Intermolecular potential and rovibrational levels of Ar–HF from symmetry‐adapted perturbation theory

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.

The nature of the intermolecular interaction in (H2X)2 (X = O, S, Se)

Hydrogen bonds (HBs) are crucial non-covalent interactions in chemistry. Recently, the occurrence of an HB in (H2S)2 has been reported (Arunan et al., Angew. Chem., Int. Ed., 2018, 57, 15199), challenging the textbook view of H2S dimers as mere van der Waals clusters. We herein try to shed light on the nature of the intermolecular interactions in the H2O, H2S, and H2Se dimers via correlated electronic structure calculations, Symmetry Adapted Perturbation Theory (SAPT) and Quantum Chemical Topology (QCT). Although (H2S)2 and (H2Se)2 meet some of the criteria for the occurrence of an HB, potential energy curves as well as SAPT and QCT analyses indicate that the nature of the interaction in (H2O)2 is substantially different (e.g. more anisotropic) from that in (H2S)2 and (H2Se)2. QCT reveals that the HB in (H2O)2 includes substantial covalent, dispersion and electrostatic contributions, while the last-mentioned component plays only a minor role in (H2S)2 and (H2Se)2. The major contributions to the interactions of the dimers of H2S and H2Se are covalency and dispersion as revealed by the exchange-correlation components of QCT energy partitions. The picture yielded by SAPT is somewhat different but compatible with that offered by QCT. Overall, our results indicate that neither (H2S)2 nor (H2Se)2 are hydrogen-bonded systems, showing how the nature of intermolecular contacts involving hydrogen atoms evolves in a group down the periodic table.

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.

Noncovalent Complexes of the Noble-Gas Atoms: Analyzing the Transition from Physical to Chemical Interactions

The bonding character of the noncovalent complexes of the noble-gas (Ng) atoms ranges from nearly purely dispersive contacts to interactions featuring appreciable contributions of induction and charge transfer. In this study, we discuss a new quantitative index that seems peculiarly informative about these diverse bonding situations. This index was termed as the degree of polarization (DoP) of Ng, as it measures, in essence, the Ng polarization promoted by the binding partner. The definition of the DoP(Ng) relies on the analysis of the local electron energy density H(r), and its physical meaning was best appreciated by studying also the charge-displacement function and the molecular electrostatic potential of the investigated benchmark species, that include nearly 60 Ngs complexes of different bonding character. The DoP(Ng) appears of general applicability, and is also positively correlated with other bonding character indices. © 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.

Dispersion Interactions and the Stability of Amine Dimers

Weak, intermolecular interactions in amine dimers were studied by using the combination of a dispersionless density functional and a function that describes the dispersion contribution to the interaction energy. The validity of this method was shown by comparison of structural and energetic properties with data obtained with a conventional density functional and the coupled cluster method. The stability of amine dimers was shown to depend on the size, the shape, and the relative orientation of the alkyl substituents, and it was shown that the stabilization energy for large substituents is dominated by dispersion interactions. In contrast to traditional chemical explanations that attribute stability and condensed matter properties solely to hydrogen bonding and, thus, to the properties of the atoms forming the hydrogen bridge, we show that without dispersion interactions not even the stability and structure of the ammonia dimer can be correctly described. The stability of amine dimers depends crucially on the interaction between the non-polar alkyl groups, which is dominated by dispersion interactions. This interaction is also responsible for the energetic part of the free energy interaction used to describe hydrophobic interactions in liquid alkanes. The entropic part has its origin in the high degeneracy of the interaction energy for complexes of alkane molecules, which exist in a great variety of conformers, having their origin in internal rotations of the alkane chains.

Next-Generation Force Fields from Symmetry-Adapted Perturbation Theory

Symmetry-adapted perturbation theory (SAPT) provides a unique set of advantages for parameterizing next-generation force fields from first principles. SAPT provides a direct, basis-set superposition error free estimate of molecular interaction energies, a physically intuitive energy decomposition, and a seamless transition to an asymptotic picture of intermolecular interactions. These properties have been exploited throughout the literature to develop next-generation force fields for a variety of applications, including classical molecular dynamics simulations, crystal structure prediction, and quantum dynamics/spectroscopy. This review provides a brief overview of the formalism and theory of SAPT, along with a practical discussion of the various methodologies utilized to parameterize force fields from SAPT calculations. It also highlights a number of applications of SAPT-based force fields for chemical systems of particular interest. Finally, the review ends with a brief outlook on the future opportunities and challenges that remain for next-generation force fields based on SAPT.

Determination of structure and properties of molecular crystals from first principles

CONSPECTUS: Until recently, it had been impossible to predict structures of molecular crystals just from the knowledge of the chemical formula for the constituent molecule(s). A solution of this problem has been achieved using intermolecular force fields computed from first principles. These fields were developed by calculating interaction energies of molecular dimers and trimers using an ab initio method called symmetry-adapted perturbation theory (SAPT) based on density-functional theory (DFT) description of monomers [SAPT(DFT)]. For clusters containing up to a dozen or so atoms, interaction energies computed using SAPT(DFT) are comparable in accuracy to the results of the best wave function-based methods, whereas the former approach can be applied to systems an order of magnitude larger than the latter. In fact, for monomers with a couple dozen atoms, SAPT(DFT) is about equally time-consuming as the supermolecular DFT approach. To develop a force field, SAPT(DFT) calculations are performed for a large number of dimer and possibly also trimer configurations (grid points in intermolecular coordinates), and the interaction energies are then fitted by analytic functions. The resulting force fields can be used to determine crystal structures and properties by applying them in molecular packing, lattice energy minimization, and molecular dynamics calculations. In this way, some of the first successful determinations of crystal structures were achieved from first principles, with crystal densities and lattice parameters agreeing with experimental values to within about 1%. Crystal properties obtained using similar procedures but empirical force fields fitted to crystal data have typical errors of several percent due to low sensitivity of empirical fits to interactions beyond those of the nearest neighbors. The first-principles approach has additional advantages over the empirical approach for notional crystals and cocrystals since empirical force fields can only be extrapolated to such cases. As an alternative to applying SAPT(DFT) in crystal structure calculations, one can use supermolecular DFT interaction energies combined with scaled dispersion energies computed from simple atom-atom functions, that is, use the so-called DFT+D approach. Whereas the standard DFT methods fail for intermolecular interactions, DFT+D performs reasonably well since the dispersion correction is used not only to provide the missing dispersion contribution but also to fix other deficiencies of DFT. The latter cancellation of errors is unphysical and can be avoided by applying the so-called dispersionless density functional, dlDF. In this case, the dispersion energies are added without any scaling. The dlDF+D method is also one of the best performing DFT+D methods. The SAPT(DFT)-based approach has been applied so far only to crystals with rigid monomers. It can be extended to partly flexible monomers, that is, to monomers with only a few internal coordinates allowed to vary. However, the costs will increase relative to rigid monomer cases since the number of grid points increases exponentially with the number of dimensions. One way around this problem is to construct force fields with approximate couplings between inter- and intramonomer degrees of freedom. Another way is to calculate interaction energies (and possibly forces) "on the fly", i.e., in each step of lattice energy minimization procedure. Such an approach would be prohibitively expensive if it replaced analytic force fields at all stages of the crystal predictions procedure, but it can be used to optimize a few dozen candidate structures determined by other methods.

Predictions for water clusters from a first-principles two- and three-body force field

A new rigid-monomer three-body potential has been developed for water by fitting it to more than 70 thousand trimer interaction energies computed ab initio using coupled-cluster methods and augmented triple-zeta-quality basis sets. This potential was used together with a modified form of a previously developed two-body potential and with a polarization model of four- and higher-body interactions to predict the energetics of the water trimer, hexamer, and 24-mer. Despite using the rigid-monomer approximation, these predictions agree better with flexible-monomer benchmarks than published results obtained with flexible-monomer force fields. An unexpected finding of our work is that simple polarization models predict four-body interactions to within a few percent, whereas for three-body interactions these models are known to have errors on the order of 50%.

Intermolecular potential energy surface and spectra of He–HCl with generalization to other rare gas–hydrogen halide complexes

A two-dimensional (rigid monomer) intermolecular potential energy surface (PES) of the He-HCl complex has been obtained from ab initio calculations utilizing the symmetry-adapted perturbation theory (SAPT) and an spdfg basis set including midbond functions. The bond length in HCl was chosen to be equal to the expectation value in the ground vibrational state of isolated HCl. The rigid-monomer potential should be a very good approximation to the complete (three-dimensional) potential for H-Cl distances corresponding to the lowest vibrational levels of the monomer since the He-HCl interaction energy was found to be only weakly dependent on the HCl bond length in this region, at least as compared to systems such as Ar-HF. The calculated points were fitted using an analytic function with ab initio computed asymptotic coefficients. As expected, the complex is loosely bound, with the dispersion energy providing the majority of the attraction. Our SAPT PES agrees with the semiempirical PES of Willey et al. [J. Chem. Phys. 96, 898 (1992)], in finding that, atypically for rare gas-hydrogen halide complexes including the lighter halide atoms, the global minimum is on the Cl side (with intermonomer separation 3.35 A and depth of 32.8 cm(-1)), rather than on the H side, where there is only a local minimum (3.85 A, 30.8 cm(-1)). The ordering of the minima was confirmed by single-point calculations in larger basis sets and complete basis set extrapolations, and also using higher levels of theory. We show that the opposite findings in the recent calculations of Zhang and Shi [J. Mol. Struct: THEOCHEM 589, 89 (2002)] are due to the lack of midbond functions in their basis set. Despite the closeness in depth of the two linear minima, the existence of a relatively high barrier between them invalidates the assumption of isotropy, a feature of some literature potentials. The trends concerning the locations of minima within the family of rare gas-hydrogen halide complexes are rationalized in terms of the physical components of the intermolecular forces and related to monomer properties. The accuracy of the SAPT PES was tested by performing calculations of rovibrational levels. The transition frequencies obtained were found to be in excellent agreement (to within 0.02 cm(-1)) with the measurements of Lovejoy and Nesbitt [J. Chem. Phys. 93, 5387 (1990)]. The SAPT PES predicts a dissociation energy for the complex of 7.74 cm(-1) which is probably more accurate than the experimental value of 10.1+/-1.2 cm(-1). Our analysis of the ground-state rovibrational wave function shows that the He-HCl configuration is favored over the He-ClH configuration despite the ordering of minima. This is due to the greater volume of the well in the former case. We have also determined positions and widths of three low-lying resonance states through scattering calculations. These predictions are expected to be more accurate than values derived from experiment.

Approximate generation of full-dimensionalab initiovan der Waals surfaces for high-resolution spectroscopy

A method for the generation of highly accurate, nearly-exact, full-dimensional interaction energy surfaces for weakly interacting subsystems is proposed. The method is based on the local expansion of the exact interaction energy surface in the Taylor series with respect to intramolecular coordinates. It is shown that without any significant loss of accuracy this expansion can be limited to a few low-order terms. This leads to significant savings in computations of the full-dimensional interaction energy surfaces. Also a method for the direct calculation of the interaction energy surface of reduced dimensionality, corresponding to averaging over the intramolecular vibrations, without explicit knowledge of the full-dimensional surface, is presented. The main ideas and computational features of the proposed scheme are comprehensively tested for the Ar-HF system.

Efficient generation of flexible-monomer intermolecular potential energy surfaces

A new method of generating flexible-monomer intermolecular interaction potentials has been proposed. The method, based on symmetry-adapted perturbation theory, extends a rigid-monomer potential into a flexible-monomer one at a cost negligible compared to performing calculations on a full-dimensional grid (i.e., including internal degrees of freedom of monomers). The non-rigidity effects are accounted for by density-overlap integrals and by asymptotic expansion coefficients. Results for a model system (Ar-HF) demonstrate that the method recovers a substantial portion of these effects.