In molecular dynamics simulations, control over temperature and pressure is typically achieved by augmenting the original system with additional dynamical variables to create a thermostat and a barostat, respectively. These variables generally evolve on timescales much longer than those of particle motion, but typical integrator implementations update the additional variables along with the particle positions and momenta at each time step. We present a framework that replaces the traditional integration procedure with separate barostat, thermostat, and Newtonian particle motion updates, allowing thermostat and barostat updates to be applied infrequently. Such infrequent updates provide a particularly substantial performance advantage for simulations parallelized across many computer processors, because thermostat and barostat updates typically require communication among all processors. Infrequent updates can also improve accuracy by alleviating certain sources of error associated with limited-precision arithmetic. In addition, separating the barostat, thermostat, and particle motion update steps reduces certain truncation errors, bringing the time-average pressure closer to its target value. Finally, this framework, which we have implemented on both general-purpose and special-purpose hardware, reduces software complexity and improves software modularity.

By means of the Ito-Nisio theorem, we introduce and discuss a general approach to series representations of path integrals. We then argue that the optimal basis for both "primitive" and partial averaged approaches is the Wiener sine-Fourier basis. The present analysis also suggests a new approach to improving the convergence of primitive path integral methods. Current work indicates that this new technique, the "reweighted" method, converges as the cube of the number of path variables for "smooth" potentials. The technique is based on a special way of approximating the Brownian bridge which enters the Feynman-Kaç formula and it does not require the Gaussian transform of the potential for its implementation.

Over the last two decades, scanning tunnelling microscopy (STM) has become one of the most important ways to investigate the structure of crystal surfaces. STM has helped achieve remarkable successes in surface science such as finding the atomic structure of Si(111) and Si(001). For highindex Si surfaces the information about the local density of states obtained by scanning does not translate directly into knowledge about the positions of atoms at the surface. A commonly accepted strategy for identifying the atomic structure is to propose several possible models and analyze their corresponding simulated STM images for a match with the experimental ones. However, the number of good candidates for the lowest-energy structure is very large for high-index surfaces, and heuristic approaches are not likely to cover all the relevant structural models. In this article, we take the view that finding the atomic structure of a surface is a problem of stochastic optimization, and we address it as such. We design a general technique for predicting the reconstruction of silicon surfaces with arbitrary orientation, which is based on parallel-tempering Monte Carlo simulations combined with an exponential cooling. The advantages of the method are illustrated using the Si(105) surface as example, with two main results: (a) the correct single-step rebonded structure [e.g., Fujikawa et al., Phys. Rev. Lett. 88, 176101 (2002)] is obtained even when starting from the paired-dimer model [Mo et al., Phys. Rev. Lett. 65, 1020(1990] that was assumed to be correct for many years, and (b) we have found several double-step reconstructions that have lower surface energies than any previously proposed double-step models.