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.

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.

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, HFDasc(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.

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.

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.

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 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.

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. While only a single monomer geometry was used for each monomer in the ab initio calculations, the PES parameterization makes it possible to produce distinct surfaces for all isotopologues within the rigid-monomer approximation. The PESs were fitted to computations at the frozen-core coupled-cluster level with single, double, and non-iterative triple excitations, employing basis sets of augmented triple- and quadruple-zeta quality plus bond functions, followed by extrapolations to the complete basis set limit. The long-range parts of the PESs are computed using the asymptotic version of symmetry-adapted perturbation theory based on a density-functional description of the monomers. All PESs are polarizable, i.e., in cluster or condensed-phase applications they approximate many-body effects by the induced dipole polarization model. The PESs were developed in a fully automated procedure applying the autoPES method, which is used for the first time to generate near-spectroscopic quality surfaces. The stationary points (SPs) on the PESs have been determined and compared with literature data. For CH4·H2O, previously unknown SPs have been identified and the first detailed study of the (CH4)2 potential energy landscape has been carried out. The PESs were used in variational quantum nuclear motion computations. For the water dimer, the resulting vibrational transitions are in excellent agreement with available high-resolution spectroscopic data. For (CH4)2, the intermonomer vibrational states are reported for the first time.

Does a pair of methane molecules aggregate in water?

Molecular dynamics (MD) simulations of methane-water mixtures were performed using ab initio force fields for the CH4-H2O, H2O-H2O, and CH4-CH4 interactions. Both methane and water molecules were polarizable. From these calculations, the potential of mean force (PMF) between two methane molecules was extracted. Our results are compared with PMFs from a density-functional-theory (DFT) based Born-Oppenheimer type MD (BOMD) simulation, from a Monte Carlo (MC) simulation with ab initio-based force fields, and from MD simulations with empirical force fields. Our PMF is qualitatively similar to that obtained from the simulations with empirical force fields but differs significantly from those resulting from the DFT-BOMD and MC simulations. The depth of the PMF global minimum obtained in the present work is in a much better agreement with the experimental estimate than the result of the DFT-BOMD simulation, possibly due to the inability of DFT to describe the dispersion interactions and the lack of extensive sampling in the BOMD simulations. Our work indicates that, for a pair of methane molecules, there are configurations where the solvent increases the attraction between the solutes, but there are also conformations in which the solvent causes a weak net repulsion. On average, the methane molecules are more likely to be in the configuration where they are separated by a water molecule than in the one in which they are in contact even though the minimum of the PMF at the latter configuration is deeper than that at the former. Finally, we found that the water structure around methane solutes does not show a greater tetrahedral ordering than in neat bulk water.

Do Semilocal Density-Functional Approximations Recover Dispersion Energies at Small Intermonomer Separations?

The methods that add dispersion energies to interaction energies computed using density-functional theory (DFT), known as DFT+D methods, taper off the dispersion energies at distances near van der Waals minima and smaller based on an assumption that DFT starts to reproduce the dispersion energies there. We show that this assumption is not correct as the alleged contribution behaves unphysically and originates to a large extent from nonexchange-correlation terms. Thus, dispersion functions correct DFT in this region for deficiencies unrelated to dispersion interactions.

Fully quantum calculation of the second and third virial coefficients of water and its isotopologues from ab initio potentials.

Path-Integral Monte Carlo methods were applied to calculate the second, B(T), and the third, C(T), virial coefficients for water. A fully quantum approach and state-of-the-art flexible-monomer pair and three-body potentials were used. Flexible-monomer potentials allow calculations for any isotopologue; we performed calculations for both H2O and D2O. For B(T) of H2O, the quantum effect contributes 25% of the value at 300 K and is not entirely negligible even at 1000 K, in accordance with recent literature findings. The effect of monomer flexibility, while not as large as some claims in the literature, is significant compared to the experimental uncertainty. It is of opposite sign to the quantum effect, smaller in magnitude than the latter below 500 K, and varies from 2% at 300 K to 10% at 700 K. When monomer flexibility is accounted for, results from the CCpol-8sf pair potential are in excellent agreement with the available experimental data and provide reliable B(T) values at temperatures outside the range of experimental data. The flexible-monomer MB-pol pair potential yields B(T) values that are slightly too high compared to experiment. For C(T), our calculations confirm earlier findings that the use of three-body potential is necessary for meaningful predictions. However, due to various uncertainties of the potentials used, especially the three-body ones, we were not able to establish benchmark values of C(T), although our results are in qualitative agreement with available experimental data. The quantum effect, never before included for water, reduces the magnitude of the classical value for H2O by a factor of 2.5 at 300 K and is not entirely negligible even at 1000 K.

Pair Potential with Submillikelvin Uncertainties and Nonadiabatic Treatment of the Halo State of the Helium Dimer.

The pair potential for helium is computed with accuracy improved by an order of magnitude relative to the best previous determination. For the well region, its uncertainties are now below 1 millikelvin. The main improvement is due to the use of explicitly correlated wave functions at the nonrelativistic Born-Oppenheimer (BO) level of theory. The diagonal BO and the relativistic corrections are obtained from large full configuration interaction calculations. Nonadiabatic perturbation theory is used to predict the properties of the halo state of the helium dimer. Its binding energy and the average value of the interatomic distance are found to be 138.9(5) neV and 47.13(8) Å. The binding energy agrees with its first experimental determination of 151.9(13.3) neV [Zeller et al., Proc. Natl. Acad. Sci. U.S.A. 113, 14651 (2016)PNASA60027-842410.1073/pnas.1610688113].

All-dimensional H2-CO potential: Validation with fully quantum second virial coefficients.

We use a new high-accuracy all-dimensional potential to compute the cross second virial coefficient B12(T) between molecular hydrogen and carbon monoxide. The path-integral method is used to fully account for quantum effects. Values are calculated from 10 K to 2000 K and the uncertainty of the potential is propagated into uncertainties of B12. Our calculated B12(T) are in excellent agreement with most of the limited experimental data available, but cover a much wider range of temperatures and have lower uncertainties. Similar to recently reported findings from scattering calculations, we find that the reduced-dimensionality potential obtained by averaging over the rovibrational motion of the monomers gives results that are a good approximation to those obtained when flexibility is fully taken into account. Also, the four-dimensional approximation with monomers taken at their vibrationally averaged bond lengths works well. This finding is important, since full-dimensional potentials are difficult to develop even for triatomic monomers and are not currently possible to obtain for larger molecules. Likewise, most types of accurate quantum mechanical calculations, e.g., spectral or scattering, are severely limited in the number of dimensions that can be handled.

Geometry-dependent distributed polarizability models for the water molecule.

Geometry-dependent distributed polarizability models have been constructed by fits to ab initio calculations at the coupled cluster level of theory with up to noniterative triple excitations in an augmented triple-zeta quality basis set for the water molecule in the field of a point charge. The investigated models include (i) charge-flow polarizabilities between chemically bonded atoms, (ii) isotropic or anisotropic dipolar polarizabilities on oxygen atom or on all atoms, and (iii) combinations of models (i) and (ii). For each model, the polarizability parameters have been optimized to reproduce the induction energy of a water molecule polarized by a point charge successively occupying a grid of points surrounding the molecule. The quality of the models is ascertained by examining their ability to reproduce these induction energies as well as the molecular dipolar and quadrupolar polarizabilities. The geometry dependence of the distributed polarizability models has been explored by changing bond lengths and HOH angle to generate 125 molecular structures (reduced to 75 symmetry-unique ones). For each considered model, the distributed polarizability components have been fitted as a function of the geometry by a Taylor expansion in monomer coordinate displacements up to the sum of powers equal to 4.

Blind test of density-functional-based methods on intermolecular interaction energies.

In the past decade, a number of approaches have been developed to fix the failure of (semi)local density-functional theory (DFT) in describing intermolecular interactions. The performance of several such approaches with respect to highly accurate benchmarks is compared here on a set of separation-dependent interaction energies for ten dimers. Since the benchmarks were unknown before the DFT-based results were collected, this comparison constitutes a blind test of these methods.

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.

Frequency-dependent polarizability of helium including relativistic effects with nuclear recoil terms.

Future metrology standards will be partly based on physical quantities computed from first principles rather than measured. In particular, a new pressure standard can be established if the dynamic polarizability of helium can be determined from theory with an uncertainty smaller than 0.2 ppm. We present calculations of the frequency-dependent part of this quantity including relativistic effects with full account of leading nuclear recoil terms and using highly optimized explicitly correlated basis sets. A particular emphasis is put on uncertainty estimates. At the He-Ne laser wavelength of 632.9908 nm, the computed polarizability value of 1.39181141 a.u. has uncertainty of 0.1 ppm that is 2 orders of magnitude smaller than those of the most accurate polarizability measurements. We also obtained an accurate expansion of the helium refractive index in powers of density.

Ab initio water pair potential with flexible monomers.

A potential energy surface for the water dimer with explicit dependence on monomer coordinates is presented. The surface was fitted to a set of previously published interaction energies computed on a grid of over a quarter million points in the 12-dimensional configurational space using symmetry-adapted perturbation theory and coupled-cluster methods. The present fit removes small errors in published fits, and its accuracy is critically evaluated. The minimum and saddle-point structures of the potential surface were found to be very close to predictions from direct ab initio optimizations. The computed second virial coefficients agreed well with experimental values. At low temperatures, the effects of monomer flexibility in the virial coefficients were found to be much smaller than the quantum effects.

Is electrostatics sufficient to describe hydrogen-bonding interactions?

The stability and geometry of a hydrogen-bonded dimer is traditionally attributed mainly to the central moiety A-H⋅⋅⋅B, and is often discussed only in terms of electrostatic interactions. The influence of substituents and of interactions other than electrostatic ones on the stability and geometry of hydrogen-bonded complexes has seldom been addressed. An analysis of the interaction energy in the water dimer and several alcohol dimers--performed in the present work by using symmetry-adapted perturbation theory--shows that the size and shape of substituents strongly influence the stabilization of hydrogen-bonded complexes. The larger and bulkier the substituents are, the more important the attractive dispersion interaction is, which eventually becomes of the same magnitude as the total stabilization energy. Electrostatics alone are a poor predictor of the hydrogen-bond stability trends in the sequence of dimers investigated, and in fact, dispersion interactions predict these trends better.

Path-integral calculation of the second virial coefficient including intramolecular flexibility effects.

We present a path-integral Monte Carlo procedure for the fully quantum calculation of the second molecular virial coefficient accounting for intramolecular flexibility. This method is applied to molecular hydrogen (H2) and deuterium (D2) in the temperature range 15-2000 K, showing that the effect of molecular flexibility is not negligible. Our results are in good agreement with experimental data, as well as with virials given by recent empirical equations of state, although some discrepancies are observed for H2 between 100 and 200 K.