-Fock, density functional theory, many-body perturbation theory, configuration interaction, density cumulant theory, symmetry-adapted perturbation theory, and coupled-cluster theory. Most of the methods are quite efficient, thanks to density fitting and multi-core parallelism. The program is a hybrid of C++ and Python, and calculations may be run with very simple text files or using the Python API, facilitating post-processing and complex workflows; method developers also have access to most of PSI4's core functionalities via Python. Job specification may be passed using The Molecular Sciences Software Institute (MolSSI) QCSCHEMA data format, facilitating interoperability. A rewrite of our top-level computation driver, and concomitant adoption of the MolSSI QCARCHIVE INFRASTRUCTURE project, makes the latest version of PSI4 well suited to distributed computation of large numbers of independent tasks. The project has fostered the development of independent software components that may be reused in other quantum chemistry programs.

The Molpro quantum chemistry package

Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

Automatic Generation of Flexible-Monomer Intermolecular Potential Energy Surfaces

A method is developed for automatic generation of nonreactive intermolecular two-body potential energy surfaces (PESs) including intramonomer degrees of freedom. This method, called flex-autoPES, is an extension of the autoPES method developed earlier, which assumes rigid monomers. In both cases, the whole PES development proceeds without any human intervention. The functional form used is a sum of products of site-site functions (both atomic and off-atomic sites can be used). The leading terms with sites involving different monomers are of physically motivated form. The long-range part of a PES is computed from monomer properties without using any dimer information. The close-range part is fitted to dimer interaction energies computed using electronic structure methods. Virtually any method can be used in such calculations, but the use of symmetry-adapted perturbation theory provides a seamless connection to the long-range part of the PES. The performance of the flex-autoPES code was tested by developing a full-dimensional PES for the water dimer and PESs including only some soft intramonomer degrees of freedom for the ethylene glycol dimer and for the ethylene glycol-water dimer. In the case of the water dimer, the root-mean-square error (RMSE) of the PES from the data points with negative total energies is 0.03 kcal/mol, and we expect this PES to be more accurate than any previously published PES of this type. For the ethylene glycol dimer and the ethylene glycol-water dimers, the analogous RMSEs are 0.25 and 0.1 kcal/mol, respectively.

A statistically guided grid generation method and its application to intermolecular potential energy surfaces

We present a method for the generation of points in space needed to create training data for fitting of nonlinear parametric models. This method uses statistical information extracted from an initial fit on a sparse grid to select optimal grid points in an iterative manner and is, therefore, called the iterative variance minimizing grid approach. We demonstrate the method in the case of six-dimensional intermolecular potential energy surfaces (PESs) fitted to ab initio computed interaction energies. The number of required grid points is reduced by roughly a factor of two in comparison to alternative systematic sampling methods. The method is not limited to fitting PESs and can be applied to any cases of fitting parametric models where data points may be chosen freely but are expensive to obtain.

Single-photon emitters in hexagonal boron nitride: a review of progress

This report summarizes progress made in understanding properties such as zero-phonon-line energies, emission and absorption polarizations, electron-phonon couplings, strain tuning and hyperfine coupling of single photon emitters in hexagonal boron nitride. The primary aims of this research are to discover the chemical nature of the emitting centres and to facilitate deployment in device applications. Critical analyses of the experimental literature and data interpretation, as well as theoretical approaches used to predict properties, are made. In particular, computational and theoretical limitations and challenges are discussed, with a range of suggestions made to overcome these limitations, striving to achieve realistic predictions concerning the nature of emitting centers. A symbiotic relationship is required in which calculations focus on properties that can easily be measured, whilst experiments deliver results in a form facilitating mass-produced calculations.

Ab Initio Extended Hartree-Fock plus Dispersion Method Applied to Dimers with Hundreds of Atoms

The Hartree-Fock plus dispersion plus first-order correlation (HFDc⁽¹⁾) method consists in augmenting the HF interaction energy by the correlation part of the first-order interaction energy and the second-order dispersion and exchange-dispersion energies. All of the augmentation terms are computed using the symmetry-adapted perturbation theory based on density functional theory description of monomers [SAPT(DFT)]; thus, HFDc⁽¹⁾ is a fully ab initio method. A partly empirical version of this method, HFD_asc⁽¹⁾, uses a damped asymptotic expansion for the dispersion plus exchange-dispersion term fitted to SAPT(DFT) ab initio values. The HFDc⁽¹⁾ interaction energies for dimers in the S22, S66, S66x8, NCCE31, IonHB, and UD-ARL benchmark data sets are more accurate than those given by most ab initio methods with comparable costs. HFDc⁽¹⁾ can be used routinely for dimers with nearly 200 atoms, such as included in the S12L benchmark set, giving results comparable to those obtained by the most expensive methods applicable.

Second-Order Exchange-Dispersion Energy Based on a Multireference Description of Monomers

We present a method for calculation of the second-order exchange-dispersion energy in the framework of the symmetry-adapted perturbation theory (SAPT) for weakly interacting monomers described with multiconfigurational wave functions. The proposed formalism is based on response properties obtained from extended random phase approximation (ERPA) equations and assumes the single-exchange (S²) approximation. The approach is applicable to closed shell systems where static correlation cannot be neglected or to systems in nondegenerate excited states. We examine the new method in combination with either generalized valence bond perfect pairing (GVB) or complete active space self-consistent field (CASSCF) description of the interacting monomers. For model multireference dimers in ground states (H₂···H₂, Be···Be, He···H₂), exchange-dispersion energies are reproduced accurately. For the interaction between the excited hydrogen molecule and the helium atom we found unacceptably large errors which is attributed to the neglect of diagonal double excitations in the employed approximation to the linear response function.

On the applicability of functional-group symmetry-adapted perturbation theory and other partitioning models for chiral recognition - the case of popular drug molecules interacting with chiral phases

The applicability of symmetry-adapted perturbation theory (SAPT) and functional-group SAPT (F-SAPT) to study chiral recognition is investigated on an example of three popular chiral drug molecules: ibuprofen, norepinephrine, and baclofen, interacting with phenethylamine or proline - two molecules that are often used as chiral phases in chromatography. The comparison of the F-SAPT with the interacting quantum atoms (IQA) approach is also provided. Accurate estimation of energetic differences of the non-covalent intermolecular complexes composed of two chiral molecules is a necessary prerequisite for the possibility of a prediction of the chiral recognition. The SAPT method with interacting molecules described on the density functional theory level provides accurate total interaction energies, while the F-SAPT approach is the most useful in determining which functional groups are responsible for strengthening or weakening of the interaction between chiral molecules. The largest difference in the interaction energies has been calculated for the baclofen-phenethylamine and norepinephrine-phenethylamine pairs, while the smallest for the ibuprofen-proline and baclofen-proline ones. In most cases, the intermolecular interaction is found to be composed of a strong directional hydrogen bond, which was stabilized by two or more weaker non-covalent interactions between groups (in accordance with the phenomological three-point rule), but in several cases more subtle factors are responsible for larger stability of one diastereoisomer, like the stabilization of the conformation involving two noninteracting functional groups attached to a chiral atom through intramolecular attraction. Additionally, the simulated IR spectra were analyzed for all pairs of diastereoisomeric complexes and the red- and blue-shifts of characteristic bond vibrations were discussed in the context of inter-group interactions.

A Linear-Scaling Method for Noncovalent Interactions: An Efficient Combination of Absolutely Localized Molecular Orbitals and a Local Random Phase Approximation Approach

A novel method for the accurate and efficient calculation of interaction energies in weakly bound complexes composed of a large number of molecules is presented. The new ALMO+RPAd method circumvents the prohibitive scaling of coupled cluster singles and doubles while still providing similar accuracy across a diverse range of weakly bound chemical systems. Linear-scaling procedures for the Fock build are given utilizing absolutely localized molecular orbitals (ALMOs), resulting in the a priori exclusion of basis set superposition errors. A bespoke data structure and algorithm using density fitting are described, leading to linear scaling for the storage and computation of the two-electron integrals. Electron correlation is included through a new, linear-scaling pairwise local random phase approximation approach, including exchange interactions, and decomposed into purely dispersive excitations (RPAxd). Collectively, these allow meaningful decomposition of the interaction energy into physically distinct contributions: electrostatic, polarization, charge transfer, and dispersion. Comparison with symmetry-adapted perturbation theory shows good qualitative agreement. Tests on various dimers and the S66 benchmark set demonstrate results within 0.5 kcal mol^-1 of coupled cluster singles and doubles results. On a large cluster of water molecules, we achieve calculations involving over 3500 orbital and 12,000 auxiliary basis functions in under 10 min on a single CPU core.

HFLD: A Nonempirical London Dispersion-Corrected Hartree-Fock Method for the Quantification and Analysis of Noncovalent Interaction Energies of Large Molecular Systems †

A nonempirical quantum mechanical method for the efficient and accurate quantification and analysis of intermolecular interactions is presented and tested on existing benchmark sets. The leading idea here is to focus on the intermolecular part of the correlation energy that contains the all-important London dispersion (LD) interaction. To keep the cost of the method low, essentially at the level of a Hartree-Fock (HF) calculation, the intramolecular part of the correlation energy is neglected. We also neglect the nondispersive parts of the intermolecular correlation energy. This scheme that we denote as Hartree-Fock plus London dispersion (HFLD) can be readily realized on the basis of the recently reported multilevel implementation of the domain-based local pair natural orbital coupled-cluster (DLPNO-CC) theory in conjunction with the well-established local energy decomposition (LED) analysis. The accuracy and efficiency of the HFLD method are evaluated on rare gas dimers, on the S66 and L7 benchmark sets of noncovalent interactions, and on an additional set (LP14) consisting of bulky Lewis pairs held together by intermolecular interactions of various strengths, with interaction energies ranging from -8 to -107 kcal/mol. It is first shown that the LD energy calculated with this approach is essentially identical to that obtained from the full DLPNO-CCSD(T)/LED calculation, with a mean absolute error of 0.2 kcal/mol on the S66 benchmark set. Moreover, in terms of the overall interaction energies, the HFLD method shows an efficiency that is comparable to that of the HF method, while retaining an accuracy between that of the DLPNO-CCSD and DLPNO-CCSD(T) schemes. Since the underlying DLPNO-CCSD method is linear scaling with respect to the system size, the HFLD approach also does not lead to new bottlenecks for large systems. As an illustrative example of its efficiency, the HFLD scheme was applied to the interaction between the substrate and the residues in the active site of the cyclohexanone monooxygenase enzyme. The excellent cost/performance ratio indicates that the HFLD method opens new avenues for the accurate calculation and analysis of noncovalent interaction energies in large molecular systems.

Ewald-based methods for Gaussian integral evaluation: application to a new parameterization of GEM

The development of accurate potentials for computational simulations has been an active area of research. Our group has been involved in the development of the Gaussian electrostatic model (GEM), a force field based on molecular densities. The philosophy of GEM is based on the pioneering work of N. Gresh and co-workers of the reproduction of individual inter-molecular interaction components obtained from quantum mechanical (QM) energy decomposition analysis (EDA). The molecular densities used in GEM are represented by fitting accurate QM molecular densities using auxiliary basis sets (comprised of Hermite Gaussians). The use of these molecular densities results in the need to evaluate a large number of Gaussian integrals. We have previously shown that the particle-mesh Ewald (PME), and fast Fourier Poisson (FFP) methods can be used for efficiently evaluating these types of integrals. Here, we present the latest parameterization of GEM* and its application for an extensive study of PME and FFP for molecular dynamics (MD) simulations using a hybrid version of our potential, GEM*. The temperature dependence of various bulk properties is presented and discussed, as well as the effect of various parameters affecting the performance/accuracy of both methods.

Physical nature of silane⋯carbene dimers revealed by state-of-the-art ab initio calculations

Using the SAPT2 + 3(CCD)δMP2 method in complete basis set (CBS) limit, it is shown that the interactions in the recently studied silane⋯carbene dimers are mainly dispersive in nature. Consequently, slow convergence of dispersion energy also forces slow convergence of the interaction energy. Therefore, obtaining very accurate values requires extrapolation of the correlation part to the CBS limit. The most accurate values obtained at the CCSD(T)/CBS level of theory show that the studied silane⋯carbene dimers are rather weakly bound, with interaction energies ranging from about -1.9 to -1.3 kcal/mol. Comparing to CCSD(T)/CBS, it will be shown that SCS-MP2 and MP2C methods clearly underestimate and methods based on SAPT2+ and having some third-order corrections, as well as the MP2 method, overestimate values of interaction energies. Popular SAPT(DFT) method performs better than SCS-MP2 and MP2C; nevertheless, underestimation is still considerable. The underestimation is slightly quenched if third-order dispersion energy and its exchange counterpart is added to the SAPT(DFT). The closest value of CCSD(T)/CBS has been given by the SAPT2 + (3)(CCD)δMP2 method in quadruple-ζ basis set. © 2019 Wiley Periodicals, Inc.

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.

Interactions of benzene, naphthalene, and azulene with alkali-metal and alkaline-earth-metal atoms for ultracold studies

We consider collisional properties of polyatomic aromatic hydrocarbon molecules immersed into ultracold atomic gases and investigate intermolecular interactions of exemplary benzene, naphthalene, and azulene with alkali-metal (Li, Na, K, Rb, and Cs) and alkaline-earth-metal (Mg, Ca, Sr, and Ba) atoms. We apply the state-of-the-art ab initio techniques to compute the potential energy surfaces (PESs). We use the coupled cluster method restricted to single, double, and noniterative triple excitations to reproduce the correlation energy and the small-core energy-consistent pseudopotentials to model the scalar relativistic effects in heavier metal atoms. We also report the leading long-range isotropic and anisotropic dispersion and induction interaction coefficients. The PESs are characterized in detail, and the nature of intermolecular interactions is analyzed and benchmarked using symmetry-adapted perturbation theory. The full three-dimensional PESs are provided for the selected systems within the atom-bond pairwise additive representation and can be employed in scattering calculations. The present study of the electronic structure is the first step toward the evaluation of prospects for sympathetic cooling of polyatomic aromatic molecules with ultracold atoms. We suggest azulene, an isomer of naphthalene which possesses a significant permanent electric dipole moment and optical transitions in the visible range, as a promising candidate for electric field manipulation and buffer-gas or sympathetic cooling.

Accurate and Efficient ab Initio Calculations for Supramolecular Complexes: Symmetry-Adapted Perturbation Theory with Many-Body Dispersion

Symmetry-adapted perturbation theory (SAPT) provides a chemically meaningful energy decomposition scheme for nonbonded interactions that is useful for interpretive purposes. Although formally a dimer theory, we have previously introduced an "extended" version (XSAPT) that incorporates many-body polarization via self-consistent charge embedding. Here, we extend the XSAPT methodology to include nonadditive dispersion, using a modified form of the many-body dispersion (MBD) method of Tkatchenko and co-workers. Dispersion interactions beyond the pairwise atom-atom approximation improve total interaction energies even in small systems, and for large π-stacked complexes these corrections can amount to several kilocalories per mole. The XSAPT+MBD method introduced here achieves errors of ≲1 kcal/mol (as compared to high-level ab initio benchmarks) for the L7 data set of large dispersion-bound complexes and ≲4 kcal/mol (as compared to experiment) for the S30L data set of host-guest complexes. This is superior to the best contemporary density functional methods for noncovalent interactions, at comparable or lower cost. XSAPT+MBD represents a promising method for application to supramolecular assemblies, including protein-ligand binding.

Dispersion Energy from Local Polarizability Density

A simple nonlocal functional for calculation of dispersion energies is proposed. Compared to a similar formula used earlier, we introduced a regularization to remove its singularities and used a dynamic polarizability density similar to those in the so-called van der Waals density functionals. The performance of the new functional is tested on dispersion energies for a set of representative dimers, and it is found that it is significantly more accurate than published nonlocal functionals.

Dimerization Behavior of Methyl Chlorophyllide a as the Model of Chlorophyll a in the Presence of Water Molecules-Theoretical Study

A dimerization of methyl chlorophyllide a molecules and a role of water in stabilization and properties of methyl chlorophyllide a dimers were studied by means of symmetry-adapted perturbation theory (SAPT), functional-group SAPT (F-SAPT), density-functional theory (DFT), and time-dependent DFT approaches. The quantification of various types of interactions, such as π-π stacking, coordinative, and hydrogen bonding by applying the F-SAPT energy decomposition scheme shows the major role of the magnesium atom and the pheophytin macrocycle in the stability of the complex. The examination of interaction energy components with respect to a mutual orientation of monomers and in the presence or absence of water molecules reveals that the dispersion energy is the main binding factor of the interaction, while water molecules tend to weaken the attraction between methyl chlorophyllide a species. The dimerization can be seen in computed UV-vis spectra, and results in a doubling of the lowest peaks, as compared to the monomer spectrum, and in an intensity rise of the lowest 1.8 and 2.4 eV peaks at a cost of the 3.5 eV peaks for the majority of dimer configurations. The complexation of water has little effect on the peaks' position; however, it affects the overall shape of simulated spectra through changes in peak intensities, which is strongly dependent on the structure of the complex. The VCD spectra for the dimers show several characteristic features attributed to the interaction of substituting groups and/or water ligand attached to macrocycle groups belonging to different monomers. VCD is sensitive to the type of the formed dimer, but not to the number of water molecules it contains. This and several other features, as well as the differential UV-vis spectra, may serve as the indicator of the presence of a given dimer structure in the experiment.

ZMP-SAPT: DFT-SAPT using ab initio densities

Symmetry Adapted Perturbation Theory (SAPT) has become an important tool when predicting and analyzing intermolecular interactions. Unfortunately, Density Functional Theory (DFT)-SAPT, which uses DFT for the underlying monomers, has some arbitrariness concerning the exchange-correlation potential and the exchange-correlation kernel involved. By using ab initio Brueckner Doubles densities and constructing Kohn-Sham orbitals via the Zhao-Morrison-Parr (ZMP) method, we are able to lift the dependence of DFT-SAPT on DFT exchange-correlation potential models in first order. This way, we can compute the monomers at the coupled-cluster level of theory and utilize SAPT for the intermolecular interaction energy. The resulting ZMP-SAPT approach is tested for small dimer systems involving rare gas atoms, cations, and anions and shown to compare well with the Tang-Toennies model and coupled cluster results.

Homogeneous Molecular Systems are Positively Cooperative, but Charged Molecular Systems are Negatively Cooperative

Molecular systems bound together through noncovalent interactions are ubiquitous in nature, many of which are involved in essential life processes, yet little is known about the principles governing their structure, stability, and function. Cooperativity as one of the intrinsic properties in these systems plays a key role. In this work, on the basis of our recent quantification scheme of the cooperativity effect, we present a general pattern to identify which systems are positively cooperative and which are negatively cooperative. We show that cooperativity in homogeneous molecular systems is positive, but cooperativity in charged molecular systems is negative. We also employ analytical tools from energetics and information perspectives to appreciate the origin of the cooperativity effect. We find that positive cooperativity is dominated by the exchange-correlation interaction and steric effect, whereas negative cooperativity is governed by the electrostatic interaction. Our results should have strong implications for better understanding molecular recognition, protein folding, signal transduction, allosteric regulation, and other processes.

Substituent effects in the so-called cationπ interaction of benzene and its boron-nitrogen doped analogues: overlooked role of σ-skeleton

Despite massive efforts to pinpoint the substituent effects in the so-called cationπ systems, no consensus has been yet reached on how substituents exercise their effects in the interaction of the aromatic molecule with the metal ion. The π-polarization (the Hunter model) and the direct local effect (the Wheeler-Houk model) are two lines of thought applied to this problem, but the justification of both approaches is based on insufficiently proven assumptions and approximations. In order to shed more light on this issue we propose a new approach which enables us to gauge directly the energetic trends resulting from the interaction of the ring with the cation. In our method we add one more partitioning level to the interacting quantum atoms (IQA) scheme and decompose the IQA interaction energies into contributions resulting from σ and π electron densities of the aromatic ring. The new approach, which is named partitioned-IQA, abbreviated as p-IQA, has been applied to complexes of derivatives of benzene or azaborine interacting with a sodium cation. The p-IQA approach reveals that in these systems both σ and π electronic moieties are polarized. Interestingly, for the majority of cases the σ-polarization outweighs the π one, contrary to the Hunter model. However, the Wheeler-Houk model is not precise, either, since the σ-polarization shows some degree of non-locality. In addition, the substituents are found to have a negligible influence on the ring orbital-overlapping capability, i.e. the covalency. Therefore, the substituent effect in the cationπ interaction is a nonlocal classical effect, indicating that neither Hunter model nor Wheeler-Houk model is able to fully describe all the aspects of the substituent effects. The p-IQA conclusions for the considered systems have been compared with the results from the functional-group SAPT (F-SAPT) method. We believe that the presented partitioning in the IQA framework will provide a deeper insight into the substituent effects in the cationπ interactions, which is beyond the σ-π atomic charge population separation.

Theoretical study of the complexes of dichlorobenzene isomers with argon. II. SAPT analysis of the intermolecular interaction

The interaction of argon with dichlorobenzene isomers (DCB-Ar) has been analyzed with the help of the symmetry-adapted perturbation theory based on the density functional description of monomer properties (DFT-SAPT). The global potential energy surface (PES) of these complexes determined from the DFT-SAPT interaction energy (E_int) values has been compared to the CCSD(T) (coupled cluster method including single and double excitations with perturbative triple excitations) PES reported in the companion Paper I [J. Makarewicz and L. Shirkov, J. Chem. Phys. 150, 074301 (2019)]. The equilibrium structures and the binding energies found using DFT-SAPT and CCSD(T) methods combined with adequate basis sets are in good agreement. Besides DCB-Ar, we confirmed that DFT-SAPT gives accurate values of these quantities for other complexes containing an aromatic molecule and Ar. However, DFT-SAPT PES of DCB-Ar is flatter than the corresponding CCSD(T) one. As a result, the intermolecular vibrational energies are systematically underestimated. The analytical form of the important interrelations between SAPT components of E_int, established previously by us [J. Makarewicz and L. Shirkov, J. Chem. Phys. 144, 204115 (2016)], has been approved for the DCB-Ar complexes. Simplified SAPT models based on these relations have been employed to explain physical reasons for differences in the structures and the binding energies of DCB-Ar isomers. It is shown that the equilibrium distance of Ar to DCB plane and the binding energy are determined mainly by dispersion energy. The shift of Ar toward Cl is caused by both exchange and dispersion terms.

Second-Order Dispersion Energy Based on Multireference Description of Monomers

We propose a method for calculating a second-order dispersion energy for weakly interacting multireference systems in arbitrary electronic states. It is based on response properties obtained from extended random phase approximation equations. The introduced formalism is general and requires only one- and two-particle reduced density matrices of monomers. We combine the new method with either generalized valence bond perfect pairing (GVB) or complete active space (CAS) self-consistent field description of the interacting systems. In addition to a general scheme, three approximations, leading to significant reduction of the computational cost, are developed by exploiting Dyall partitioning of the monomer Hamiltonians. For model multireference systems (H₂···H₂ and Be···Be) the method is accurate, unlike its single-reference-based counterpart. Neither GVB nor CAS description of single-reference monomers improves the dispersion energy with respect to the Hartree-Fock-based results.