Nuclear quantum effects in liquid water from path-integral simulations using an ab initio force-matching approach

We have applied path integral simulations, in combination with new ab initio based water potentials, to investigate nuclear quantum effects in liquid water. Because direct ab initio path integral simulations are computationally expensive, a flexible water model is parameterised by force-matching to density functional theory-based molecular dynamics simulations. Static and dynamic properties of liquid water at ambient conditions are presented and the role of nuclear quantum effects, exchange-correlation functionals and dispersion corrections are discussed in regards to reproducing the experimental properties of liquid water.

[1]  Matthias Krack,et al.  Pseudopotentials for H to Kr optimized for gradient-corrected exchange-correlation functionals , 2005 .

[2]  R. Brent Table errata: Algorithms for minimization without derivatives (Prentice-Hall, Englewood Cliffs, N. J., 1973) , 1975 .

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

[4]  R. Car,et al.  Dipolar correlations and the dielectric permittivity of water. , 2007, Physical review letters.

[5]  Michiel Sprik,et al.  Hydrogen bonding and the static dielectric constant in liquid water , 1991 .

[6]  Gregory A Voth,et al.  A comparative study of imaginary time path integral based methods for quantum dynamics. , 2006, The Journal of chemical physics.

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

[8]  Michiel Sprik,et al.  A polarizable model for water using distributed charge sites , 1988 .

[9]  J. Kolafa,et al.  A classical polarizable model for simulations of water and ice. , 2011, Physical chemistry chemical physics : PCCP.

[10]  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.

[11]  Rustam Z Khaliullin,et al.  Electronic signature of the instantaneous asymmetry in the first coordination shell of liquid water , 2013, Nature Communications.

[12]  P. Kusalik,et al.  Quantum effects in light and heavy liquid water: A rigid-body centroid molecular dynamics study. , 2004, The Journal of chemical physics.

[13]  James B. Adams,et al.  Interatomic Potentials from First-Principles Calculations: The Force-Matching Method , 1993, cond-mat/9306054.

[14]  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.

[15]  Mariana Rossi,et al.  Ab initio molecular dynamics , 2013 .

[16]  A. Lyubartsev,et al.  Calculation of effective interaction potentials from radial distribution functions: A reverse Monte Carlo approach. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Mark E. Tuckerman,et al.  Reversible multiple time scale molecular dynamics , 1992 .

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

[19]  David E Manolopoulos,et al.  Zero point energy leakage in condensed phase dynamics: an assessment of quantum simulation methods for liquid water. , 2009, The Journal of chemical physics.

[20]  Walter Kauzmann,et al.  The Structure and Properties of Water , 1969 .

[21]  D. Adams Computer simulation of highly polar liquids: The hard sphere plus point dipole potential , 1980 .

[22]  Thomas D Kühne,et al.  Optimal calculation of the pair correlation function for an orthorhombic system. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Michele Parrinello,et al.  Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach , 2005, Comput. Phys. Commun..

[24]  Michele Parrinello,et al.  Structural, electronic, and bonding properties of liquid water from first principles , 1999 .

[25]  B. Berne,et al.  Quantum effects in liquid water: Path-integral simulations of a flexible and polarizable ab initio model , 2001 .

[26]  D. Ceperley Path integrals in the theory of condensed helium , 1995 .

[27]  Emilio Artacho,et al.  Density, structure, and dynamics of water: the effect of van der Waals interactions. , 2010, The Journal of chemical physics.

[28]  E. R. Smith Electrostatic energy in ionic crystals , 1981, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[29]  S. Goedecker,et al.  Relativistic separable dual-space Gaussian pseudopotentials from H to Rn , 1998, cond-mat/9803286.

[30]  Thomas F. Miller,et al.  Quantum diffusion in liquid water from ring polymer molecular dynamics. , 2005, The Journal of chemical physics.

[31]  Ali Hassanali,et al.  Proton transfer through the water gossamer , 2013, Proceedings of the National Academy of Sciences.

[32]  J. Perram,et al.  Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants , 1980, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[33]  Anders Wallqvist,et al.  Path-integral simulation of pure water☆ , 1985 .

[34]  Roger Impey,et al.  Spectroscopic and transport properties of water , 1982 .

[35]  J. Reimers,et al.  Unit cells for the simulation of hexagonal ice , 1997 .

[36]  G. Scuseria,et al.  Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids. , 2003, Physical review letters.

[37]  Kurt Kremer,et al.  Molecular dynamics simulation of a polymer chain in solution , 1993 .

[38]  Yang Song,et al.  Developing ab initio quality force fields from condensed phase quantum-mechanics/molecular-mechanics calculations through the adaptive force matching method. , 2008, The Journal of chemical physics.

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

[40]  R. L. Henderson A uniqueness theorem for fluid pair correlation functions , 1974 .

[41]  L. Dang,et al.  MOLECULAR DYNAMICS STUDY OF WATER CLUSTERS, LIQUID, AND LIQUID-VAPOR INTERFACE OF WATER WITH MANY-BODY POTENTIALS , 1997 .

[42]  Michele Parrinello,et al.  Water Molecule Dipole in the Gas and in the Liquid Phase , 1999 .

[43]  J. Perdew,et al.  Density-functional approximation for the correlation energy of the inhomogeneous electron gas. , 1986, Physical review. B, Condensed matter.

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

[45]  S. Grimme,et al.  A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. , 2010, The Journal of chemical physics.

[46]  C. Vega,et al.  A general purpose model for the condensed phases of water: TIP4P/2005. , 2005, The Journal of chemical physics.

[47]  Yingkai Zhang,et al.  Comment on “Generalized Gradient Approximation Made Simple” , 1998 .

[48]  Network equilibration and first-principles liquid water. , 2004, The Journal of chemical physics.

[49]  Ivano Tavernelli,et al.  Structure and Dynamics of Liquid Water from ab Initio Molecular Dynamics-Comparison of BLYP, PBE, and revPBE Density Functionals with and without van der Waals Corrections. , 2012, Journal of chemical theory and computation.

[50]  G. Galli,et al.  Entropy of liquid water from ab initio molecular dynamics. , 2011, The journal of physical chemistry. B.

[51]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

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

[53]  Dominik Marx,et al.  On the applicability of centroid and ring polymer path integral molecular dynamics for vibrational spectroscopy. , 2009, The Journal of chemical physics.

[54]  Efthimios Kaxiras,et al.  New Insights into the Structure of the Vapor/Water Interface from Large-Scale First-Principles Simulations. , 2011, The journal of physical chemistry letters.

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

[56]  Michele Parrinello,et al.  Efficient and general algorithms for path integral Car–Parrinello molecular dynamics , 1996 .

[57]  A. Haymet,et al.  Ice 1h/water interface of the SPC/E model: Molecular dynamics simulations of the equilibrium basal and prism interfaces , 2002 .

[58]  R. A. Kuharski,et al.  A quantum mechanical study of structure in liquid H2O and D2O , 1985 .

[59]  J. Perram,et al.  Computer simulation of the static dielectric constant of systems with permanent electric dipoles. , 1986, Annual review of physical chemistry.

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

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

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

[63]  M. Parrinello,et al.  Canonical sampling through velocity rescaling. , 2007, The Journal of chemical physics.

[64]  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 .

[65]  Ivano Tavernelli,et al.  Variational optimization of effective atom centered potentials for molecular properties. , 2005, The Journal of chemical physics.

[66]  V. Buch,et al.  Simulations of H2O Solid, Liquid, and Clusters, with an Emphasis on Ferroelectric Ordering Transition in Hexagonal Ice , 1998 .

[67]  Alan K. Soper,et al.  The radial distribution functions of water and ice from 220 to 673 K and at pressures up to 400 MPa , 2000 .

[68]  F. Gygi,et al.  Structural and Vibrational Properties of Liquid Water from van der Waals Density Functionals. , 2011, Journal of chemical theory and computation.

[69]  Marco Masia,et al.  Improving the force matching algorithm: Application to a simple point charge flexible model of water , 2011, Comput. Phys. Commun..

[70]  David E Manolopoulos,et al.  Comparison of path integral molecular dynamics methods for the infrared absorption spectrum of liquid water. , 2008, The Journal of chemical physics.

[71]  Teodora Todorova,et al.  Molecular dynamics simulation of liquid water: hybrid density functionals. , 2006, The journal of physical chemistry. B.

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

[73]  Dominik Marx,et al.  Communications: On artificial frequency shifts in infrared spectra obtained from centroid molecular dynamics: Quantum liquid water. , 2010, The Journal of chemical physics.

[74]  F. Stillinger,et al.  Improved simulation of liquid water by molecular dynamics , 1974 .

[75]  Michele Parrinello,et al.  A hybrid Gaussian and plane wave density functional scheme , 1997 .

[76]  Joost VandeVondele,et al.  The influence of temperature and density functional models in ab initio molecular dynamics simulation of liquid water. , 2005, The Journal of chemical physics.

[77]  N. Marzari,et al.  Maximally localized generalized Wannier functions for composite energy bands , 1997, cond-mat/9707145.

[78]  Maximally-localized Wannier functions for disordered systems: application to amorphous silicon , 1998, cond-mat/9804019.

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

[80]  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.

[81]  Joost VandeVondele,et al.  Ab initio molecular dynamics using hybrid density functionals. , 2008, The Journal of chemical physics.

[82]  Martin Neumann,et al.  Dipole moment fluctuation formulas in computer simulations of polar systems , 1983 .

[83]  Y. Furukawa,et al.  Anisotropy in growth kinetics at interfaces between proton-disordered hexagonal ice and water: A molecular dynamics study using the six-site model of H2O , 2005 .

[84]  Mark E Tuckerman,et al.  Ab initio molecular dynamics study of water at constant pressure using converged basis sets and empirical dispersion corrections. , 2012, The Journal of chemical physics.

[85]  D. Sebastiani,et al.  NMR chemical shifts as a tool to analyze first principles molecular dynamics simulations in condensed phases: the case of liquid water , 2010, Magnetic resonance in chemistry : MRC.

[86]  Rustam Z. Khaliullin,et al.  Microscopic properties of liquid water from combined ab initio molecular dynamics and energy decomposition studies. , 2013, Physical chemistry chemical physics : PCCP.

[87]  Joost VandeVondele,et al.  Auxiliary Density Matrix Methods for Hartree-Fock Exchange Calculations. , 2010, Journal of chemical theory and computation.

[88]  D. Adams Theory of the dielectric constant of ice , 1981, Nature.

[89]  Kari Laasonen,et al.  ‘‘Ab initio’’ liquid water , 1993 .

[90]  C. Vega,et al.  The melting point of ice Ih for common water models calculated from direct coexistence of the solid-liquid interface. , 2006, The Journal of chemical physics.

[91]  H. C. Andersen Molecular dynamics simulations at constant pressure and/or temperature , 1980 .

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

[93]  S. Yoo,et al.  Communication: The effect of dispersion corrections on the melting temperature of liquid water. , 2011, The Journal of chemical physics.

[94]  B. M. Fulk MATH , 1992 .

[95]  Gregory A Voth,et al.  A quantitative assessment of the accuracy of centroid molecular dynamics for the calculation of the infrared spectrum of liquid water. , 2010, The Journal of chemical physics.

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

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

[98]  C. Vega,et al.  The melting temperature of the most common models of water. , 2005, The Journal of chemical physics.

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

[100]  Matthias Krack,et al.  Static and Dynamical Properties of Liquid Water from First Principles by a Novel Car-Parrinello-like Approach. , 2009, Journal of chemical theory and computation.

[101]  Free energy of liquid water on the basis of quasichemical theory and ab initio molecular dynamics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[102]  Joost VandeVondele,et al.  Isobaric-isothermal molecular dynamics simulations utilizing density functional theory: an assessment of the structure and density of water at near-ambient conditions. , 2009, The journal of physical chemistry. B.

[103]  Peter J Rossky,et al.  Static and dynamic quantum effects in molecular liquids: a linearized path integral description of water. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[104]  D. Case,et al.  Quantum dynamical effects in liquid water: A semiclassical study on the diffusion and the infrared absorption spectrum. , 2009, The Journal of chemical physics.

[105]  C. Vega,et al.  Relation between the melting temperature and the temperature of maximum density for the most common models of water. , 2005, The Journal of chemical physics.

[106]  M. Klein,et al.  Hydrogen bonding in water. , 2003, Physical review letters.

[107]  H. Berendsen,et al.  Molecular dynamics with coupling to an external bath , 1984 .

[108]  S. Venyaminov,et al.  Water (H2O and D2O) molar absorptivity in the 1000-4000 cm-1 range and quantitative infrared spectroscopy of aqueous solutions. , 1997, Analytical biochemistry.

[109]  M. V. Subbotin,et al.  Water properties from first principles: simulations by a general-purpose quantum mechanical polarizable force field. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[110]  Lisandro Hernández de la Peña,et al.  Quantum effects in liquid water and ice: model dependence. , 2006, The Journal of chemical physics.

[111]  William S. Price,et al.  Self-Diffusion of Supercooled Water to 238 K Using PGSE NMR Diffusion Measurements , 1999 .

[112]  Dean R. Haeffner,et al.  Electron distribution in water , 2000 .

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

[114]  Dirk Reith,et al.  Deriving effective mesoscale potentials from atomistic simulations , 2002, J. Comput. Chem..

[115]  Rustam Z. Khaliullin,et al.  Vibrational Signature of Water Molecules in Asymmetric Hydrogen Bonding Environments , 2013 .

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

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

[118]  A. Becke Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals , 1997 .

[119]  Nicola Marzari,et al.  Static and dynamical properties of heavy water at ambient conditions from first-principles molecular dynamics. , 2005, The Journal of chemical physics.

[120]  M. Parrinello,et al.  Study of an F center in molten KCl , 1984 .

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

[122]  A. R. H. Goodwin,et al.  A Database for the Static Dielectric Constant of Water and Steam , 1995 .

[123]  William H Miller,et al.  Quantum dynamics of complex molecular systems. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[124]  Hannes Jónsson,et al.  Multipole moments of water molecules in clusters and ice Ih from first principles calculations , 1999 .

[125]  Dieter Kraft,et al.  Algorithm 733: TOMP–Fortran modules for optimal control calculations , 1994, TOMS.

[126]  Michiel Sprik,et al.  Ab initio molecular dynamics simulation of liquid water: Comparison of three gradient‐corrected density functionals , 1996 .

[127]  S. Yoo,et al.  On the phase diagram of water with density functional theory potentials: The melting temperature of ice I(h) with the Perdew-Burke-Ernzerhof and Becke-Lee-Yang-Parr functionals. , 2009, The Journal of chemical physics.

[128]  David E. Manolopoulos,et al.  A refined ring polymer contraction scheme for systems with electrostatic interactions , 2008 .

[129]  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.

[130]  Bin Chen,et al.  Liquid Water from First Principles: Investigation of Different Sampling Approaches , 2004 .

[131]  Teter,et al.  Separable dual-space Gaussian pseudopotentials. , 1996, Physical review. B, Condensed matter.

[132]  Joost VandeVondele,et al.  Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases. , 2007, The Journal of chemical physics.

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

[134]  M. Tuckerman,et al.  Structure of liquid water at ambient temperature from ab initio molecular dynamics performed in the complete basis set limit. , 2006, The Journal of chemical physics.

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

[136]  J. D. Bernal,et al.  A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and Hydroxyl Ions , 1933 .

[137]  Gerhard Hummer,et al.  System-Size Dependence of Diffusion Coefficients and Viscosities from Molecular Dynamics Simulations with Periodic Boundary Conditions , 2004 .

[138]  Steven J. Stuart,et al.  Dynamical fluctuating charge force fields: Application to liquid water , 1994 .

[139]  K. Kremer,et al.  Nuclear Quantum Effects in Water: A Multiscale Study. , 2014, Journal of chemical theory and computation.

[140]  M. Tuckerman,et al.  Dynamical properties of liquid water from ab initio molecular dynamics performed in the complete basis set limit. , 2007, The Journal of chemical physics.

[141]  J. Kirkwood The Dielectric Polarization of Polar Liquids , 1939 .

[142]  F. Stillinger,et al.  Molecular Dynamics Study of Liquid Water , 1971 .

[143]  Matthias Krack,et al.  Efficient and accurate Car-Parrinello-like approach to Born-Oppenheimer molecular dynamics. , 2007, Physical review letters.

[144]  Ian R. Craig,et al.  Quantum statistics and classical mechanics: real time correlation functions from ring polymer molecular dynamics. , 2004, The Journal of chemical physics.

[145]  Wolfgang Wagner,et al.  A Fundamental Equation for Water Covering the Range from the Melting Line to 1273 K at Pressures up to 25 000 MPa , 1989 .