Multiple elliptical-Gaussian-density annealing as a tool for finding
the most stable structures. Application to Lennard-Jones atomic clusters
Pillardy J, Piela L
POLISH JOURNAL OF CHEMISTRY 72 (7): 1849-1857, Suppl. S JUL 1998
| Document type: Article |
Language: English |
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Abstract:
Smoothing of the potential energy hypersurface is a promising way to reduce
complexity of the original hypersurface, thus facilitating the search for the
most stable configuration of a molecular system. Despite of the effort made in
the last decade to find an efficient smoothing technique, a reliable and
economical method is still sought. One of the powerful approaches is the
Gaussian Density Method (GDA) of Straub and coworkers. In the method one solves
the reduced Bloch equation that describes the evolution of the spatial part of
the canonical density distribution, when the temperature changes. In the GDA
method this distribution is assumed, for each atom, as a single
three-dimensional isotropic Gaussian with the position and width changing
according to known equations of motion, when the temperature changes. In the
present paper we allow for a three-dimensional elliptical Gaussian distribution
for each atom. Additionally, when in the course of lowering the temperature the
anisotropy of the ellipse becomes large enough, the single Gaussian distribution
for an atom may branch into two elliptical Gaussian distributions. Evolution in
temperature of the new distributions for the system is calculated by solving for
each of them the independent reduced Bloch equation. Finally, when the
temperature reaches 0 K, one has a number of Gaussian distributions, each
corresponding to a structure and (usually low) energy of the system. The method
has been applied to the clusters of N argon atoms (N = 5,..., 33), the system
serving usually as benchmark. Allowing for the anisotropy of the Gaussian
distributions results in a remarkable increase of numerical stability.
Author Keywords:
global optimization, potential energy, smoothing, elliptical Gaussian
distribution, diffusion equation
KeyWords Plus:
DIFFUSION EQUATION METHOD, ENERGY, PROTEINS