Getting the Right Answers for the Right Reasons: Toward Predictive

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Getting the Right Answers for the Right Reasons: Toward Predictive Molecular Simulations of Water with Many-Body Potential Energy Functions Francesco Paesani* Department of Chemistry and Biochemistry, University of CaliforniaSan Diego, La Jolla, California 92093, United States CONSPECTUS: 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 manybody 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.

1. INTRODUCTION

level model capable of correctly reproducing the properties of water across different phases remains elusive. Different computational techniques are nowadays available for modeling the interactions between water molecules, ranging from empirical force fields (FFs)2−5 to ab initio approaches based on wave function theory (WFT)6,7 and density functional theory (DFT).8,9 Although correlated WFT approaches, such as coupled cluster with single, double, and perturbative triple excitations, CCSD(T), the current “gold standard” for chemical accuracy,10 can enable molecular-level studies of water without resorting on ad hoc simplifications, the associated computa-

As demonstrated by the 2013 Nobel Prize in Chemistry awarded to Karplus, Levitt, and Warshel, computer simulations have become a powerful tool for molecular sciences, often providing fundamental insights into complex phenomena which are difficult (if not impossible) to obtain by other means. However, both the realism and the predictive power of a computer simulation depend sensitively on the accuracy with which the molecular interactions and actual molecular dynamics are represented. Water is perhaps the most classic example of this. Despite almost 50 years have passed since the first computer simulation of liquid water1 and numerous computational studies have been reported since then,2−5 a molecular© XXXX American Chemical Society

Received: June 8, 2016

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DOI: 10.1021/acs.accounts.6b00285 Acc. Chem. Res. XXXX, XXX, XXX−XXX

Article

Accounts of Chemical Research

Figure 1. Correlation plots for the low-order terms of the MBE for water. On the x-axes are the ab initio interaction energies calculated at the CCSD(T)/CBS (for 2B and 3B terms) and MP2/aVTZ+mb (for the 4B term) levels of theory, while on the y-axes are the corresponding MB-pol values.

polarization effects in many-body systems.5 As a result, several MB potential energy functions have been proposed in the last years, the most notable of which are CC-pol,17 WHBB,18 HBB2-pol,19 and MB-pol.20−22 In this Account, recent progress in modeling the properties of water across different phases using molecular dynamics (MD) simulations with the MB-pol potential energy function is discussed. The interested reader is referred to ref 5. for a broader overview of recent water models. After a brief review of the theoretical formulation of MB-pol and associated computational algorithms, a systematic analysis of the MBE for water clusters is presented. The accuracy with which MB-pol describes the underlying Born−Oppenheimer PES of water is then connected to the ability of MB-pol to predict several structural, thermodynamic, and dynamical properties as well as vibrational spectra from the gas-phase dimer to the liquid phase and ice. This is followed by a brief outlook on future developments and applications of MB-pol to molecular-level studies of hydration processes.

tional cost is currently prohibitive for systems containing more than a handful of molecules. Despite recent progress in the implementation of WFT methods based on Möller-Plesset perturbation theory,6,7 DFT still remains the most common ab initio approach for simulations in periodic boundary conditions. However, existing DFT models have been shown not to be particularly accurate in describing the properties of water.9 On the other hand, popular FFs exhibit limited accuracy and effectively lack any predictive power, often representing molecular interactions through relatively simple expressions based on harmonic potentials and classical electrostatics.2−5 A new class of analytical potential energy functions has recently been introduced which builds upon a rigorous representation of the many-body expansion (MBE) of the interaction energy between N water molecules,11 N

VN (r1 , ..., rN ) =

N

∑ V1B(ri) + ∑ V2B(ri , rj) i=1

i