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