43 research outputs found
The incomplete beta function law for parallel tempering sampling of classical canonical systems
We show that the acceptance probability for swaps in the parallel tempering
Monte Carlo method for classical canonical systems is given by a universal
function that depends on the average statistical fluctuations of the potential
and on the ratio of the temperatures. The law, called the incomplete beta
function law, is valid in the limit that the two temperatures involved in swaps
are close to one another. An empirical version of the law, which involves the
heat capacity of the system, is developed and tested on a Lennard-Jones
cluster. We argue that the best initial guess for the distribution of
intermediate temperatures for parallel tempering is a geometric progression and
we also propose a technique for the computation of optimal temperature
schedules. Finally, we demonstrate that the swap efficiency of the parallel
tempering method for condensed-phase systems decreases naturally to zero at
least as fast as the inverse square root of the dimensionality of the physical
system.Comment: 11 pages, 4 figures; minor changes; to appear in J. Chem. Phy
Evolutionary approach for finding the atomic structure of steps on stable crystal surfaces
The problem addressed here can be concisely formulated as follows: Given a stable surface orientation with a known reconstruction and given a direction in the plane of this surface, find the atomic structure of the steps oriented along that direction. We report a robust and generally applicable variable-number genetic algorithm for determining the atomic configuration of crystallographic steps, and exemplify it by finding structures for several types of monatomic steps on Si(114)-2×1. We show that the location of the step edge with respect to the terrace reconstructions, the step width (number of atoms), and the positions of the atoms in the step region can all be simultaneously determined
The stability of strained H:Si(105) and H:Ge(105) surfaces
We report atomic scale studies of the effect of applied strain and hydrogen
environment on the reconstructions of the (105) Si and Ge surfaces. Surface
energy calculations for monohydride-terminated (001) and (105) reconstructions
reveal that the recently established single-height rebonded model is unstable
not only with respect to (001), but also in comparison to other monohydride
(105) structures. This finding persists for both Si and Ge, for applied biaxial
strains from -4% to 4%, and for nearly the entire relevant domain of the
chemical potential of hydrogen, thus providing an explanation for the recently
observed H-induced destabilization of the Ge(105) surface