Intermolecular potential and second virial coefficient of the water-hydrogen complex.

We construct a rigid-body (five-dimensional) potential-energy surface for the water-hydrogen complex using scaled perturbation theory (SPT). An analytic fit of this surface is obtained, and, using this, two minima are found. The global minimum has C2v symmetry, with the hydrogen molecule acting as a proton donor to the oxygen atom on water. A local minimum with Cs symmetry has the hydrogen molecule acting as a proton acceptor to one of the hydrogen atoms on water, where the OH bond and H2 are in a T-shaped configuration. The SPT global minimum is bound by 1097 microEh (Eh approximately 4.359744 x 10(-18) J). Our best estimate of the binding energy, from a complete basis set extrapolation of coupled-cluster calculations, is 1076.1 microEh. The fitted surface is used to calculate the second cross virial coefficient over a wide temperature range (100-3000 K). Three complementary methods are used to quantify quantum statistical mechanical effects that become significant at low temperatures. We compare our results with experimental data, which are available over a smaller temperature range (230-700 K). Generally good agreement is found, but the experimental data are subject to larger uncertainties.

[1]  J. W. Little,et al.  The NBS Two-Pressure Humidity Generator, Mark 2 , 1977, Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry.

[2]  D. Nesbitt,et al.  High-resolution diode laser study of H2–H2O van der Waals complexes: H2O as proton acceptor and the role of large amplitude motion , 1999 .

[3]  J. Poll,et al.  The quadrupole moment of the H2 molecule , 1978 .

[4]  R. Wheatley,et al.  Extrapolation of intermolecular interaction energies in weakly bound Van der Waals complexes , 2002 .

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

[6]  Roland Span,et al.  A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa , 2000 .

[7]  R. Wheatley,et al.  Intermolecular potential for the interaction of helium with ammonia , 2001 .

[8]  K. P. Birch,et al.  An Updated Edln Equation for the Refractive Index of Air , 1993 .

[9]  Wolfgang Wagner,et al.  International Equations for the Pressure Along the Melting and Along the Sublimation Curve of Ordinary Water Substance , 1994 .

[10]  G. Herzberg,et al.  Constants of diatomic molecules , 1979 .

[11]  I. Velasco,et al.  Water dew points of binary nitrogen+water and propane+water mixtures. Measurement and correlation , 1999 .

[12]  B. Rowland,et al.  Vibrational spectra of water complexes with H2, N2, and CO , 1995 .

[13]  Trygve Helgaker,et al.  A numerically stable procedure for calculating Møller-Plesset energy derivatives, derived using the theory of Lagrangians , 1989 .

[14]  P. T. Eubank,et al.  Optimum mixture compositions for measurement of cross virial coefficients , 1990 .

[15]  M. Szczęśniak,et al.  THE COMPLEX OF N2 WITH H2O, D2O, AND HDO : A COMBINED AB INITIO AND DIFFUSION MONTE CARLO STUDY , 1994 .

[16]  A. D. McLean,et al.  Anisotropic rigid rotor potential energy function for H2O–H2 , 1994 .

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

[18]  C. Wormald,et al.  Excess enthalpies and cross-term second virial coefficients for mixtures containing water vapour , 1988 .

[19]  I. Velasco,et al.  Dew Points of Binary Nitrogen + Water Mixtures , 2002 .

[20]  R. Wheatley,et al.  Application of the overlap model to calculating correlated exchange energies , 2000 .

[21]  K. Szalewicz,et al.  Effects of monomer geometry and basis set saturation on computed depth of water dimer potential , 1996 .

[22]  C. Wormald,et al.  Excess molar enthalpies of nine binary steam mixtures: new and corrected values , 1990 .

[23]  C. Wormald,et al.  Excess enthalpies for (water + nitrogen)(g) up to 698.2 K and 12.6 MPa , 1983 .

[24]  M. Szczęśniak,et al.  Intermolecular potential of H2O...H2 in the van der Waals region. An ab initio study , 1992 .

[25]  K. Tang,et al.  An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients , 1984 .

[26]  Trygve Helgaker,et al.  Accuracy of atomization energies and reaction enthalpies in standard and extrapolated electronic wave function/basis set calculations , 2000 .

[27]  R. Wheatley,et al.  Scaled perturbation theory for weak intermolecular forces: the helium dimer , 2002 .

[28]  J. S. Rowlinson,et al.  Molecular Thermodynamics of Fluid-Phase Equilibria , 1969 .

[29]  M. Szczęśniak,et al.  On the connection between the supermolecular Møller-Plesset treatment of the interaction energy and the perturbation theory of intermolecular forces , 1988 .

[30]  M. Moldover,et al.  Ab Initio Values of the Thermophysical Properties of Helium as Standards , 2000, Journal of research of the National Institute of Standards and Technology.

[31]  P. Taylor,et al.  A potential energy surface for the process H2+H2O→H+H+H2O : Ab initio calculations and analytical representation , 1991 .

[32]  R. C. Cohen,et al.  Determination of an improved intermolecular global potential energy surface for Ar–H2O from vibration–rotation–tunneling spectroscopy , 1993 .

[33]  Allan H. Harvey,et al.  Intermolecular potentials and second virial coefficients of the water–neon and water–argon complexes , 2002 .

[34]  G. R. Smith,et al.  The excess enthalpy of (water + hydrogen) vapour and (water + methane) vapour , 1983 .

[35]  Sadik Kakac,et al.  Two‐dimensional model for proton exchange membrane fuel cells , 1998 .

[36]  A. Wexler.  Vapor Pressure Formulation for Ice , 1977, Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry.

[37]  D. Wiesenburg,et al.  Hydrogen and deuterium , 1981 .

[38]  R. Mcweeny,et al.  Methods Of Molecular Quantum Mechanics , 1969 .

[39]  Patrick W. Fowler,et al.  Do electrostatic interactions predict structures of van der Waals molecules , 1983 .

[40]  G. Herzberg.  Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules , 1939 .

[41]  R. Tibshirani,et al.  An introduction to the bootstrap , 1993 .

[42]  U. Buck,et al.  Surface vibrations of large water clusters by helium atom scattering , 2000 .

[43]  David E. Woon,et al.  Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties , 1994 .

[44]  A. Stone,et al.  Spherical tensor theory of long-range intermolecular forces , 1984 .

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

[46]  R. Suenram,et al.  Microwave spectrum and molecular structure of the N2–H2O complex , 1989 .

[47]  J. V. Lenthe,et al.  Computation of inelastic rotational rates and collision cross-sections for astrophysically important systems: H2+ H2O and the water maser , 1993 .

[48]  Keith E. Gubbins,et al.  Theory of molecular fluids , 1984 .

[49]  J. Rychlewski.  An accurate calculation of the polarizability of the hydrogen molecule and its dependence on rotation, vibration and isotopic substitution , 1980 .

[50]  Phong Diep,et al.  Erratum: “An accurate H2–H2 interaction potential from first principles” [J. Chem. Phys. 112, 4465 (2000)] , 2000 .

[51]  Allan H. Harvey,et al.  Henry’s Constants and Vapor–Liquid Distribution Constants for Gaseous Solutes in H2O and D2O at High Temperatures , 2003 .

[52]  J. Prausnitz,et al.  Solubility of water in compressed nitrogen, argon, and methane , 1968 .

[53]  William H. Press,et al.  Book-Review - Numerical Recipes in Pascal - the Art of Scientific Computing , 1989 .

[54]  Trygve Helgaker,et al.  Basis set convergence of the interaction energy of hydrogen-bonded complexes , 1999 .

[55]  C. Wormald,et al.  The excess enthalpy of (water + nitrogen) vapour and (water + n-heptane) vapour , 1981 .

[56]  F. Tao,et al.  An accurate ab initio potential energy surface of HeH2O , 1996 .

[57]  E. Shock,et al.  Second cross virial coefficients for interactions involving water. Critical data compilation , 2003 .

[58]  R. Battino,et al.  Solubility of gases in liquids. XVI. Henry's law coefficients for nitrogen in water at 5 to 50°C , 1984 .

[59]  A. Thakkar.  The generator coordinate method applied to variational perturbation theory. Multipole polarizabilities, spectral sums, and dispersion coefficients for helium , 1981 .

[60]  P. G. Hill,et al.  Virial equations for light and heavy water , 1988 .

[61]  Sl,et al.  Many‐body theory of intermolecular induction interactions , 1994 .

[62]  G. Schenter.  The development of effective classical potentials and the quantum statistical mechanical second virial coefficient of water , 2002 .

[63]  John S. Muenter,et al.  The dipole moment of water. I. Dipole moments and hyperfine properties of H2O and HDO in the ground and excited vibrational states , 1991 .

[64]  Gabriel G. Balint-Kurti,et al.  The Fourier grid Hamiltonian method for bound state eigenvalues and eigenfunctions , 1989 .

[65]  Mukund R. Patel,et al.  Thermophysical properties of gaseous carbon dioxide-water mixtures , 1987 .

[66]  R. Davis,et al.  Equation for the Determination of the Density of Moist Air (1981/91) , 1992 .

[67]  R. Hyland,et al.  Formulations for the thermodynamic properties of dry air from 173.15 K to 473.15 K, and of saturated moist air from 173.15 K to 372.15 K, at pressures to 5 MPa , 1983 .

[68]  D. Margoliash,et al.  Pseudospectral dipole oscillator strength distributions and some related two body interaction coefficients for H, He, Li, N, O, H2, N2, O2, NO, N2O, H2O, NH3, and CH4 , 1978 .

[69]  John B. O. Mitchell,et al.  Gaussian multipoles in practice: Electrostatic energies for intermolecular potentials , 1994, J. Comput. Chem..

[70]  William A. Lester,et al.  Trajectory studies of O+H2 reactions on fitted abinitio surfaces. II. Singlet case , 1979 .

[71]  C. N. Colling,et al.  Excess enthalpies of (water + hydrogen)(g) up to 698.2 K and 11.13 MPa , 1985 .

[72]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[73]  C. A. T. Seldam,et al.  Virial coefficients of hydrogen and deuterium at temperatures between −175°C and +150°C. Conclusions from the second virial coefficient with regards to the intermolecular potential , 1960 .

[74]  A. D. McLean,et al.  Comment on broadening of water microwave lines by collisions with helium atoms , 1992 .

[75]  J. Johnson,et al.  An accurate H2–H2 interaction potential from first principles , 2000 .

[76]  Laurence S. Rothman,et al.  Dipole moment of water from Stark measurements of H2O, HDO, and D2O , 1973 .

[77]  I. Abdulagatov,et al.  Measurements of the (p, ρ, T) properties and virial coefficients of pure water, methane, n-hexane, n-octane, benzene, and of their aqueous mixtures in the supercritical region , 1996 .

[78]  W. Adams.  The problem of unphysical states in the theory of intermolecular interactions , 1992 .

[79]  A. D. McLean,et al.  Calculations of H2O microwave line broadening in collisions with He atoms: sensitivity to potential energy surfaces. , 1991, The Journal of chemical physics.