Integrating the Car–Parrinello equations. II. Multiple time scale techniques

In this paper, new techniques for integrating the Car–Parrinello equations based on multiple time scale methodology are presented. The formalism of multiple time scale methodology based on operator factorizations of the classical Liouville propagator is reviewed. It is shown how the techniques are applied to Car–Parrinello for use with the velocity Verlet and Gaussian dynamics schemes presented in the preceding paper [M. E. Tuckerman and M. Parrinello, J. Chem. Phys. 101, 1302 (1994)], and a detailed discussion is presented of how a reference system for Car–Parrinello simulations may be chosen. It is shown that the use of such techniques can save up to a factor of 5–10 in cpu time over the standard methods.

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

[2]  J. Haile,et al.  A multiple time-step method for molecular dynamics simulations of fluids of chain molecules , 1984 .

[3]  Allan,et al.  Molecular dynamics and ab initio total energy calculations. , 1986, Physical review letters.

[4]  B. Jönsson,et al.  Vectorizing a general purpose molecular dynamics simulation program , 1986 .

[5]  Mark E. Tuckerman,et al.  Molecular dynamics algorithm for condensed systems with multiple time scales , 1990 .

[6]  D. Vanderbilt,et al.  Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. , 1990, Physical review. B, Condensed matter.

[7]  Mark E. Tuckerman,et al.  Molecular dynamics algorithm for multiple time scales: Systems with long range forces , 1991 .

[8]  Lin,et al.  Real-space implementation of nonlocal pseudopotentials for first-principles total-energy calculations. , 1991, Physical review. B, Condensed matter.

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

[10]  Mark E. Tuckerman,et al.  Molecular dynamics algorithm for multiple time scales: Systems with disparate masses , 1991 .

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

[12]  Lee,et al.  Car-Parrinello molecular dynamics with Vanderbilt ultrasoft pseudopotentials. , 1993, Physical review. B, Condensed matter.

[13]  E. Carter,et al.  Multiple time scale Hartree–Fock molecular dynamics , 1993 .

[14]  P. Madden,et al.  Order N ab initio Molecular Dynamics with an Orbital-Free Density Functional , 1993 .

[15]  Mark E. Tuckerman,et al.  Vibrational relaxation in simple fluids: Comparison of theory and simulation , 1993 .

[16]  E. Carter,et al.  Time-Reversible Multiple Time Scale ab Initio Molecular Dynamics , 1993 .

[17]  M. Parrinello,et al.  Electronic structure optimization in plane-wave-based density functional calculations by direct inversion in the iterative subspace , 1994 .

[18]  Michele Parrinello,et al.  Integrating the Car–Parrinello equations. I. Basic integration techniques , 1994 .