Ca. Hixson et Ra. Wheeler, Rigorous classical-mechanical derivation of a multiple-copy algorithm for sampling statistical mechanical ensembles - art. no. 026701, PHYS REV E, 6402(2), 2001, pp. 6701
We derive a rigorous, multiple-copy simulation algorithm that is formally e
quivalent to conventional classical molecular dynamics for an ensemble of s
ystems, but may be used for rapid geometry optimizations. The derivation is
accomplished by starting from an ensemble of copies of the entire system a
nd applying a point coordinate transformation to a large subsystem defined
as the bath. After the transformation, each atom of the bath is described b
y one "major" set of coordinates located at the average position of the ens
emble of equivalent atoms and a set of "minor" coordinates that when combin
ed with the "major" coordinates represent exact dynamics. Neglecting the "m
inor" set of coordinates results in a Hamiltonian and a probability density
equivalent to those used in existing multiple-copy methods. Neglecting Ham
ilton's equations of motion for the minor variables gives the equations of
motion for locally enhanced sampling. Numerical tests indicate that the alg
orithm can recover exact molecular dynamics of the ensemble, conventional m
ultiple-copy dynamics, or results of intermediate accuracy. Thus, the algor
ithm provides a rigorous basis for multiple-copy dynamics, resolves many of
the uncertainties associated with their current implementations, and offer
s the potential for calculating ensemble average properties in conjunction
with finding a system's global minimum energy geometry.