Flexible constraints : An adiabatic treatment of quantum degrees of freedom, with application to the flexible and polarizable mobile charge densities in harmonic oscillators model for water

In classical molecular simulations chemical bonds and bond angles have been modeled either as rigid constraints, or as nearly harmonic oscillators. However, neither model is a good description of a chemical bond, which is a quantum oscillator that in most cases occupies the ground state only. A quantum oscillator in the ground state can be represented more faithfully by a flexible constraint. This means that the constraint length adapts itself, in time, to the environment, such that the rotational and potential forces on the constraint cancel out. An accurate algorithm for flexible constraints is presented in this work and applied to study liquid water with the flexible and the polarizable “mobile charge densities in harmonic oscillators” model. The iterations for the flexible constraints are done simultaneously with those for the electronic polarization, resulting in negligible additional computational costs. A comparison with fully flexible and rigidly constrained simulations shows little effect on structure and energetics of the liquid, while the dynamics is somewhat faster with flexible constraints.

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

[2]  Rahman,et al.  Molecular-dynamics study of atomic motions in water. , 1985, Physical review. B, Condensed matter.

[3]  W. Vangunsteren.  Constrained dynamics of flexible molecules , 1980 .

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

[5]  Y. Kameda,et al.  The intra-molecular structure of a water molecule in hydrated and incompletely hydrated LiCl solutions , 1989 .

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

[7]  R. A. Kuharski,et al.  Quantum mechanical contributions to the structure of liquid water , 1984 .

[8]  Kazimierz Krynicki,et al.  Pressure and temperature dependence of self-diffusion in water , 1978 .

[9]  Roland Lindh,et al.  The water dimer interaction energy: Convergence to the basis set limit at the correlated level , 1997 .

[10]  B. Halle,et al.  Interpretation of magnetic resonance data from water nuclei in heterogeneous systems , 1981 .

[11]  David van der Spoel,et al.  Molecular Dynamics Simulations of Water with Novel Shell-Model Potentials , 2001 .

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

[13]  P. Rossky,et al.  Model dependence of quantum isotope effects in liquid water , 1991 .

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

[15]  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 .

[16]  S. Yip,et al.  Molecular dynamics simulation of dielectric properties of water , 1987 .

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

[18]  Bernard R. Brooks,et al.  Elastic molecular dynamics with self-consistent flexible constraints , 2000 .

[19]  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 .

[20]  Jianshu Cao,et al.  The formulation of quantum statistical mechanics based on the Feynman path centroid density. III. Phase space formalism and analysis of centroid molecular dynamics , 1994 .

[21]  Toshio Yamaguchi,et al.  Neutron-diffraction investigation of the intramolecular structure of a water molecule in the liquid phase at high temperatures , 1991 .

[22]  P. Kollman,et al.  Settle: An analytical version of the SHAKE and RATTLE algorithm for rigid water models , 1992 .

[23]  Wilfred F. van Gunsteren,et al.  On the relative merits of flexible versus rigid models for use in computer simulations of molecular liquids , 1996 .

[24]  R. Wagner,et al.  Exploring the open pore of the potassium channel from Streptomyces lividans , 1999, FEBS letters.

[25]  B. Chait,et al.  The structure of the potassium channel: molecular basis of K+ conduction and selectivity. , 1998, Science.

[26]  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 .

[27]  Herman J. C. Berendsen,et al.  A mobile charge densities in harmonic oscillators (MCDHO) molecular model for numerical simulations: The water-water interaction , 2000 .

[28]  G. Karlström,et al.  Geometry optimization of a water molecule in water. A combined quantum chemical and statistical mechanical treatment , 1997 .

[29]  Berend Smit,et al.  Understanding molecular simulation: from algorithms to applications , 1996 .

[30]  A. Narten,et al.  Neutron diffraction study of light and heavy water mixtures at 25 °C , 1982 .

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

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

[33]  T. Darden,et al.  Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems , 1993 .

[34]  H. C. Andersen.  Rattle: A “velocity” version of the shake algorithm for molecular dynamics calculations , 1983 .

[35]  Jianshu Cao,et al.  The formulation of quantum statistical mechanics based on the Feynman path centroid density. II. Dynamical properties , 1994 .

[36]  G. Ciccotti,et al.  Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-Alkanes , 1977 .

[37]  Jianshu Cao,et al.  The formulation of quantum statistical mechanics based on the Feynman path centroid density. IV. Algorithms for centroid molecular dynamics , 1994 .

[38]  Berk Hess,et al.  LINCS: A linear constraint solver for molecular simulations , 1997, J. Comput. Chem..

[39]  Sebastian Reich,et al.  Smoothed dynamics of highly oscillatory Hamiltonian systems , 1995 .

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

[41]  Jianshu Cao,et al.  A new perspective on quantum time correlation functions , 1993 .

[42]  E. Marcos,et al.  Coupling a polarizable water model to the hydrated ion–water interaction potential: A test on the Cr3+ hydration , 2000 .

[43]  G. Corongiu.  Molecular dynamics simulation for liquid water using a polarizable and flexible potential , 1992 .

[44]  P. Åstrand,et al.  Calculation of the Geometry of the Water Molecule in Liquid Water , 1997 .

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

[46]  Wim Klopper,et al.  Computational determination of equilibrium geometry and dissociation energy of the water dimer , 2000 .

[47]  Berk Hess,et al.  GROMACS 3.0: a package for molecular simulation and trajectory analysis , 2001 .

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