Anisotropy of the Proton Momentum Distribution in Water.

One of the many peculiar properties of water is the pronounced deviation of the proton momentum distribution from Maxwell-Boltzmann behavior. This deviation from the classical limit is a manifestation of the quantum mechanical nature of protons. Its extent, which can be probed directly by deep inelastic neutron scattering experiments, gives important insight on the potential of mean force felt by H atoms. The determination of the full distribution of particle momenta, however, is a real tour de force for both experiments and theory, which has led to unresolved discrepancies between the two. In this study, we present comprehensive, fully converged momentum distributions for water at several thermodynamic state points, focusing on the components that cannot be described in terms of a scalar contribution to the quantum kinetic energy, and providing a benchmark that can serve as a reference for future simulations and experiments. In doing so, we also introduce a number of technical developments that simplify and accelerate greatly the calculation of momentum distributions by means of atomistic simulations.

[1]  G. Galli,et al.  The quantum nature of the OH stretching mode in ice and water probed by neutron scattering experiments. , 2013, The Journal of chemical physics.

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

[3]  S. Imberti,et al.  Proton momentum distribution of liquid water from room temperature to the supercritical phase. , 2008, Physical review letters.

[4]  P. Platzman,et al.  The proton momentum distribution in water and ice , 2004 .

[5]  S. Mukamel,et al.  The proton momentum distribution in strongly H-bonded phases of water: a critical test of electrostatic models. , 2011, The Journal of chemical physics.

[6]  T. Morawietz,et al.  How van der Waals interactions determine the unique properties of water , 2016, Proceedings of the National Academy of Sciences.

[7]  Francesco Paesani,et al.  Getting the Right Answers for the Right Reasons: Toward Predictive Molecular Simulations of Water with Many-Body Potential Energy Functions. , 2016, Accounts of chemical research.

[8]  F. Paesani,et al.  Temperature-dependent vibrational spectra and structure of liquid water from classical and quantum simulations with the MB-pol potential energy function. , 2017, The Journal of chemical physics.

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

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

[11]  Ab initio simulation of particle momentum distributions in high-pressure water , 2014 .

[12]  Oliver Riordan,et al.  The inefficiency of re-weighted sampling and the curse of system size in high-order path integration , 2011, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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

[14]  Jörg Behler,et al.  Nuclear Quantum Effects in Water at the Triple Point: Using Theory as a Link Between Experiments. , 2016, The journal of physical chemistry letters.

[15]  Michele Parrinello,et al.  Displaced path integral formulation for the momentum distribution of quantum particles. , 2010, Physical review letters.

[16]  C. Herrero,et al.  Kinetic energy of protons in ice Ih and water: A path integral study , 2011, 1108.2145.

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

[18]  F. Bruni,et al.  Excess of proton mean kinetic energy in supercooled water. , 2009, Physical review letters.

[19]  Michele Ceriotti,et al.  i-PI: A Python interface for ab initio path integral molecular dynamics simulations , 2014, Comput. Phys. Commun..

[20]  Joseph A Morrone,et al.  Proton momentum distribution in water: an open path integral molecular dynamics study. , 2007, The Journal of chemical physics.

[21]  Jörg Behler,et al.  High order path integrals made easy. , 2016, The Journal of chemical physics.

[22]  Michele Parrinello,et al.  Nuclear quantum effects in ab initio dynamics: Theory and experiments for lithium imide , 2010, 1009.2862.

[23]  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.

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

[25]  R. Car,et al.  Spherical momentum distribution of the protons in hexagonal ice from modeling of inelastic neutron scattering data. , 2012, The Journal of chemical physics.

[26]  Roberto Senesi,et al.  Measurement of momentum distribution of lightatoms and molecules in condensed matter systems using inelastic neutron scattering , 2005 .

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

[28]  R. Feynman,et al.  Quantum Mechanics and Path Integrals , 1965 .

[29]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[30]  M. Adams,et al.  Temperature dependence of the zero point kinetic energy in ice and water above room temperature , 2013 .

[31]  Jörg Behler,et al.  Automatic selection of atomic fingerprints and reference configurations for machine-learning potentials. , 2018, The Journal of chemical physics.

[32]  C. Andreani,et al.  Direct Measurements of Quantum Kinetic Energy Tensor in Stable and Metastable Water near the Triple Point: An Experimental Benchmark. , 2016, The journal of physical chemistry letters.

[33]  V Kapil,et al.  Accurate molecular dynamics and nuclear quantum effects at low cost by multiple steps in real and imaginary time: Using density functional theory to accelerate wavefunction methods. , 2015, The Journal of chemical physics.

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

[35]  F. Bruni,et al.  A new water anomaly: the temperature dependence of the proton mean kinetic energy. , 2009, The Journal of chemical physics.

[36]  H. Stanley,et al.  Supercooled water reveals its secrets , 2017, Science.

[37]  Momentum-distribution spectroscopy using deep inelastic neutron scattering , 1999, cond-mat/9904095.

[38]  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.

[39]  F. Fernandez-Alonso,et al.  Electron-volt neutron spectroscopy: beyond fundamental systems , 2017 .

[40]  Michele Parrinello,et al.  Generalized neural-network representation of high-dimensional potential-energy surfaces. , 2007, Physical review letters.

[41]  Michele Ceriotti,et al.  Efficient first-principles calculation of the quantum kinetic energy and momentum distribution of nuclei. , 2012, Physical review letters.