Classical dynamics and the Schrödinger theory

This chapter covers the introduction of quantum mechanics into computer simulation methods. The chapter begins by explaining how electronic degrees of freedom may be handled in an ab initio fashion and how the resulting forces are included in the classical dynamics of the nuclei. The technique for combining the ab initio molecular dynamics of a small region, with classical dynamics or molecular mechanics applied to the surrounding environment, is explained. There is a section on handling quantum degrees of freedom, such as low-mass nuclei, by discretized path integral methods, complete with practical code examples. The problem of calculating quantum time correlation functions is addressed. Ground-state quantum Monte Carlo methods are explained, and the chapter concludes with a forward look to the future development of such techniques particularly to systems that include excited electronic states.

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Classical dynamics of a coupled double well oscillator in condensed media. II

The Journal of Chemical Physics ◽

10.1063/1.446941 ◽

1984 ◽

Vol 80 (5) ◽

pp. 1826-1830 ◽

Cited By ~ 12

Author(s):

Teresa Fonseca ◽

J. A. N. F. Gomes ◽

Paolo Grigolini ◽

Fabio Marchesoni

Keyword(s):

Classical Dynamics ◽

Condensed Media

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Classical dynamics of macroscopic strings

Nuclear Physics B ◽

10.1016/0550-3213(93)90039-r ◽

1993 ◽

Vol 403 (1-2) ◽

pp. 335-350 ◽

Cited By ~ 10

Author(s):

Ramzi R. Khuri

Keyword(s):

Classical Dynamics

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Simulated annealing using coarse grained classical dynamics: Smoluchowski dynamics in the Gaussian density approximation

The Journal of Chemical Physics ◽

10.1063/1.469779 ◽

1995 ◽

Vol 103 (4) ◽

pp. 1574-1581 ◽

Cited By ~ 19

Author(s):

John E. Straub ◽

Jianpeng Ma ◽

Patricia Amara

Keyword(s):

Simulated Annealing ◽

Coarse Grained ◽

Classical Dynamics ◽

Density Approximation ◽

Gaussian Density ◽

Smoluchowski Dynamics

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Computer studies of fast ion trajectories in crystals

Canadian Journal of Physics ◽

10.1139/p68-064 ◽

1968 ◽

Vol 46 (6) ◽

pp. 503-516 ◽

Cited By ~ 60

Author(s):

D. V. Morgan ◽

D. van Vliet

Keyword(s):

Large Angle ◽

Classical Dynamics ◽

Perfect Lattice ◽

Fast Ions ◽

Angle Scattering ◽

Initial Work ◽

Fast Ion ◽

Thermal Vibrations ◽

Computer Studies ◽

Good Agreement

A computer program has been developed which follows the trajectories of fast ions in crystals, based on the assumption of classical dynamics and binary collisions. Initial work has been directed at various aspects of proton channeling in copper in the energy range 5–500 keV. The critical angle and distance of closest approach in a perfect lattice have been evaluated for both rows and planes and compare well with the predictions of the continuum model as developed by Lindhard (1965). We also discuss the overlap of close-packed rows and planes, and the modifications necessary to the basic theory when thermal vibrations are introduced. Experiments have been simulated directly by obtaining a statistical analysis of the velocity distribution of protons reflected from a (100) face of copper and transmitted through a thin (~1800 Â) crystal. In reflection, distinct minima were obtained along directions corresponding to close-packed rows and planes, in good agreement with experimental "blocking patterns" (Nelson 1967a). Transmission patterns also revealed a lack of large-angle scattering parallel to close-packed planes, analogous to the white arms observed experimentally with thinner crystals.

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