Polarizable interaction potential for water from coupled cluster calculations. II. Applications to dimer spectra, virial coefficients, and simulations of liquid water

Simulating the isotropic Raman spectra of O-H stretching mode in liquid H2O based on a machine learning potential: the influence of vibrational couplings

In this study, we trained a deep potential (DP) for H2O, an accurate machine learning (ML) potential. We performed molecular dynamics (MD) simulations of liquid water using the DP model (or DeePMD simulations). Our results showed that the DP model exhibits DFT-level accuracy, and the DeePMD simulation is a promising approach for modeling the structural properties of liquid water. Based on the DeePMD simulation trajectories, we calculated the isotropic Raman spectra of the O-H stretching mode using the surface-specific velocity-velocity correlation function (ssVVCF), showing that the DeePMD/ssVVCF approach can correctly capture the bimodal characteristics of the experimental Raman spectra, with one peak located near 3400 cm-1 and the other near 3250 cm-1. The success of the DeePMD/ssVVCF approach should be credited to (1) the DFT-level accuracy of the DP model for H2O, (2) the ssVVCF formulation considering the coupling between vibrational modes, and (3) non-Condon effects. Furthermore, the DeePMD simulations revealed that the anharmonic interactions between the coupled water molecules in the first and second hydration shells should play an essential role in the strong mixing of the H-O-H bending mode and the O-H stretching mode, leading to the delocalization of the O-H stretching band. In particular, increasing the strength of hydrogen bonds would enhance the bend-stretch coupling, leading to the red-shifting of the O-H vibrational spectra and the increase in the intensity of the shoulder around 3250 cm-1.

A "short blanket" dilemma for a state-of-the-art neural network potential for water: Reproducing experimental properties or the physics of the underlying many-body interactions?

Deep neural network (DNN) potentials have recently gained popularity in computer simulations of a wide range of molecular systems, from liquids to materials. In this study, we explore the possibility of combining the computational efficiency of the DeePMD framework and the demonstrated accuracy of the MB-pol data-driven, many-body potential to train a DNN potential for large-scale simulations of water across its phase diagram. We find that the DNN potential is able to reliably reproduce the MB-pol results for liquid water, but provides a less accurate description of the vapor-liquid equilibrium properties. This shortcoming is traced back to the inability of the DNN potential to correctly represent many-body interactions. An attempt to explicitly include information about many-body effects results in a new DNN potential that exhibits the opposite performance, being able to correctly reproduce the MB-pol vapor-liquid equilibrium properties, but losing accuracy in the description of the liquid properties. These results suggest that DeePMD-based DNN potentials are not able to correctly "learn" and, consequently, represent many-body interactions, which implies that DNN potentials may have limited ability to predict the properties for state points that are not explicitly included in the training process. The computational efficiency of the DeePMD framework can still be exploited to train DNN potentials on data-driven many-body potentials, which can thus enable large-scale, "chemically accurate" simulations of various molecular systems, with the caveat that the target state points must have been adequately sampled by the reference data-driven many-body potential in order to guarantee a faithful representation of the associated properties.

On the many-body nature of intramolecular forces in FFLUX and its implications

FFLUX is a biomolecular force field under construction, based on Quantum Chemical Topology (QCT) and machine learning (kriging), with a minimalistic and physically motivated design. A detailed analysis of the forces within the kriging models as treated in FFLUX is presented, taking as a test example a liquid water model. The energies of topological atoms are modeled as 3N_atoms -6 dimensional potential energy surfaces, using atomic local frames to represent the internal degrees of freedom. As a result, the forces within the kriging models in FFLUX are inherently N-body in nature where N refers to N_atoms . This provides a fuller picture that is closer to a true quantum mechanical representation of interactions between atoms. The presented computational example quantitatively showcases the non-negligible (as much as 9%) three-body nature of bonded forces and angular forces in a water molecule. We discuss the practical impact on the pressure calculation with N-body forces and periodic boundary conditions (PBC) in molecular dynamics, as opposed to classical force fields with two-body forces. The equivalence between the PBC-related correction terms in the general virial equation is shown mathematically.

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.

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.

Full quantum calculation of the rovibrational states and intensities for a symmetric top-linear molecule dimer: Hamiltonian, basis set, and matrix elements

The rovibrational energy levels and intensities of the CH₃F-H₂ dimer have been obtained using our recent global intermolecular potential energy surface [X.-L. Zhang et al., J. Chem. Phys. 148, 124302 (2018)]. The Hamiltonian, basis set, and matrix elements are derived and given for a symmetric top-linear molecule complex. This approach to the generation of energy levels and wavefunctions can readily be utilized for studying the rovibrational spectra of other van der Waals complexes composed of a symmetric top molecule and a linear molecule, and may readily be extended to other complexes of nonlinear molecules and linear molecules. To confirm our method, the rovibrational levels of the H₂O-H₂ dimer have been computed and shown to be in good agreement with experiment and with previous theoretical results. The rovibrational Schrödinger equation has been solved using a Lanczos algorithm together with an uncoupled product basis set. As expected, dimers containing ortho-H₂ are more strongly bound than dimers containing para-H₂. Energies and wavefunctions of the discrete rovibrational levels of CH₃F-paraH₂ complexes obtained from the direct vibrationally averaged 5-dimensional potentials are in good agreement with the results of the reduced 3-dimensional adiabatic-hindered-rotor (AHR) approximation. Accurate calculations of the transition line strengths for the orthoCH₃F-paraH₂ complex are also carried out, and are consistent with results obtained using the AHR approximation. The microwave spectrum associated with the orthoCH₃F-orthoH₂ dimer has been predicted for the first time.

Many-Body Effects Determine the Local Hydration Structure of Cs+ in Solution

A systematic analysis of the hydration structure of Cs⁺ ions in solution is derived from simulations carried out using a series of molecular models built upon a hierarchy of approximate representations of many-body effects in ion-water interactions. It is found that a pairwise-additive model, commonly used in biomolecular simulations, provides poor agreement with experimental X-ray spectra, indicating an incorrect description of the underlying hydration structure. Although the agreement with experiment improves in simulations with a polarizable model, the predicted hydration structure is found to lack the correct sequence of water shells. Progressive inclusion of explicit many-body effects in the representation of Cs⁺-water interactions as well as accounting for nuclear quantum effects is shown to be necessary for quantitatively reproducing the experimental X-ray spectra. Besides emphasizing the importance of many-body effects, these results suggest that molecular models rigorously derived from many-body expansions hold promise for realistic simulations of aqueous solutions.

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.

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.

Intermolecular potential energy surface and thermophysical properties of propane

A six-dimensional potential energy surface (PES) for the interaction of two rigid propane molecules was determined from supermolecular ab initio calculations up to the coupled cluster with single, double, and perturbative triple excitations level of theory for 9452 configurations. An analytical site-site potential function with 14 sites per molecule was fitted to the calculated interaction energies. To validate the analytical PES, the second virial coefficient and the dilute gas shear viscosity and thermal conductivity of propane were computed. The dispersion part of the potential function was slightly adjusted such that quantitative agreement with the most accurate experimental data for the second virial coefficient at room temperature was achieved. The adjusted PES yields values for the three properties that are in very good agreement with the best experimental data at all temperatures.

Getting the Right Answers for the Right Reasons: Toward Predictive Molecular Simulations of Water with Many-Body Potential Energy Functions

The central role played by water in fundamental processes relevant to different disciplines, including chemistry, physics, biology, materials science, geology, and climate research, cannot be overemphasized. It is thus not surprising that, since the pioneering work by Stillinger and Rahman, many theoretical and computational studies have attempted to develop a microscopic description of the unique properties of water under different thermodynamic conditions. Consequently, numerous molecular models based on either molecular mechanics or ab initio approaches have been proposed over the years. However, despite continued progress, the correct prediction of the properties of water from small gas-phase clusters to the liquid phase and ice through a single molecular model remains challenging. To large extent, this is due to the difficulties encountered in the accurate modeling of the underlying hydrogen-bond network in which both number and strength of the hydrogen bonds vary continuously as a result of a subtle interplay between energetic, entropic, and nuclear quantum effects. In the past decade, the development of efficient algorithms for correlated electronic structure calculations of small molecular complexes, accompanied by tremendous progress in the analytical representation of multidimensional potential energy surfaces, opened the doors to the design of highly accurate potential energy functions built upon rigorous representations of the many-body expansion (MBE) of the interaction energies. This Account provides a critical overview of the performance of the MB-pol many-body potential energy function through a systematic analysis of energetic, structural, thermodynamic, and dynamical properties as well as of vibrational spectra of water from the gas to the condensed phase. It is shown that MB-pol achieves unprecedented accuracy across all phases of water through a quantitative description of each individual term of the MBE, with a physically correct representation of both short- and long-range many-body contributions. Comparisons with experimental data probing different regions of the water potential energy surface from clusters to bulk demonstrate that MB-pol represents a major step toward the long-sought-after "universal model" capable of accurately describing the molecular properties of water under different conditions and in different environments. Along this path, future challenges include the extension of the many-body scheme adopted by MB-pol to the description of generic solutes as well as the integration of MB-pol in an efficient theoretical and computational framework to model acid-base reactions in aqueous environments. In this context, given the nontraditional form of the MB-pol energy and force expressions, synergistic efforts by theoretical/computational chemists/physicists and computer scientists will be critical for the development of high-performance software for many-body molecular dynamics simulations.

Modeling Molecular Interactions in Water: From Pairwise to Many-Body Potential Energy Functions

Almost 50 years have passed from the first computer simulations of water, and a large number of molecular models have been proposed since then to elucidate the unique behavior of water across different phases. In this article, we review the recent progress in the development of analytical potential energy functions that aim at correctly representing many-body effects. Starting from the many-body expansion of the interaction energy, specific focus is on different classes of potential energy functions built upon a hierarchy of approximations and on their ability to accurately reproduce reference data obtained from state-of-the-art electronic structure calculations and experimental measurements. We show that most recent potential energy functions, which include explicit short-range representations of two-body and three-body effects along with a physically correct description of many-body effects at all distances, predict the properties of water from the gas to the condensed phase with unprecedented accuracy, thus opening the door to the long-sought "universal model" capable of describing the behavior of water under different conditions and in different environments.

Two-dimensional interlocked pentagonal bilayer ice: how do water molecules form a hydrogen bonding network?

The tradeoff between the conditions of an ideal hydrogen bonding network can serve as a generic guidance to understand the rich phase behaviors of nanoconfined water.

Ab initio intermolecular potential energy surface and thermophysical properties of nitrous oxide

We present an analytical intermolecular potential energy surface (PES) for two rigid nitrous oxide (N2O) molecules derived from high-level quantum-chemical ab initio calculations. Interaction energies for 2018 N2O-N2O configurations were computed utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory using basis sets up to aug-cc-pVQZ supplemented with bond functions. A site-site potential function with seven sites per N2O molecule was fitted to the pair interaction energies. We validated our PES by computing the second virial coefficient as well as shear viscosity and thermal conductivity in the dilute-gas limit. The values of these properties are substantiated by the best experimental data.

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.

Infrared and Raman Spectroscopy of Liquid Water through "First-Principles" Many-Body Molecular Dynamics

Vibrational spectroscopy is a powerful technique to probe the structure and dynamics of water. However, deriving an unambiguous molecular-level interpretation of the experimental spectral features remains a challenge due to the complexity of the underlying hydrogen-bonding network. In this contribution, we present an integrated theoretical and computational framework (named many-body molecular dynamics or MB-MD) that, by systematically removing uncertainties associated with existing approaches, enables a rigorous modeling of vibrational spectra of water from quantum dynamical simulations. Specifically, we extend approaches used to model the many-body expansion of interaction energies to develop many-body representations of the dipole moment and polarizability of water. The combination of these "first-principles" representations with centroid molecular dynamics simulations enables the simulation of infrared and Raman spectra of liquid water under ambient conditions that, without relying on any ad hoc parameters, are in good agreement with the corresponding experimental results. Importantly, since the many-body energy, dipole, and polarizability surfaces employed in the simulations are derived independently from accurate fits to correlated electronic structure data, MB-MD allows for a systematic analysis of the calculated spectra in terms of both electronic and dynamical contributions. The present analysis suggests that, while MB-MD correctly reproduces both the shifts and the shapes of the main spectroscopic features, an improved description of quantum dynamical effects possibly combined with a dissociable water potential may be necessary for a quantitative representation of the OH stretch band.

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%.

A Critical Assessment of Two-Body and Three-Body Interactions in Water

The microscopic behavior of water under different conditions and in different environments remains the subject of intense debate. A great number of the controversies arise due to the contradictory predictions obtained within different theoretical models. Relative to conclusions derived from force fields or density functional theory, there is comparably less room to dispute highly correlated electronic structure calculations. Unfortunately, such ab initio calculations are severely limited by system size. In this study, a detailed analysis of the two- and three-body water interactions evaluated at the CCSD(T) level is carried out to quantitatively assess the accuracy of several force fields, DFT models, and ab initio based interaction potentials that are commonly used in molecular simulations. On the basis of this analysis, a new model, HBB2-pol, is introduced which is capable of accurately mapping CCSD(T) results for water dimers and trimers into an efficient analytical function. The accuracy of HBB2-pol is further established through comparison with the experimentally determined second and third virial coefficients.

Spectra of water dimer from a new ab initio potential with flexible monomers

We report the definition and testing of a new ab initio 12-dimensional potential for the water dimer with flexible monomers. Using our recent accurate CCpol-8s rigid water pair potential [W. Cencek, K. Szalewicz, C. Leforestier, R. van Harrevelt, and A. van der Avoird, Phys. Chem. Chem. Phys. 10, 4716 (2008)] as a reference for the undistorted monomers' geometries, a distortion correction has been added, which was taken from a former flexible-monomer ab initio potential. This correction allows us to retrieve the correct binding energy D(e)=21.0 kJ mol(-1), and leads to an equilibrium geometry in close agreement with the one obtained from benchmark calculations. The kinetic energy operator describing the flexible-monomer water dimer has been expressed in terms of Radau coordinates for each monomer and a recent general cluster polyspherical formulation describing their relative motions. Within this formulation, an adiabatic scheme has been invoked in order to decouple fast (intramolecular) modes and slow (intermolecular) ones. Different levels of approximation were tested, which differ in the way in which the residual potential coupling between the intramolecular modes located on different monomers and the dependence of the monomer rotational constants on the dimer geometry are handled. Accurate calculations of the vibration-rotation-tunneling levels of (H(2)O)(2) and (D(2)O)(2) were performed, which show the best agreement with experiments achieved so far for any water potential. Intramolecular excitations of the two monomers were calculated within two limiting cases, to account for the lack of non-adiabatic coupling between intramolecular modes due to the intermolecular motion. In the first model, the excitation was assumed to stay either on the donor or the acceptor molecule, and to hop between the two moieties upon donor-acceptor interchange. In the second model, the excitation remains on the same molecule whatever is the dimer geometry. Marginal frequency differences, less than 2 cm(-1), were obtained for all modes, and the resulting infrared shifts are in good agreement with experiments.

Development of polarizable models for molecular mechanical calculations. 3. Polarizable water models conforming to Thole polarization screening schemes

As an integrated step toward a coherent polarizable force field for biomolecular modeling, we analyzed four polarizable water models to evaluate their consistencies with the Thole polarization screening schemes utilized in our latest Amber polarizable force field. Specifically, we studied the performance of both the Thole linear and exponential schemes in these water models to assess their abilities to reproduce experimental water properties. The analysis shows that the tested water models reproduce most of the room-temperature properties of liquid water reasonably well but fall short of reproducing the dynamic properties and temperature-dependent properties. This study demonstrates the necessity to further fine-tune water polarizable potentials for more robust polarizable force fields for biomolecular simulations.

An adiabatic model for calculating overtone spectra of dimers such as (H(2)O)(2)

The near-infrared and visible wavelength spectrum of the water dimer is considered to be the major contributor to the so-called water continuum at these wavelengths. However, theoretical models of this spectrum require the simultaneous treatment of both monomer and dimer excitations. A model for treating this problem is proposed which is based upon a Franck-Condon-like separation between the monomer and dimer vibrational motions. In this model, one of the monomers is treated as the chromophore and its absorption is assumed to be given by its, possibly perturbed, vibrational band intensity. The main computational issue is the treatment of separate monomer and dimer motions. Various approaches for obtaining dimer vibration-rotation tunnelling spectra that allow for monomer motion are explored. These approaches include ways of treating the adiabatic separation of dimer vibrational modes from monomer vibrational modes. We classify the adiabatic separation methods under four main approaches: namely fixed-geometry, free-monomer, perturbed-monomer and coupled-monomer methods. The latter being the most computationally expensive as the monomer wave functions are dependent on the dimer coordinates. For each of these approaches, expectation values over the full potential are calculated for the given monomer vibrational wave functions. Various full (named VAP 2pD in the text) and partial (VAP (+p)D) averaging techniques are outlined to calculate the vibrationally averaged, monomer state-dependent, dimer interaction potentials. The computational costs associated with application of these techniques to the water dimer are estimated and the prospects for full calculations based on this approach are assessed.