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.

[1]  Y. Mo,et al.  Energy decomposition analysis of intermolecular interactions using a block-localized wave function approach , 2000 .

[2]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[3]  Pengyu Y. Ren,et al.  Temperature and Pressure Dependence of the AMOEBA Water Model , 2004 .

[4]  Paul S. Bagus,et al.  A new analysis of charge transfer and polarization for ligand–metal bonding: Model studies of Al4CO and Al4NH3 , 1984 .

[5]  Carlos Vega,et al.  Simulating water with rigid non-polarizable models: a general perspective. , 2011, Physical chemistry chemical physics : PCCP.

[6]  L. Coudert,et al.  The submillimeter rotation tunneling spectrum of the water dimer , 1991 .

[7]  E. Clementi,et al.  Nonadditivity of interaction in water trimers , 1980 .

[8]  Margaret E. Johnson,et al.  Current status of the AMOEBA polarizable force field. , 2010, The journal of physical chemistry. B.

[9]  Wilfred F. van Gunsteren,et al.  Development of a simple, self-consistent polarizable model for liquid water , 2003 .

[10]  G. Voth,et al.  Quantum effects in liquid water from an ab initio-based polarizable force field. , 2007, The Journal of chemical physics.

[11]  G. Voth,et al.  Infrared spectroscopy and hydrogen-bond dynamics of liquid water from centroid molecular dynamics with an ab initio-based force field. , 2009, The journal of physical chemistry. B.

[12]  P. Mankoo,et al.  The vibrational proton potential in bulk liquid water and ice. , 2008, The Journal of chemical physics.

[13]  G. Voth,et al.  Flexible simple point-charge water model with improved liquid-state properties. , 2006, The Journal of chemical physics.

[14]  Thomas S. Hofer,et al.  Ab initio quantum mechanical charge field (QMCF) molecular dynamics: a QM/MM – MD procedure for accurate simulations of ions and complexes , 2006 .

[15]  A. W. Götz,et al.  The i-TTM model for ab initio-based ion-water interaction potentials. II. Alkali metal ion-water potential energy functions. , 2016, Physical chemistry chemical physics : PCCP.

[16]  Shubin Liu,et al.  DFT-steric-based energy decomposition analysis of intermolecular interactions , 2014, Theoretical Chemistry Accounts.

[17]  J. Bowman,et al.  The water hexamer: cage, prism, or both. Full dimensional quantum simulations say both. , 2012, Journal of the American Chemical Society.

[18]  Lie,et al.  Molecular-dynamics simulation of liquid water with an ab initio flexible water-water interaction potential. , 1986, Physical review. A, General physics.

[19]  Asbjørn Holt,et al.  Inclusion of the quadrupole moment when describing polarization. The effect of the dipole‐quadrupole polarizability , 2008, J. Comput. Chem..

[20]  Francesco Paesani,et al.  Dissecting the Molecular Structure of the Air/Water Interface from Quantum Simulations of the Sum-Frequency Generation Spectrum. , 2016, Journal of the American Chemical Society.

[21]  P. Rossky,et al.  Water-like solvation thermodynamics in a spherically symmetric solvent model with two characteristic lengths , 2007, Proceedings of the National Academy of Sciences.

[22]  J. E. Quinn,et al.  Cooperative effects in simulated water , 1979, Nature.

[23]  Water pair and three-body potential of spectroscopic quality from Ab initio calculations , 2000, Physical review letters.

[24]  P. Popelier,et al.  Properties of liquid water from a systematic refinement of a high-rank multipolar electrostatic potential. , 2010, The Journal of chemical physics.

[25]  Stefan Grimme,et al.  Semiempirical GGA‐type density functional constructed with a long‐range dispersion correction , 2006, J. Comput. Chem..

[26]  Georg Jansen,et al.  Interaction energy contributions of H-bonded and stacked structures of the AT and GC DNA base pairs from the combined density functional theory and intermolecular perturbation theory approach. , 2006, Journal of the American Chemical Society.

[27]  K. Szalewicz,et al.  Ab initio three-body interactions for water. I. Potential and structure of water trimer , 2003 .

[28]  Joel M. Bowman,et al.  Flexible, ab initio potential, and dipole moment surfaces for water. I. Tests and applications for clusters up to the 22-mer. , 2011, The Journal of chemical physics.

[29]  J. Bowman,et al.  Experimental and Theoretical Investigations of the Dissociation Energy ( D 0 ) and Dynamics of the Water Trimer , ( H 2 O ) 3 , 2013 .

[30]  F. Paesani.  Temperature-dependent infrared spectroscopy of water from a first-principles approach. , 2011, The journal of physical chemistry. A.

[31]  E. Clementi,et al.  Revisiting small clusters of water molecules , 1986 .

[32]  Brooks H. Pate,et al.  Structures of Cage, Prism, and Book Isomers of Water Hexamer from Broadband Rotational Spectroscopy , 2012, Science.

[33]  J. Skinner,et al.  Vibrational spectroscopy as a probe of structure and dynamics in liquid water. , 2010, Chemical reviews.

[34]  G. Karlström,et al.  Improvement of the NEMO Potential by Inclusion of Intramolecular Polarization , 2009 .

[35]  B. Roux,et al.  The Solvation Structure of Na(+) and K(+) in Liquid Water Determined from High Level ab Initio Molecular Dynamics Simulations. , 2012, Journal of chemical theory and computation.

[36]  Gregory S. Tschumper,et al.  Benchmark Structures and Harmonic Vibrational Frequencies Near the CCSD(T) Complete Basis Set Limit for Small Water Clusters: (H2O)n = 2, 3, 4, 5, 6. , 2015, Journal of chemical theory and computation.

[37]  Bernard R. Brooks,et al.  New spherical‐cutoff methods for long‐range forces in macromolecular simulation , 1994, J. Comput. Chem..

[38]  Stanley,et al.  Effect of hydrogen bonds on the thermodynamic behavior of liquid water. , 1994, Physical review letters.

[39]  Robert Moszynski,et al.  Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van der Waals Complexes , 1994 .

[40]  Isaiah Shavitt,et al.  Potential models for simulations of the solvated proton in water , 1998 .

[41]  Kenneth D Jordan,et al.  Theoretical characterization of the (H2O)21 cluster: application of an n-body decomposition procedure. , 2006, The journal of physical chemistry. B.

[42]  J. Crifo,et al.  A refined evaluation of the gas-phase water-dimerization equilibrium constant within non-rigid BJH- and MCY-type potentials , 1992 .

[43]  L. Shi,et al.  Reparametrized E3B (Explicit Three-Body) Water Model Using the TIP4P/2005 Model as a Reference. , 2015, Journal of chemical theory and computation.

[44]  Douglas B Kell,et al.  Optimal construction of a fast and accurate polarisable water potential based on multipole moments trained by machine learning. , 2009, Physical chemistry chemical physics : PCCP.

[45]  J. Stewart.  Optimization of parameters for semiempirical methods I. Method , 1989 .

[46]  J. Bowman,et al.  Quantum calculations of the IR spectrum of liquid water using ab initio and model potential and dipole moment surfaces and comparison with experiment. , 2015, The Journal of chemical physics.

[47]  W. L. Jorgensen,et al.  Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids , 1996 .

[48]  P. Cummings,et al.  Simple transferable intermolecular potential for the molecular simulation of water over wide ranges of state conditions , 1998 .

[49]  Thomas E. Markland,et al.  Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges. , 2016, Chemical reviews.

[50]  Sotiris S. Xantheas,et al.  Ab initio studies of cyclic water clusters (H2O)n, n=1–6. II. Analysis of many‐body interactions , 1994 .

[51]  G. Groenenboom,et al.  Polarizable interaction potential for water from coupled cluster calculations. I. Analysis of dimer potential energy surface. , 2008, The Journal of chemical physics.

[52]  Arieh Warshel,et al.  Polarizable Force Fields:  History, Test Cases, and Prospects. , 2007, Journal of chemical theory and computation.

[53]  Frederick R. Manby,et al.  Machine-learning approach for one- and two-body corrections to density functional theory: Applications to molecular and condensed water , 2013 .

[54]  V. Barone,et al.  Toward reliable density functional methods without adjustable parameters: The PBE0 model , 1999 .

[55]  Bertrand Guillot,et al.  A reappraisal of what we have learnt during three decades of computer simulations on water , 2002 .

[56]  Mark S. Gordon,et al.  An interpretation of the enhancement of the water dipole moment due to the presence of other water molecules. , 2008, The journal of physical chemistry. A.

[57]  Margaret E. Johnson,et al.  Representability problems for coarse-grained water potentials. , 2007, The Journal of chemical physics.

[58]  Joel M Bowman,et al.  Full-dimensional, ab initio potential energy and dipole moment surfaces for water. , 2009, The Journal of chemical physics.

[59]  Michael L. Klein,et al.  Effective pair potentials and the properties of water , 1989 .

[60]  K. Hermansson.  Many‐body effects in tetrahedral water clusters , 1988 .

[61]  Nohad Gresh,et al.  Many‐body exchange‐repulsion in polarizable molecular mechanics. I. orbital‐based approximations and applications to hydrated metal cation complexes , 2011, J. Comput. Chem..

[62]  Jules W. Moskowitz,et al.  Water Molecule Interactions , 1970 .

[63]  Kenneth D. Jordan,et al.  Binding energy of the ring form of (H2O)6: Comparison of the predictions of conventional and localized‐orbital MP2 calculations , 1996 .

[64]  J. Bowman,et al.  Experimental and theoretical investigations of the dissociation energy (D0) and dynamics of the water trimer, (H2O)3. , 2013, The journal of physical chemistry. A.

[65]  Nohad Gresh,et al.  S/G-1: an ab initio force-field blending frozen Hermite Gaussian densities and distributed multipoles. Proof of concept and first applications to metal cations. , 2014, The journal of physical chemistry. A.

[66]  Bo Jönsson,et al.  A molecular dynamics simulation of a water model with intramolecular degrees of freedom , 1987 .

[67]  Alexander D. MacKerell,et al.  A simple polarizable model of water based on classical Drude oscillators , 2003 .

[68]  Gregory A Voth,et al.  The properties of water: insights from quantum simulations. , 2009, The journal of physical chemistry. B.

[69]  N. Forsberg,et al.  A comparison between the NEMO intermolecular water potential and ab initio quantum chemical calculations for the water trimer tetramer , 1997 .

[70]  Andrew Jones,et al.  The adaptive buffered force QM/MM method in the CP2K and AMBER software packages , 2014, J. Comput. Chem..

[71]  G. Matheron.  The intrinsic random functions and their applications , 1973, Advances in Applied Probability.

[72]  So Hirata,et al.  Why Is MP2-Water "Cooler" and "Denser" than DFT-Water? , 2016, The journal of physical chemistry letters.

[73]  Junmei Wang,et al.  Development and testing of a general amber force field , 2004, J. Comput. Chem..

[74]  Alexander D. MacKerell,et al.  Six-site polarizable model of water based on the classical Drude oscillator. , 2013, The Journal of chemical physics.

[75]  B. Thole.  Molecular polarizabilities calculated with a modified dipole interaction , 1981 .

[76]  T. Darden,et al.  Towards a force field based on density fitting. , 2006, The Journal of chemical physics.

[77]  W G Noid,et al.  Perspective: Coarse-grained models for biomolecular systems. , 2013, The Journal of chemical physics.

[78]  C. J. Keoshian,et al.  Spectroscopic determination of the water dimer intermolecular potential-energy surface , 2002 .

[79]  J. Bowman,et al.  Experimental and theoretical investigations of energy transfer and hydrogen-bond breaking in the water dimer. , 2012, Journal of the American Chemical Society.

[80]  M. Beck,et al.  The multiconfiguration time-dependent Hartree (MCTDH) method: A highly efficient algorithm for propa , 1999 .

[81]  Lucas Visscher,et al.  Toward a Practical Method for Adaptive QM/MM Simulations. , 2009, Journal of chemical theory and computation.

[82]  Volodymyr Babin,et al.  A Critical Assessment of Two-Body and Three-Body Interactions in Water. , 2012, Journal of chemical theory and computation.

[83]  David,et al.  Gaussian basis sets for use in correlated molecular calculations . Ill . The atoms aluminum through argon , 1999 .

[84]  Sotiris S Xantheas,et al.  The bend angle of water in ice Ih and liquid water: The significance of implementing the nonlinear monomer dipole moment surface in classical interaction potentials. , 2006, The Journal of chemical physics.

[85]  Nohad Gresh,et al.  Anisotropic, Polarizable Molecular Mechanics Studies of Inter- and Intramolecular Interactions and Ligand-Macromolecule Complexes. A Bottom-Up Strategy. , 2007, Journal of chemical theory and computation.

[86]  T. Dunning,et al.  The structure of the water trimer from ab initio calculations , 1993 .

[87]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[88]  Joel M Bowman,et al.  Ab initio potential energy and dipole moment surfaces for H5O2 +. , 2005, The Journal of chemical physics.

[89]  Alexander D. MacKerell,et al.  A polarizable model of water for molecular dynamics simulations of biomolecules , 2006 .

[90]  M. Gillan,et al.  Perspective: How good is DFT for water? , 2016, The Journal of chemical physics.

[91]  D. Truhlar,et al.  Fragment-based quantum mechanical methods for periodic systems with Ewald summation and mean image charge convention for long-range electrostatic interactions. , 2012, Physical chemistry chemical physics : PCCP.

[92]  Philippe Sautet,et al.  Multiscale Modeling of Chemistry in Water: Are We There Yet? , 2013, Journal of chemical theory and computation.

[93]  Michele Parrinello,et al.  Efficient stochastic thermostatting of path integral molecular dynamics. , 2010, The Journal of chemical physics.

[94]  J. Bowman,et al.  Coupling of Low- and High-Frequency Vibrational Modes: Broadening in the Infrared Spectrum of F–(H2O)2 , 2013 .

[95]  Claude Millot,et al.  Revised Anisotropic Site Potentials for the Water Dimer and Calculated Properties , 1998 .

[96]  Donald G. Truhlar,et al.  Assessing the Accuracy of Density Functional and Semiempirical Wave Function Methods for Water Nanoparticles: Comparing Binding and Relative Energies of (H2O)16 and (H2O)17 to CCSD(T) Results. , 2013, Journal of chemical theory and computation.

[97]  F. Paesani,et al.  A refined MS-EVB model for proton transport in aqueous environments. , 2012, The journal of physical chemistry. B.

[98]  Kenneth D Jordan,et al.  A second generation distributed point polarizable water model. , 2010, The Journal of chemical physics.

[99]  T. Dunning,et al.  Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions , 1992 .

[100]  Jean-Philip Piquemal,et al.  Quantum mechanics/molecular mechanics electrostatic embedding with continuous and discrete functions. , 2006, The journal of physical chemistry. B.

[101]  Car,et al.  Unified approach for molecular dynamics and density-functional theory. , 1985, Physical review letters.

[102]  J. Stewart.  Optimization of parameters for semiempirical methods V: Modification of NDDO approximations and application to 70 elements , 2007, Journal of molecular modeling.

[103]  J. Bowman,et al.  Local-monomer calculations of the intramolecular IR spectra of the cage and prism isomers of HOD(D2O)5 and HOD and D2O ice Ih. , 2014, The journal of physical chemistry. B.

[104]  K. Kitaura,et al.  A new form for intermolecular potential energy functions , 1987 .

[105]  Krzysztof Szalewicz,et al.  Towards the complete understanding of water by a first-principles computational approach , 2009 .

[106]  Sergey V. Buldyrev,et al.  Generic mechanism for generating a liquid–liquid phase transition , 2001, Nature.

[107]  R. Podeszwa,et al.  Predictions for water clusters from a first-principles two- and three-body force field. , 2014, The Journal of chemical physics.

[108]  Pengyu Y. Ren,et al.  Systematic improvement of a classical molecular model of water. , 2013, The journal of physical chemistry. B.

[109]  Greg L. Hura,et al.  Development of an improved four-site water model for biomolecular simulations: TIP4P-Ew. , 2004, The Journal of chemical physics.

[110]  J. Ilja Siepmann,et al.  Development of Polarizable Water Force Fields for Phase Equilibrium Calculations , 2000 .

[111]  N. Gresh,et al.  Inter- and intramolecular interactions. Inception and refinements of the SIBFA, molecular mechanics (SMM) procedure, a separable, polarizable methodology grounded on ab initio SCF/MP2 computations. Examples of applications to molecular recognition problems , 1997 .

[112]  Alexander P. Lyubartsev,et al.  Determination of effective pair potentials from ab initio simulations: application to liquid water , 2000 .

[113]  Volodymyr Babin,et al.  Development of a "First-Principles" Water Potential with Flexible Monomers. III. Liquid Phase Properties. , 2014, Journal of chemical theory and computation.

[114]  Zhongwu Zhou,et al.  Role of nonadditive forces on the structure and properties of liquid water. , 2007, The Journal of chemical physics.

[115]  Giorgina Corongiu,et al.  Molecular dynamics simulations of liquid water using the NCC ab initio potential , 1990 .

[116]  Y. Tanimura,et al.  A polarizable water model for intramolecular and intermolecular vibrational spectroscopies. , 2011, The journal of physical chemistry. B.

[117]  Gregory A Voth,et al.  Are many-body electronic polarization effects important in liquid water? , 2007, The Journal of chemical physics.

[118]  Robert J. Harrison,et al.  Development of transferable interaction models for water. II. Accurate energetics of the first few water clusters from first principles , 2002 .

[119]  Francesco Paesani,et al.  Many-Body Convergence of the Electrostatic Properties of Water. , 2013, Journal of chemical theory and computation.

[120]  Gregory A. Voth,et al.  A quantum model for water: Equilibrium and dynamical properties , 1997 .

[121]  H. Jónsson,et al.  A transferable H2O interaction potential based on a single center multipole expansion: SCME. , 2013, Physical chemistry chemical physics : PCCP.

[122]  Volodymyr Babin,et al.  Development of a "First Principles" Water Potential with Flexible Monomers: Dimer Potential Energy Surface, VRT Spectrum, and Second Virial Coefficient. , 2014, Journal of chemical theory and computation.

[123]  Jay W Ponder,et al.  Revised Parameters for the AMOEBA Polarizable Atomic Multipole Water Model. , 2015, The journal of physical chemistry. B.

[124]  Joel M. Bowman,et al.  Permutationally invariant potential energy surfaces in high dimensionality , 2009 .

[125]  Daniel Spångberg,et al.  Derivation and evaluation of a flexible SPC model for liquid water , 2004 .

[126]  J. Murrell,et al.  Effect of Overlap on Dispersion Energies near the van der Waals Minimum , 1968 .

[127]  Thomas E. Markland,et al.  Competing quantum effects in the dynamics of a flexible water model. , 2009, The Journal of chemical physics.

[128]  Pengyu Y. Ren,et al.  Classical electrostatics for biomolecular simulations. , 2014, Chemical reviews.

[129]  J. Murrell,et al.  Intermolecular Forces in the Region of Small Orbital Overlap , 1967 .

[130]  P. Kiss,et al.  A systematic development of a polarizable potential of water. , 2013, The Journal of chemical physics.

[131]  K. Szalewicz,et al.  Ab initio three-body interactions for water. II. Effects on structure and energetics of liquid , 2003 .

[132]  Rita Prosmiti,et al.  i-TTM Model for Ab Initio-Based Ion-Water Interaction Potentials. 1. Halide-Water Potential Energy Functions. , 2016, The journal of physical chemistry. B.

[133]  Yingkai Zhang,et al.  Directional Dependence of Hydrogen Bonds: a Density-based Energy Decomposition Analysis and Its Implications on Force Field Development. , 2011, Journal of chemical theory and computation.

[134]  Berhane Temelso,et al.  Benchmark structures and binding energies of small water clusters with anharmonicity corrections. , 2011, The journal of physical chemistry. A.

[135]  V. Babin,et al.  The curious case of the water hexamer: Cage vs. Prism , 2013 .

[136]  K. Szalewicz,et al.  Spectra of water dimer from a new ab initio potential with flexible monomers. , 2012, The Journal of chemical physics.

[137]  W. L. Jorgensen,et al.  Comparison of simple potential functions for simulating liquid water , 1983 .

[138]  A. Scemama,et al.  Further refinements of next-generation force fields — Nonempirical localization of off-centered points in molecules , 2013 .

[139]  P. Åstrand,et al.  Intermolecular Interactions of Urea and Water , 1991 .

[140]  K. Szalewicz,et al.  Pair potential for water from symmetry-adapted perturbation theory , 1997 .

[141]  Joost VandeVondele,et al.  Periodic MP2, RPA, and Boundary Condition Assessment of Hydrogen Ordering in Ice XV. , 2014, The journal of physical chemistry letters.

[142]  H. Berendsen,et al.  Interaction Models for Water in Relation to Protein Hydration , 1981 .

[143]  J. Kolafa,et al.  Implementation of the Dahl-Andersen-Wertheim theory for realistic water-water potentials , 1989 .

[144]  Peng Bai,et al.  Water 26-mers Drawn from Bulk Simulations: Benchmark Binding Energies for Unprecedentedly Large Water Clusters and Assessment of the Electrostatically Embedded Three-Body and Pairwise Additive Approximations. , 2014, The journal of physical chemistry letters.

[145]  Sotiris S. Xantheas,et al.  Development of transferable interaction models for water. III. Reparametrization of an all-atom polarizable rigid model (TTM2–R) from first principles , 2002 .

[146]  Michael J. M. Mazack,et al.  Quantum mechanical force field for water with explicit electronic polarization. , 2013, The Journal of chemical physics.

[147]  E. Davidson,et al.  Structure of ice Ih. Ab initio two- and three-body water-water potentials and geometry optimization , 1985 .

[148]  Alexander D. MacKerell,et al.  CHARMM general force field: A force field for drug‐like molecules compatible with the CHARMM all‐atom additive biological force fields , 2009, J. Comput. Chem..

[149]  Miguel A Morales,et al.  Quantum Monte Carlo Benchmark of Exchange-Correlation Functionals for Bulk Water. , 2014, Journal of chemical theory and computation.

[150]  Gregory S. Tschumper,et al.  CCSD(T) complete basis set limit relative energies for low-lying water hexamer structures. , 2009, The journal of physical chemistry. A.

[151]  DAVID M. FERGUSON,et al.  Parameterization and evaluation of a flexible water model , 1995, J. Comput. Chem..

[152]  P. Popelier,et al.  Dynamically Polarizable Water Potential Based on Multipole Moments Trained by Machine Learning. , 2009, Journal of chemical theory and computation.

[153]  O. Matsuoka,et al.  CI study of the water dimer potential surface , 1976 .

[154]  So Hirata,et al.  Ab initio molecular dynamics of liquid water using embedded-fragment second-order many-body perturbation theory towards its accurate property prediction , 2015, Scientific Reports.

[155]  Donald G. Truhlar,et al.  Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods , 2010 .

[156]  S. L. Mayo,et al.  DREIDING: A generic force field for molecular simulations , 1990 .

[157]  Evans,et al.  Molecular-dynamics simulation of liquid water with an ab initio flexible water-water interaction potential. II. The effect of internal vibrations on the time correlation functions. , 1987, Physical review. A, General physics.

[158]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[159]  J. Abascal,et al.  A flexible model for water based on TIP4P/2005. , 2011, The Journal of chemical physics.

[160]  G. T. Fraser.  (H2O)2: spectroscopy, structure and dynamics , 1991 .

[161]  P. Cummings,et al.  From dimer to condensed phases at extreme conditions: accurate predictions of the properties of water by a Gaussian charge polarizable model. , 2005, The Journal of chemical physics.

[162]  Francesco Paesani,et al.  Infrared and Raman Spectroscopy of Liquid Water through "First-Principles" Many-Body Molecular Dynamics. , 2015, Journal of chemical theory and computation.

[163]  Donald G Truhlar,et al.  Conservative Algorithm for an Adaptive Change of Resolution in Mixed Atomistic/Coarse-Grained Multiscale Simulations. , 2008, Journal of chemical theory and computation.

[164]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[165]  J. Bowman,et al.  Ab initio potential and dipole moment surfaces for water. II. Local-monomer calculations of the infrared spectra of water clusters. , 2011, The Journal of chemical physics.

[166]  B. Slater,et al.  Proton ordering energetics in ice phases , 2006 .

[167]  Jean-Philip Piquemal,et al.  A CSOV study of the difference between HF and DFT intermolecular interaction energy values: The importance of the charge transfer contribution , 2005, J. Comput. Chem..

[168]  M. Parrinello,et al.  AB INITIO PATH INTEGRAL MOLECULAR DYNAMICS : BASIC IDEAS , 1996 .

[169]  J. Pople,et al.  Intermolecular energies of small water polymers , 1969 .

[170]  J. Bowman,et al.  The calculated infrared spectrum of Cl- H2O using a full dimensional ab initio potential surface and dipole moment surface. , 2006, The Journal of chemical physics.

[171]  A. Stone,et al.  Contribution of Many-Body Terms to the Energy for Small Water Clusters: A Comparison of ab Initio Calculations and Accurate Model Potentials , 1997 .

[172]  Sotiris S. Xantheas,et al.  Development of transferable interaction models for water. IV. A flexible, all-atom polarizable potential (TTM2-F) based on geometry dependent charges derived from an ab initio monomer dipole moment surface , 2002 .

[173]  Mark A. Johnson,et al.  Thermodynamics of water dimer dissociation in the primary hydration shell of the iodide ion with temperature-dependent vibrational predissociation spectroscopy. , 2015, The journal of physical chemistry. A.

[174]  T. Darden,et al.  Progress Towards Accurate Molecular Modeling of Metal Complexes Using Polarizable Force Fields , 2009 .

[175]  K. Szalewicz,et al.  Symmetry-adapted perturbation theory of potential-energy surfaces for weakly bound molecular complexes , 1994 .

[176]  Teodoro Laino,et al.  Semiempirical self-consistent polarization description of bulk water, the liquid-vapor interface, and cubic ice. , 2011, The journal of physical chemistry. A.

[177]  G. Jansen,et al.  A new potential energy surface for the water dimer obtained from separate fits of ab initio electrostatic, induction, dispersion and exchange energy contributions , 2006 .

[178]  Peter G. Wolynes,et al.  Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids , 1981 .

[179]  Donald G Truhlar,et al.  Adaptive partitioning in combined quantum mechanical and molecular mechanical calculations of potential energy functions for multiscale simulations. , 2007, The journal of physical chemistry. B.

[180]  Angela K. Wilson,et al.  Gaussian basis sets for use in correlated molecular calculations. IX. The atoms gallium through krypton , 1993 .

[181]  Giovanni Bussi,et al.  Colored-Noise Thermostats à la Carte , 2010, 1204.0822.

[182]  Lori A Burns,et al.  Levels of symmetry adapted perturbation theory (SAPT). I. Efficiency and performance for interaction energies. , 2014, The Journal of chemical physics.

[183]  Donald G Truhlar,et al.  X-Pol Potential: An Electronic Structure-Based Force Field for Molecular Dynamics Simulation of a Solvated Protein in Water. , 2009, Journal of chemical theory and computation.

[184]  Pengyu Y. Ren,et al.  Development of an AMOEBA water model using GEM distributed multipoles , 2015, Theoretical Chemistry Accounts.

[185]  E. Clementi,et al.  Preliminary observations on a new water–water potential , 2009 .

[186]  Anders Nilsson,et al.  Benchmark oxygen-oxygen pair-distribution function of ambient water from x-ray diffraction measurements with a wide Q-range. , 2013, The Journal of chemical physics.

[187]  V. Babin,et al.  Development of a "First Principles" Water Potential with Flexible Monomers. II: Trimer Potential Energy Surface, Third Virial Coefficient, and Small Clusters. , 2014, Journal of chemical theory and computation.

[188]  Z. Slanina.  Flexible BJH- and MCYL-type Potentials for the Water Dimer (H2O)2(g): A Successful Reproduction of the Observed Monomer/Dimer Vibrational Frequency Shifts* , 1991 .

[189]  M. Tuckerman.  Statistical Mechanics: Theory and Molecular Simulation , 2010 .

[190]  Nohad Gresh,et al.  Improved Formulas for the Calculation of the Electrostatic Contribution to the Intermolecular Interaction Energy from Multipolar Expansion of the Electronic Distribution. , 2003, The journal of physical chemistry. A.

[191]  Harold A. Scheraga,et al.  A polarizable force field for water using an artificial neural network , 2002 .

[192]  B. Braams,et al.  Ab initio potential energy and dipole moment surfaces of (H2O)2. , 2006, The journal of physical chemistry. A.

[193]  G. Groenenboom,et al.  Polarizable interaction potential for water from coupled cluster calculations. II. Applications to dimer spectra, virial coefficients, and simulations of liquid water. , 2008, The Journal of chemical physics.

[194]  Gregory S. Tschumper,et al.  Getting down to the Fundamentals of Hydrogen Bonding: Anharmonic Vibrational Frequencies of (HF)2 and (H2O)2 from Ab Initio Electronic Structure Computations. , 2014, Journal of chemical theory and computation.

[195]  Hannah R. Leverentz,et al.  Water 16-mers and hexamers: assessment of the three-body and electrostatically embedded many-body approximations of the correlation energy or the nonlocal energy as ways to include cooperative effects. , 2013, The journal of physical chemistry. A.

[196]  Gunnar Karlström,et al.  Molecular dynamics study of water adopting a potential function with explicit atomic dipole moments and anisotropic polarizabilities , 1995 .

[197]  Anna-Pitschna E. Kunz,et al.  Development of a nonlinear classical polarization model for liquid water and aqueous solutions: COS/D. , 2009, The journal of physical chemistry. A.

[198]  L. Shi,et al.  Dielectric constant and low-frequency infrared spectra for liquid water and ice Ih within the E3B model. , 2014, The Journal of chemical physics.

[199]  J. Skinner,et al.  Water simulation model with explicit three-molecule interactions. , 2008, The journal of physical chemistry. B.

[200]  Martin Head-Gordon,et al.  Alternative definitions of the frozen energy in energy decomposition analysis of density functional theory calculations. , 2016, The Journal of chemical physics.

[201]  Frank H. Stillinger,et al.  Polarization model for water and its ionic dissociation products , 1978 .

[202]  Rustam Z. Khaliullin,et al.  An efficient self-consistent field method for large systems of weakly interacting components. , 2006, The Journal of chemical physics.

[203]  H Eugene Stanley,et al.  Thermodynamics and dynamics of the two-scale spherically symmetric Jagla ramp model of anomalous liquids. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[204]  Jason Crain,et al.  Signature properties of water: Their molecular electronic origins , 2015, Proceedings of the National Academy of Sciences.

[205]  Eric D. Glendening,et al.  Natural energy decomposition analysis: An energy partitioning procedure for molecular interactions with application to weak hydrogen bonding, strong ionic, and moderate donor–acceptor interactions , 1994 .

[206]  R. Saykally,et al.  A ‘first principles’ potential energy surface for liquid water from VRT spectroscopy of water clusters , 2004, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[207]  F. Keutsch,et al.  Complete characterization of the water dimer vibrational ground state and testing the VRT(ASP-W)III, SAPT-5st, and VRT(MCY-5f) surfaces , 2003 .

[208]  Glenn I. Hawe,et al.  A water potential based on multipole moments trained by machine learning—Reducing maximum energy errors , 2010 .

[209]  Sotiris S Xantheas,et al.  Development of transferable interaction potentials for water. V. Extension of the flexible, polarizable, Thole-type model potential (TTM3-F, v. 3.0) to describe the vibrational spectra of water clusters and liquid water. , 2008, The Journal of chemical physics.

[210]  U. Singh,et al.  A water dimer potential based on ab initio calculations using Morokuma component analyses , 1985 .

[211]  Valeria Molinero,et al.  Water modeled as an intermediate element between carbon and silicon. , 2009, The journal of physical chemistry. B.

[212]  Wojciech Cencek,et al.  Interaction energies of large clusters from many-body expansion. , 2011, The Journal of chemical physics.

[213]  Rustam Z. Khaliullin,et al.  Unravelling the origin of intermolecular interactions using absolutely localized molecular orbitals. , 2007, The journal of physical chemistry. A.

[214]  J. Bowman,et al.  Vibrational analysis of an ice Ih model from 0 to 4000 cm(-1) using the ab initio WHBB potential energy surface. , 2013, The journal of physical chemistry. B.

[215]  A. Hesselmann,et al.  Intermolecular symmetry-adapted perturbation theory study of large organic complexes. , 2014, The Journal of chemical physics.

[216]  Thomas F. Miller,et al.  Ring-polymer molecular dynamics: quantum effects in chemical dynamics from classical trajectories in an extended phase space. , 2013, Annual review of physical chemistry.

[217]  Thomas M Truskett,et al.  A single-bond approach to orientation-dependent interactions and its implications for liquid water , 1999 .

[218]  C. Leforestier.  Infrared shifts of the water dimer from the fully flexible ab initio HBB2 potential , 2012, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[219]  Stefan Grimme,et al.  Effect of the damping function in dispersion corrected density functional theory , 2011, J. Comput. Chem..

[220]  Jean-Philip Piquemal,et al.  GEM*: A Molecular Electronic Density-Based Force Field for Molecular Dynamics Simulations. , 2014, Journal of chemical theory and computation.

[221]  A. W. Götz,et al.  Application of Adaptive QM/MM Methods to Molecular Dynamics Simulations of Aqueous Systems. , 2012, Journal of chemical theory and computation.

[222]  J. Bowman,et al.  IR Spectra of the Water Hexamer: Theory, with Inclusion of the Monomer Bend Overtone, and Experiment Are in Agreement. , 2013, The journal of physical chemistry letters.

[223]  Krzysztof Szalewicz,et al.  Predictions of the Properties of Water from First Principles , 2007, Science.

[224]  G. Schenter,et al.  A quantitative account of quantum effects in liquid water. , 2006, The Journal of chemical physics.

[225]  F. Paesani.  Hydrogen bond dynamics in heavy water studied with quantum dynamical simulations. , 2011, Physical chemistry chemical physics : PCCP.

[226]  K. Honda.  An effective potential function with enhanced charge-transfer-type interaction for hydrogen-bonding liquids , 2002 .

[227]  A. Stone.  Electrostatic damping functions and the penetration energy. , 2011, The journal of physical chemistry. A.

[228]  J. Hirschfelder.  Perturbation theory for exchange forces, II , 1967 .

[229]  Andreas W Götz,et al.  On the representation of many-body interactions in water. , 2015, The Journal of chemical physics.

[230]  Kai Liu,et al.  Terahertz laser spectroscopy of the water dimer intermolecular vibrations. II. (H2O)2 , 2000 .

[231]  Yuqing Qiu,et al.  Coarse-Graining of TIP4P/2005, TIP4P-Ew, SPC/E, and TIP3P to Monatomic Anisotropic Water Models Using Relative Entropy Minimization. , 2014, Journal of chemical theory and computation.

[232]  G. Karlström,et al.  Polarizable Ions in Polarizable Water: A Molecular Dynamics Study , 1997 .

[233]  Gábor Csányi,et al.  Gaussian approximation potentials: A brief tutorial introduction , 2015, 1502.01366.

[234]  Sotiris S Xantheas,et al.  The flexible, polarizable, thole-type interaction potential for water (TTM2-F) revisited. , 2006, The journal of physical chemistry. A.

[235]  Claude Leforestier,et al.  A comparison of different propagation schemes for the time dependent Schro¨dinger equation , 1991 .

[236]  R. van Harrevelt,et al.  An accurate analytic representation of the water pair potential. , 2008, Physical chemistry chemical physics : PCCP.

[237]  Kazuo Kitaura,et al.  A new energy decomposition scheme for molecular interactions within the Hartree‐Fock approximation , 1976 .

[238]  M. Gordon,et al.  A combined effective fragment potential-fragment molecular orbital method. I. The energy expression and initial applications. , 2009, The Journal of chemical physics.

[239]  Robert M Parrish,et al.  Spatial assignment of symmetry adapted perturbation theory interaction energy components: The atomic SAPT partition. , 2014, The Journal of chemical physics.

[240]  J. Bowman,et al.  Ab Initio Quantum Approaches to the IR Spectroscopy of Water and Hydrates. , 2015, The journal of physical chemistry letters.

[241]  Troy Van Voorhis,et al.  Nonlocal van der Waals density functional: the simpler the better. , 2010, The Journal of chemical physics.

[242]  G. Kell.  Density, thermal expansivity, and compressibility of liquid water from 0.deg. to 150.deg.. Correlations and tables for atmospheric pressure and saturation reviewed and expressed on 1968 temperature scale , 1975 .

[243]  S. Xantheas,et al.  Optimal geometries and harmonic vibrational frequencies of the global minima of water clusters (H2O)n, n = 2-6, and several hexamer local minima at the CCSD(T) level of theory. , 2013, The Journal of chemical physics.

[244]  Pengyu Y. Ren,et al.  Polarizable Atomic Multipole Water Model for Molecular Mechanics Simulation , 2003 .

[245]  C. Brooks.  Computer simulation of liquids , 1989 .

[246]  Sotiris S. Xantheas,et al.  Cooperativity and Hydrogen Bonding Network in Water Clusters , 2000 .

[247]  Weber,et al.  Computer simulation of local order in condensed phases of silicon. , 1985, Physical review. B, Condensed matter.

[248]  P. Kollman,et al.  Structure and Properties of Neat Liquids Using Nonadditive Molecular Dynamics: Water, Methanol, and N-Methylacetamide , 1995 .

[249]  B. C. Garrett,et al.  Self-consistent polarization neglect of diatomic differential overlap: application to water clusters. , 2008, The Journal of chemical physics.

[250]  S. Yoo,et al.  Nuclear Quantum Effects in the Reorientation of Water , 2010 .

[251]  Mark S Gordon,et al.  Systematic fragmentation method and the effective fragment potential: an efficient method for capturing molecular energies. , 2009, The journal of physical chemistry. A.

[252]  A. Stone,et al.  Towards an accurate intermolecular potential for water , 1992 .

[253]  D. Manolopoulos,et al.  An efficient ring polymer contraction scheme for imaginary time path integral simulations. , 2008, The Journal of chemical physics.

[254]  Harry Partridge,et al.  The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data , 1997 .

[255]  J. Bowman,et al.  Towards an ab initio flexible potential for water, and post-harmonic quantum vibrational analysis of water clusters , 2010 .

[256]  Gregory A. Voth,et al.  Path‐Integral Centroid Methods in Quantum Statistical Mechanics and Dynamics , 2007 .

[257]  J. VandeVondele,et al.  Correction to "Bulk Liquid Water at Ambient Temperature and Pressure from MP2 Theory". , 2013, The journal of physical chemistry letters.

[258]  Roberto Car,et al.  Nuclear quantum effects in water. , 2008, Physical review letters.

[259]  G. Shields,et al.  The Role of Anharmonicity in Hydrogen-Bonded Systems: The Case of Water Clusters. , 2011, Journal of chemical theory and computation.

[260]  T. Straatsma,et al.  THE MISSING TERM IN EFFECTIVE PAIR POTENTIALS , 1987 .

[261]  B. Montgomery Pettitt,et al.  Simple intramolecular model potentials for water , 1987 .

[262]  Lu Wang,et al.  Quantum fluctuations and isotope effects in ab initio descriptions of water. , 2014, The Journal of chemical physics.

[263]  P. Jankowski,et al.  Ab initio water pair potential with flexible monomers. , 2015, The journal of physical chemistry. A.

[264]  H. Jónsson,et al.  Molecular multipole moments of water molecules in ice Ih , 1998 .

[265]  Kersti Hermansson,et al.  AB-INITIO STUDY OF COOPERATIVITY IN WATER CHAINS - BINDING-ENERGIES AND ANHARMONIC FREQUENCIES , 1994 .

[266]  P. Pieniazek,et al.  Robust three-body water simulation model. , 2011, The Journal of chemical physics.

[267]  Michael W. Mahoney,et al.  A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions , 2000 .

[268]  William H. Fink,et al.  Frozen fragment reduced variational space analysis of hydrogen bonding interactions. Application to the water dimer , 1987 .

[269]  Volodymyr Babin,et al.  Toward a Universal Water Model: First Principles Simulations from the Dimer to the Liquid Phase. , 2012, The journal of physical chemistry letters.

[270]  S. Xantheas,et al.  Development of transferable interaction models for water. I. Prominent features of the water dimer potential energy surface , 2002 .

[271]  Heather A. Harker,et al.  Water dimer hydrogen bond stretch, donor torsion overtone, and “in-plane bend” vibrations , 2003 .

[272]  G. Groenenboom,et al.  Water pair potential of near spectroscopic accuracy. I. Analysis of potential surface and virial coefficients , 2000 .

[273]  Wei Zhang,et al.  An accurate and simple quantum model for liquid water. , 2006, The Journal of chemical physics.

[274]  Jean-Philip Piquemal,et al.  Numerical fitting of molecular properties to Hermite Gaussians. , 2007, The journal of physical chemistry. A.

[275]  S. F. Boys,et al.  The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors , 1970 .

[276]  Zhenyu Yan,et al.  Structural order for one-scale and two-scale potentials. , 2005, Physical review letters.

[277]  William H. Miller,et al.  The Semiclassical Initial Value Representation: A Potentially Practical Way for Adding Quantum Effects to Classical Molecular Dynamics Simulations , 2001 .

[278]  E. A. Jagla.  CORE-SOFTENED POTENTIALS AND THE ANOMALOUS PROPERTIES OF WATER , 1999 .

[279]  Cristiano L. Dias,et al.  Three-dimensional "Mercedes-Benz" model for water. , 2009, The Journal of chemical physics.

[280]  Mark S. Gordon,et al.  The Effective Fragment Potential Method: A QM-Based MM Approach to Modeling Environmental Effects in Chemistry , 2001 .

[281]  Gábor Csányi,et al.  Reactive Many-Body Expansion for a Protonated Water Cluster. , 2014, Journal of chemical theory and computation.

[282]  R. Kondor,et al.  Gaussian approximation potentials: the accuracy of quantum mechanics, without the electrons. , 2009, Physical review letters.

[283]  Gregory A Voth,et al.  The multiscale coarse-graining method. VI. Implementation of three-body coarse-grained potentials. , 2010, The Journal of chemical physics.

[284]  Donald G. Truhlar,et al.  Explicit Polarization: A Quantum Mechanical Framework for Developing Next Generation Force Fields , 2014, Accounts of chemical research.

[285]  G Andrés Cisneros,et al.  Application of Gaussian Electrostatic Model (GEM) Distributed Multipoles in the AMOEBA Force Field. , 2012, Journal of chemical theory and computation.

[286]  M. Mezei,et al.  Use of a non‐pair‐additive intermolecular potential function to fit quantum‐mechanical data on water molecule interactions , 1977 .

[287]  W. V. van Gunsteren,et al.  Charge-on-spring polarizable water models revisited: from water clusters to liquid water to ice. , 2004, The Journal of chemical physics.

[288]  P. Mankoo,et al.  POLIR: polarizable, flexible, transferable water potential optimized for IR spectroscopy. , 2008, The Journal of chemical physics.

[289]  J. Skinner,et al.  The water hexamer: three-body interactions, structures, energetics, and OH-stretch spectroscopy at finite temperature. , 2012, The Journal of chemical physics.

[290]  Roberto Car,et al.  The individual and collective effects of exact exchange and dispersion interactions on the ab initio structure of liquid water. , 2014, The Journal of chemical physics.

[291]  B. Berne,et al.  Combined fluctuating charge and polarizable dipole models: Application to a five-site water potential function , 2001 .

[292]  M. Gordon,et al.  The effective fragment potential: small clusters and radial distribution functions. , 2004, The Journal of chemical physics.

[293]  J. Bowman,et al.  Ab initio potential energy and dipole moment surfaces of the F(-)(H2O) complex. , 2014, Spectrochimica Acta Part A - Molecular and Biomolecular Spectroscopy.

[294]  P. Kollman,et al.  Water–water and water–ion potential functions including terms for many body effects , 1985 .

[295]  Klaus R. Liedl,et al.  A QM/MM simulation method applied to the solution of Li+ in liquid ammonia , 1996 .

[296]  F. Paesani,et al.  On the interplay of the potential energy and dipole moment surfaces in controlling the infrared activity of liquid water. , 2015, The Journal of chemical physics.

[297]  P. Kollman,et al.  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules , 1995 .

[298]  Jonas Boström,et al.  A NEMO potential that includes the dipole–quadrupole and quadrupole–quadrupole polarizability , 2010, J. Comput. Chem..

[299]  H. Jónsson,et al.  Electric fields in ice and near water clusters , 2000 .

[300]  E. A. Jagla.  PHASE BEHAVIOR OF A SYSTEM OF PARTICLES WITH CORE COLLAPSE , 1998 .

[301]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series , 1964 .

[302]  F. Paesani,et al.  Toward Chemical Accuracy in the Description of Ion-Water Interactions through Many-Body Representations. I. Halide-Water Dimer Potential Energy Surfaces. , 2016, Journal of chemical theory and computation.