Using Kohn−Sham Orbitals in Symmetry-Adapted Perturbation Theory to Investigate Intermolecular Interactions

Optimization of damping function parameters for -D3 and -D4 dispersion models for Hartree-Fock based symmetry-adapted perturbation theory

Symmetry-adapted perturbation theory (SAPT) directly computes intermolecular interaction energy in terms of electrostatics, exchange-repulsion, induction/polarization, and London dispersion components. In SAPT based on Hartree-Fock ("SAPT0") or based on density functional theory, the most time-consuming step is the computation of the dispersion terms. Previous work has explored the replacement of these expensive dispersion terms with simple damped asymptotic models. We recently examined [Schriber et al. J. Chem. Phys. 154, 234107 (2021)] the accuracy of SAPT0 when replacing its dispersion term with Grimme's popular -D3 correction, reducing the computational cost scaling from O(N5) to O(N3). That work optimized damping function parameters for SAPT0-D3/jun-cc-pVDZ using estimates of the coupled-cluster complete basis set limit [CCSD(T)/CBS] on a 8299 dimer dataset. Here, we explore the accuracy of SAPT0-D3 with additional basis sets, along with an analogous model using -D4. Damping parameters are rather insensitive to basis sets, and the resulting SAPT0-D models are more accurate on average for total interaction energies than SAPT0. Our results are surprising in several respects: (1) improvement of -D4 over -D3 is negligible for these systems, even charged systems where -D4 should, in principle, be more accurate; (2) addition of Axilrod-Teller-Muto terms for three-body dispersion does not improve error statistics for this test set; and (3) SAPT0-D is even more accurate on average for total interaction energies than the much more computationally costly density functional theory based SAPT [SAPT(DFT)] in an aug-cc-pVDZ basis. However, SAPT0 and SAPT0-D3/D4 interaction energies benefit from significant error cancellation between exchange and dispersion terms.

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.

Stabilization of the Protein Structure by the Many-Body Cooperative Effect in the NH/π Hydrogen-bonding Tryptophan Triad

The indole ring of tryptophan can form NH/π hydrogen bonds, acting both as a hydrogen donor at the NH group in the pyrrole subring and as a hydrogen acceptor at the benzene subring. In the structural core of the trimeric stable protein Pholiota squarrosa lectin (PhoSL), three indoles are symmetrically arranged and form NH/π hydrogen bonds among each other. Here, we conducted quantum chemical calculations on this indole triad by using various methods and basis sets. The analyses revealed cooperativity in triad formation, with the many-body effect contributing approximately -2 kcal mol-1, which significantly stabilizes this protein. Symmetry-adapted perturbation theory ascribed this effect to the induced polarization. The electrostatic potential and atomic charges indeed revealed a charge redistribution through the NH/π hydrogen bond, which was favorable for triad formation.

Balance between Physical Interpretability and Energetic Predictability in Widely Used Dispersion-Corrected Density Functionals

We assess the performance of different dispersion models for several popular density functionals across a diverse set of noncovalent systems, ranging from the benzene dimer to molecular crystals. By analyzing the interaction energies and their individual components, we demonstrate that there exists variability across different systems for empirical dispersion models, which are calibrated for reproducing the interaction energies of specific systems. Thus, parameter fitting may undermine the underlying physics, as dispersion models rely on error compensation among the different components of the interaction energy. Energy decomposition analyses reveal that, the accuracy of revPBE-D3 for some aqueous systems originates from significant compensation between dispersion and charge transfer energies. However, revPBE-D3 is less accurate in describing systems where error compensation is incomplete, such as the benzene dimer. Such cases highlight the propensity for unpredictable behavior in various dispersion-corrected density functionals across a wide range of molecular systems, akin to the behavior of force fields. On the other hand, we find that SCAN-rVV10, a targeted-dispersion approach, affords significant reductions in errors associated with the lattice energies of molecular crystals, while it has limited accuracy in reproducing structural properties. Given the ubiquitous nature of noncovalent interactions and the key role of density functional theory in computational sciences, the future development of dispersion models should prioritize the faithful description of the dispersion energy, a shift that promises greater accuracy in capturing the underlying physics across diverse molecular and extended systems.

Benchmarking Swaths of Intermolecular Interaction Components with Symmetry-Adapted Perturbation Theory

A benchmark database for interaction energy components of various noncovalent interactions (NCIs) along their dissociation curve is one of the essential needs in theoretical chemistry, especially for the development of force fields and machine-learning methods. We utilize DFT-SAPT or SAPT(DFT) as one of the most accurate methods to generate an extensive stock of the energy components, including dispersion energies extrapolated to the complete basis set limit (CBS). Precise analyses of the created data, and benchmarking the total interaction energies against the best available CCSD(T)/CBS values, reveal different aspects of the methodology and the nature of NCIs. For example, error cancellation effects between the S2 approximation and nonexact xc-potentials occur, and large charge transfer energies in some systems, including heavy atoms, can explain the lower accuracy of DFT-SAPT. This method is perfect for neutral complexes containing light nonmetals, while other systems with heavier atoms should be treated carefully. In the last part, a representative data set for all NCIs is extracted from the original data.

DMFF: An Open-Source Automatic Differentiable Platform for Molecular Force Field Development and Molecular Dynamics Simulation

In the simulation of molecular systems, the underlying force field (FF) model plays an extremely important role in determining the reliability of the simulation. However, the quality of the state-of-the-art molecular force fields is still unsatisfactory in many cases, and the FF parameterization process largely relies on human experience, which is not scalable. To address this issue, we introduce DMFF, an open-source molecular FF development platform based on an automatic differentiation technique. DMFF serves as a powerful tool for both top-down and bottom-up FF development. Using DMFF, both energies/forces and thermodynamic quantities such as ensemble averages and free energies can be evaluated in a differentiable way, realizing an automatic, yet highly flexible FF optimization workflow. DMFF also eases the evaluation of forces and virial tensors for complicated advanced FFs, helping the fast validation of new models in molecular dynamics simulation. DMFF has been released as an open-source package under the LGPL-3.0 license and is available at https://github.com/deepmodeling/DMFF.

Physical mechanisms of intermolecular interactions from symmetry-adapted perturbation theory

Symmetry-adapted perturbation theory (SAPT) is a method for computational studies of noncovalent interactions between molecules. This method will be discussed here from the perspective of establishing the paradigm for understanding mechanisms of intermolecular interactions. SAPT interaction energies are obtained as sums of several contributions. Each contribution possesses a clear physical interpretation as it results from some specific physical process. It also exhibits a specific dependence on the intermolecular separation R. The four major contributions are the electrostatic, induction, dispersion, and exchange energies, each due to a different mechanism, valid at any R. In addition, at large R, SAPT interaction energies are seamlessly connected with the corresponding terms in the asymptotic multipole expansion of interaction energy in inverse powers of R. Since such expansion explicitly depends on monomers' multipole moments and polarizabilities, this connection provides additional insights by rigorously relating interaction energies to monomers' properties.

Implementation of Symmetry-Adapted Perturbation Theory based on density functional theory and using hybrid exchange-correlation kernels for dispersion terms

We report the implementation of a symmetry-adapted perturbation theory algorithm based on a density functional theory description of the monomers [SAPT(DFT)]. The implementation adopts a density-fitting treatment of hybrid exchange-correlation kernels to enable the description of monomers with hybrid functionals, as in the algorithm by Bukowski, Podeszwa, and Szalewicz [Chem. Phys. Lett. 414, 111(2005)]. We have improved the algorithm by increasing numerical stability with QR factorization, and optimized the computation of the exchange-correlation kernel with its 2-index density-fitted representation. The algorithm scales as O(N5) formally and is usable for systems with up to ∼3000 basis functions, as demonstrated forthe C60-buckycatcher complex with the aug-cc-pVDZ basis set. The hybrid-kernel-based SAPT(DFT) algorithm is shown to be as accurate as SAPT(DFT) implementations based on local effective exact exchange potentials obtained from the local Hartree-Fock (LHF) method, while avoiding the lower-scaling [O(N4)] but iterative and sometimes hard-to-converge LHF process. The hybrid-kernel algorithm outperforms Hartree-Fock-based SAPT (SAPT0) for the S66 test set, and its accuracy is comparable to the many-body perturbation theory based SAPT2+ approach, which scales as O(N7), although SAPT2+ exhibits a more narrow distribution of errors.

Factors influencing hydrogen peroxide versus water inclusion in molecular crystals

Hydrate formation is often unavoidable during crystallization, leading to performance degradation of pharmaceuticals and energetics. In some cases, water molecules trapped within crystal lattices can be substituted for hydrogen peroxide, improving the solubility of drugs and detonation performance of explosives. The present work compares hydrates and hydrogen peroxide solvates in two ways: (1) analyzing structural motifs present in crystal structures accessed from the Cambridge Structural Database and (2) developing potential energy surfaces for water and hydrogen peroxide interacting with functional groups of interest at geometries relevant to the solid state. By elucidating fundamental differences in local interactions that can be formed with molecules of hydrogen peroxide and/or water, the analyses presented here provide a foundation for the design and selection of candidate molecules for the formation of hydrogen peroxide solvates.

Towards the simulation of large scale protein-ligand interactions on NISQ-era quantum computers

We explore the use of symmetry-adapted perturbation theory (SAPT) as a simple and efficient means to compute interaction energies between large molecular systems with a hybrid method combining NISQ-era quantum and classical computers. From the one- and two-particle reduced density matrices of the monomer wavefunctions obtained by the variational quantum eigensolver (VQE), we compute SAPT contributions to the interaction energy [SAPT(VQE)]. At first order, this energy yields the electrostatic and exchange contributions for non-covalently bound systems. We empirically find from ideal statevector simulations that the SAPT(VQE) interaction energy components display orders of magnitude lower absolute errors than the corresponding VQE total energies. Therefore, even with coarsely optimized low-depth VQE wavefunctions, we still obtain sub kcal mol-1 accuracy in the SAPT interaction energies. In SAPT(VQE), the quantum requirements, such as qubit count and circuit depth, are lowered by performing computations on the separate molecular systems. Furthermore, active spaces allow for large systems containing thousands of orbitals to be reduced to a small enough orbital set to perform the quantum portions of the computations. We benchmark SAPT(VQE) (with the VQE component simulated by ideal statevector simulators) against a handful of small multi-reference dimer systems and the iron center containing human cancer-relevant protein lysine-specific demethylase 5 (KDM5A).

Tuning the metal-ligand bond in the σ-complexes of stannylenes and azabenzenes

The metal-ligand bond in a set of 60 σ-complexes has been investigated by electronic structure computations. These σ-complexes originate from the unique combination of 12 stannylenes (SnX₂ ) with five azabenzene ligands (pyridine, pyrazine, pyrimidine, pyridazine, and s-triazine), where the nitrogen center of the ligand acts as σ-donor and the tin(II) center as σ-acceptor in a 1:1 fashion. The Sn ← N bond and the total interaction between the stannylene and azabenzene moieties of the σ-complexes are characterized in depth to relate the Sn ← N strength to the substitution pattern at SnX₂ and to the number and the positioning of N atoms in the azabenzenes. Such X substituents as (iso)cyano and trifluoromethyl groups enhance the interaction strength, while the presence of alkyl, phenyl, and silyl substituents in SnX₂ diminishes the stability of σ-complexes. A gradual weakening of the total interaction is associated with the growing number of N atoms in the azabenzenes, while the N-atom positioning in pyridazine is particularly effective in strengthening the interaction with stannylenes. Variations in the Sn ← N bond strength usually follow those in the total interaction between the moieties but the interacting quantum atoms picture of Sn ← N reveals certain intriguing exceptions.

CONI-Net: Machine Learning of Separable Intermolecular Force Fields

Noncovalent interactions (NCIs) play an essential role in soft matter and biomolecular simulations. The ab initio method symmetry-adapted perturbation theory allows a precise quantitative analysis of NCIs and offers an inherent energy decomposition, enabling a deeper understanding of the nature of intermolecular interactions. However, this method is limited to small systems, for instance, dimers of molecules. Here, we present a scale-bridging approach to systematically derive an intermolecular force field from ab initio data while preserving the energy decomposition of the underlying method. We apply the model in molecular dynamics simulations of several solvents and compare two predicted thermodynamic observables-mass density and enthalpy of vaporization-to experiments and established force fields. For a data set limited to hydrocarbons, we investigate the extrapolation capabilities to molecules absent from the training set. Overall, despite the affordable moderate quality of the reference ab initio data, we find promising results. With the straightforward data set generation procedure and the lack of target data in the fitting process, we have developed a method that enables the rapid development of predictive force fields with an extra dimension of insights into the balance of NCIs.

Simplified tuning of long-range corrected density functionals for use in symmetry-adapted perturbation theory

Long considered a failure, second-order symmetry-adapted perturbation theory (SAPT) based on Kohn-Sham orbitals, or SAPT0(KS), can be resurrected for semiquantitative purposes using long-range corrected density functionals whose asymptotic behavior is adjusted separately for each monomer. As in other contexts, correct asymptotic behavior can be enforced via "optimal tuning" based on the ionization energy theorem of density functional theory, but the tuning procedure is tedious, expensive for large systems, and comes with a troubling dependence on system size. Here, we show that essentially identical results are obtained using a fast, convenient, and automated tuning procedure based on the size of the exchange hole. In conjunction with "extended" (X)SAPT methods that improve the description of dispersion, this procedure achieves benchmark-quality interaction energies, along with the usual SAPT energy decomposition, without the hassle of system-specific tuning.

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.

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.

Structural and Optical Properties of Struvite. Elucidating Structure of Infrared Spectrum in High Frequency Range

Study of structure and optical properties of magnesium ammonium phosphate hexahydrate crystal known as struvite is presented. Experimentally determined infrared (IR) and ultraviolet-visible (UV-vis) spectra are compared with the theoretical predictions of density functional methods. Examination of the interatomic bond lengths, Mulliken atomic charges, and binding energies of water in the magnesium hexahydrate cation, together with the analysis of the hydrogen bond pattern have allowed us to explain a special feature of the IR spectrum of struvite, a blueshift of the band corresponding to the O-H stretching mode. This mode has been assigned to a "dangling" hydroxyl group in one of the water molecules in magnesium hexahydrate. Using experimentally obtained UV-vis spectrum and performing Tauc plots analysis, optical bandgap of struvite has been narrowed to a range from 5.92 to 6.06 eV.

Toward Simple, Predictive Understanding of Protein-Ligand Interactions: Electronic Structure Calculations on Torpedo Californica Acetylcholinesterase Join Forces with the Chemist's Intuition

Contemporary efforts for empirically-unbiased modeling of protein-ligand interactions entail a painful tradeoff - as reliable information on both noncovalent binding factors and the dynamic behavior of a protein-ligand complex is often beyond practical limits. We demonstrate that information drawn exclusively from static molecular structures can be used for reproducing and predicting experimentally-measured binding affinities for protein-ligand complexes. In particular, inhibition constants (Ki) were calculated for seven different competitive inhibitors of Torpedo californica acetylcholinesterase using a multiple-linear-regression-based model. The latter, incorporating five independent variables - drawn from QM cluster, DLPNO-CCSD(T) calculations and LED analyses on the seven complexes, each containing active amino-acid residues found within interacting distance (3.5 Å) from the corresponding ligand - is shown to recover 99.9% of the sum of squares for measured Ki values, while having no statistically-significant residual errors. Despite being fitted to a small number of data points, leave-one-out cross-validation statistics suggest that it possesses surprising predictive value (Q2LOO=0.78, or 0.91 upon removal of a single outlier). This thus challenges ligand-invariant definitions of active sites, such as implied in the lock-key binding theory, as well as in alternatives highlighting shape-complementarity without taking electronic effects into account. Broader implications of the current work are discussed in dedicated appendices.

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.

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.

Cyclic versus straight chain oligofuran as sensor: A detailed DFT study

This study presents a novel approach for exploring the sensitivity and selectivity of cyclic oligofuran (5/6/7CF) toward gaseous analytes and their comparison with straight chain analogues (5/6/7SF). The work is not only vital to understand the superior sensitivity but also for rational design of new sensors based on cyclic ring structures of oligofuran. Interaction of cyclic and straight chain oligofuran with NH₃, CO, CO₂, N₂H₄, HCN, H₂O₂, H₂S, CH₄, CH₃OH, SO₂, SO₃ and H₂O analytes is studied via DFT calculation at B3LYP-D3/6-31++G (d, p) level of theory. The sensitivity and selectivity are illustrated by the thermodynamic parameters (E_bind, SAPT0 energies, NCI analysis), electronic properties (H-L gap, percentage of average energy gap, CHELPG charge transfer, DOS spectra), and UV-Vis analysis. All these properties are simulated at B3LYP/6-31G (d) level of theory while UV-Vis is calculated at TD-DFT method. Cyclic oligofurans have high binding energies with analytes compared to 5/6/7SF which corresponds to higher sensitivity of 5/6/7CF. Furthermore, the cyclization of oligofuran significantly improves the sensitivity and selectivity of the system. Alteration in electronic properties of 5/6/7CF and 5/6/7SF is remarkably high upon complexation with SO₂ and SO₃. Further the stability of rings (5, 6 and 7 membered cyclic oligofurans) and their SO₃ complexes is also confirmed by molecular dynamics calculations. The findings of the work clearly suggest that the cyclic geometry enhances not only sensitivity but also selectivity of conducting polymers (oligofuran).

Density Functional Theory as a Data Science

The development of density functional theory (DFT) functionals and physical corrections are reviewed focusing on the physical meanings and the semiempirical parameters from the viewpoint of data science. This review shows that DFT exchange-correlation functionals have been developed under many strict physical conditions with minimizing the number of the semiempirical parameters, except for some recent functionals. Major physical corrections for exchange-correlation function- als are also shown to have clear physical meanings independent of the functionals, though they inevitably require minimum semiempirical parameters dependent on the functionals combined. We, therefore, interpret that DFT functionals with physical corrections are the most sophisticated target functions that are physically legitimated, even from the viewpoint of data science.

Intermolecular Interactions in Ionic Crystals of Nucleobase Chlorides—Combining Topological Analysis of Electron Densities with Energies of Electrostatic Interactions

Understanding intermolecular interactions in crystals of molecular ions continues to be difficult. On the one hand, the analysis of interactions from the point of view of formal charges of molecules, similarly as it is commonly done for inorganic ionic crystals, should be performed. On the other hand, when various functional groups are present in the crystal, it becomes natural to look at the interactions from the point of view of hydrogen bonding, π…π stacking and many other kinds of non-covalent atom–atom bonding. Often, these two approaches seem to lead to conflicting conclusions. On the basis of experimental charge densities of cytosinium chloride, adeninium chloride hemihydrate, and guanine dichloride crystals, with the help of theoretical simulations, we have deeply analysed intermolecular interactions among protonated nucleobases, chloride anions and water molecules. Here, in the second paper of the series of the two (Kumar et al., 2018, IUCrJ 5, 449–469), we focus on applying the above two approaches to the large set of dimers identified in analysed crystals. To understand electrostatic interactions, we analysed electrostatic interaction energies (Ees) computed directly from molecular charge densities and contrasted them with energies computed only from net molecular charges, or from a sum of electric multipolar moments, to find the charge penetration contribution to Ees. To characterize non-covalent interactions we performed topological analyses of crystal electron densities and estimated their interaction energies (EEML) from properties of intermolecular bond critical points. We show that the overall crystal architecture of the studied compounds is governed by the tight packing principle and strong electrostatic attractions and repulsions between ions. Many ions are oriented to each other in a way to strengthen attractive electrostatic interactions or weaken strong repulsion, but not all of them. Numerous bond critical points and bond paths were found between ions, including nucleobase cations despite their overall repulsive interactions. It is clear there is no correlation between EEML and Ees. However, strong relation between EEML and the charge penetration component of Ees is observed. The relation holds regardless of interaction types or whether or not interacting molecules bear the same or opposite charges. Thus, a charge density-based approach for computing intermolecular interaction energies and the atom–atom approach to analyse non-covalent interactions do complement each other, even in ionic systems.

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.

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.

Molecular dimers of methane clathrates: ab initio potential energy surfaces and variational vibrational states

Motivated by the energetic and environmental relevance of methane clathrates, highly accurate ab initio potential energy surfaces (PESs) have been developed for the three possible dimers of the methane and water molecules: (H₂O)₂, CH₄·H₂O, and (CH₄)₂.

Theory and practice of modeling van der Waals interactions in electronic-structure calculations

The accurate description of long-range electron correlation, most prominently including van der Waals (vdW) dispersion interactions, represents a particularly challenging task in the modeling of molecules and materials. vdW forces arise from the interaction of quantum-mechanical fluctuations in the electronic charge density. Within (semi-)local density functional approximations or Hartree-Fock theory such interactions are neglected altogether. Non-covalent vdW interactions, however, are ubiquitous in nature and play a key role for the understanding and accurate description of the stability, dynamics, structure, and response properties in a plethora of systems. During the last decade, many promising methods have been developed for modeling vdW interactions in electronic-structure calculations. These methods include vdW-inclusive Density Functional Theory and correlated post-Hartree-Fock approaches. Here, we focus on the methods within the framework of Density Functional Theory, including non-local van der Waals density functionals, interatomic dispersion models within many-body and pairwise formulation, and random phase approximation-based approaches. This review aims to guide the reader through the theoretical foundations of these methods in a tutorial-style manner and, in particular, highlight practical aspects such as the applicability and the advantages and shortcomings of current vdW-inclusive approaches. In addition, we give an overview of complementary experimental approaches, and discuss tools for the qualitative understanding of non-covalent interactions as well as energy decomposition techniques. Besides representing a reference for the current state-of-the-art, this work is thus also designed as a concise and detailed introduction to vdW-inclusive electronic structure calculations for a general and broad audience.

On the importance of accounting for nuclear quantum effects in ab initio calibrated force fields in biological simulations

In many important processes in chemistry, physics, and biology the nuclear degrees of freedom cannot be described using the laws of classical mechanics. At the same time, the vast majority of molecular simulations that employ wide-coverage force fields treat atomic motion classically. In light of the increasing desire for and accelerated development of quantum mechanics (QM)-parameterized interaction models, we reexamine whether the classical treatment is sufficient for a simple but crucial chemical species: alkanes. We show that when using an interaction model or force field in excellent agreement with the "gold standard" QM data, even very basic simulated properties of liquid alkanes, such as densities and heats of vaporization, deviate significantly from experimental values. Inclusion of nuclear quantum effects via techniques that treat nuclear degrees of freedom using the laws of classical mechanics brings the simulated properties much closer to reality.

Protonated nucleobases are not fully ionized in their chloride salt crystals and form metastable base pairs further stabilized by the surrounding anions

This paper presents experimental charge-density studies of cytosinium chloride, adeninium chloride hemihydrate and guaninium dichloride crystals based on ultra-high-resolution X-ray diffraction data and extensive theoretical calculations. The results confirm that the cohesive energies of the studied systems are dominated by contributions from intermolecular electrostatic interactions, as expected for ionic crystals. Electrostatic interaction energies (Ees) usually constitute 95% of the total interaction energy. The Ees energies in this study were several times larger in absolute value when compared, for example, with dimers of neutral nucleobases. However, they were not as large as some theoretical calculations have predicted. This was because the molecules appeared not to be fully ionized in the studied crystals. Apart from charge transfer from chlorine to the protonated nucleobases, small but visible charge redistribution within the nucleobase cations was observed. Some dimers of singly protonated bases in the studied crystals, namely a cytosinium-cytosinium trans sugar/sugar edge pair and an adeninium-adeninium trans Hoogsteen/Hoogsteen edge pair, exhibited attractive interactions (negative values of Ees) or unusually low repulsion despite identical molecular charges. The pairs are metastable as a result of strong hydrogen bonding between bases which overcompensates the overall cation-cation repulsion, the latter being weakened due to charge transfer and molecular charge-density polarization.

First-order symmetry-adapted perturbation theory for multiplet splittings

We present a symmetry-adapted perturbation theory (SAPT) for the interaction of two high-spin open-shell molecules (described by their restricted open-shell Hartree-Fock determinants) resulting in low-spin states of the complex. The previously available SAPT formalisms, except for some system-specific studies for few-electron complexes, were restricted to the high-spin state of the interacting system. Thus, the new approach provides, for the first time, a SAPT-based estimate of the splittings between different spin states of the complex. We have derived and implemented the lowest-order SAPT term responsible for these splittings, that is, the first-order exchange energy. We show that within the so-called S² approximation commonly used in SAPT (neglecting effects that vanish as fourth or higher powers of intermolecular overlap integrals), the first-order exchange energies for all multiplets are linear combinations of two matrix elements: a diagonal exchange term that determines the spin-averaged effect and a spin-flip term responsible for the splittings between the states. The numerical factors in this linear combination are determined solely by the Clebsch-Gordan coefficients: accordingly, the S² approximation implies a Heisenberg Hamiltonian picture with a single coupling strength parameter determining all the splittings. The new approach is cast into both molecular-orbital and atomic-orbital expressions: the latter enable an efficient density-fitted implementation. We test the newly developed formalism on several open-shell complexes ranging from diatomic systems (Li⋯H, Mn⋯Mn, …) to the phenalenyl dimer.

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.

Extension of the interacting quantum atoms (IQA) approach to B3LYP level density functional theory (DFT)

An interaction between two atoms, bonded or non-bonded, consists of interatomic contributions: electrostatic energy, exchange energy and electronic correlation energy. Together with the intra-atomic energy of an atom, these contributions are the basic components of the Interacting Quantum Atom (IQA) energy decomposition scheme. Here, we investigate IQA's proper use in conjunction with an explicit implementation of the B3LYP functional. The recovery of the total molecular energy from the IQA components is emphasised, for the first time. A systematic study of three model systems of biological relevance, N-methylacetamide (NMA), the doubly capped tripeptide GlyGlyGly and an alloxan dimer, shows the stabilization effect of B3LYP on most of the interatomic exchange energies (V) compared to their Hartree-Fock values. Diagrams of exchange energies versus interatomic distance show the clustering of interactions, one cluster for each 1,n (n = 1 to 6 where the atoms are separated by n - 1 bonds). The positioning of some V values outside their expected cluster marks interesting interactions.

Physical Molecular Mechanics Method for Damped Dispersion

Damped dispersion can be a significant component of the interaction energy in many physical and chemical processes, for example, physisorption and noncovalent complexation. For physically interpreting and modeling such processes, it is convenient to have an analytic method to calculate damped dispersion that is readily applicable across the entire periodic table. Of the available methods to calculate damped dispersion energy for interacting systems with overlapping charge distributions, we select symmetry-adapted perturbation theory (SAPT) as providing a reasonable definition, and of the possible analytic forms, we choose the D3(BJ) method. However, the available parametrizations of D3(BJ) include not only damped dispersion energy but also corrections for errors in specific exchange-correlation functionals. Here we present a parametrization that provides a physical measure of damped dispersion without such density functional corrections. The method generalizes an earlier method of Pernal and co-workers to all elements from hydrogen to plutonium.

B–H⋯π: a nonclassical hydrogen bond or dispersion contact?

Quantum mechanical calculations disprove the attractive electrostatic nature of B–H⋯π motif and define it as dispersion-driven contact.