Integrating the Car–Parrinello equations. I. Basic integration techniques

In this paper and in a companion paper [M. E. Tuckerman and M. Parrinello, J. Chem. Phys. 101, 1316 (1994)] the problem of integrating the equations of motion in Car–Parrinello simulations is addressed. In this paper, new techniques for treating the constraint problem based on the velocity Verlet integrator and the Gaussian dynamics are presented. Questions of adiabaticity and temperature control are discussed, and it is shown how to combine the new techniques with the recently developed Nose–Hoover chain thermostat method. All new techniques are described using the formalism of operator factorizations applied to the classical Liouville propagator. In the companion paper, the formalism and application of multiple time scale methodology in Car–Parrinello simulations are discussed.

[1]  P. Madden,et al.  Control of the adiabatic electronic state in ab initio molecular dynamics , 1993 .

[2]  Michiel Sprik,et al.  COMPUTER-SIMULATION OF THE DYNAMICS OF INDUCED POLARIZATION FLUCTUATIONS IN WATER , 1991 .

[3]  L. Verlet.  Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules , 1967 .

[4]  Pastore,et al.  Theory of ab initio molecular-dynamics calculations. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[5]  R. Feynman.  Forces in Molecules , 1939 .

[6]  Hoover,et al.  Canonical dynamics: Equilibrium phase-space distributions. , 1985, Physical review. A, General physics.

[7]  Ladislas P. Kubin,et al.  Computer Simulation in Materials Science , 1991 .

[8]  Denis J. Evans,et al.  Non-Newtonian molecular dynamics , 1984 .

[9]  Denis J. Evans,et al.  Constrained molecular dynamics: Simulations of liquid alkanes with a new algorithm , 1986 .

[10]  H. Yoshida.  Construction of higher order symplectic integrators , 1990 .

[11]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

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

[13]  D. Remler,et al.  Molecular dynamics without effective potentials via the Car-Parrinello approach , 1990 .

[14]  H. Trotter.  On the product of semi-groups of operators , 1959 .

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

[16]  M. Klein,et al.  Nosé-Hoover chains : the canonical ensemble via continuous dynamics , 1992 .

[17]  Leonard Kleinman,et al.  Efficacious Form for Model Pseudopotentials , 1982 .

[18]  M. Suzuki,et al.  General theory of fractal path integrals with applications to many‐body theories and statistical physics , 1991 .

[19]  S. Nosé.  A unified formulation of the constant temperature molecular dynamics methods , 1984 .

[20]  D. R. Hamann,et al.  Pseudopotentials that work: From H to Pu , 1982 .

[21]  S. Nosé.  A molecular dynamics method for simulations in the canonical ensemble , 1984 .

[22]  Michele Parrinello,et al.  Integrating the Car–Parrinello equations. II. Multiple time scale techniques , 1994 .

[23]  Parrinello,et al.  Adiabaticity in first-principles molecular dynamics. , 1992, Physical review. B, Condensed matter.

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