Accelerating flat-histogram methods for potential of mean force calculations.

Potential of mean force calculations along a reaction coordinate (RC) demand exhaustive sampling, which often leads to prohibitively long computational times. The expanded ensemble density of states (EXEDOS) [E. B. Kim, R. Faller, Q. Yan et al., J. Chem. Phys. 117, 7781 (2002)] is a simple flat-histogram Monte Carlo method based on the density of states algorithm proposed by Wang and Landau [Phys. Rev. Lett. 86, 2050 (2001)]. EXEDOS offers the advantage of continuous uniform sampling of the RC with no a priori knowledge of the free energy profile. However, the method is not certain to converge within accessible simulation time. Furthermore, the strongly asymmetric distribution of tunneling times inherent in flat-histogram sampling imposes additional limitations. We propose several improvements that accelerate the EXEDOS method and can be generally applicable in free energy calculations. First, we propose an asynchronous parallel implementation of the density of states algorithm in a multiple-walkers multiple-windows scheme and extend the algorithm in an expanded ensemble [(MW)(2)-XDOS] for PMF calculations as the original EXEDOS. Despite the nonideal scaling over a number of processors this technique overcomes limitations by extreme values of tunneling times and allows consistent evaluations of performance. The second set of improvements addresses the dependence of convergence times on system size, density, and sampling rate of the RC. At low densities, the coupling of (MW)(2)-XDOS with the rejection-free geometric cluster move provides impressive performance that overshadows any other technique. However, the limited applicability of cluster moves at high densities requires an alternative approach. We propose the coupling of (MW)(2)-XDOS with preferential sampling methods. In the systems studied, single displacements in the proximity of particles defining the RC accelerate calculations significantly and render the simulation nearly size-independent. A further modification of preferential sampling involves collective displacements of particles performed in a "smart Monte Carlo" scheme. This "local Brownian dynamics" algorithm can be generally applicable to many free energy simulation methods and would be particularly beneficial at high densities and molecular systems with strong intramolecular potentials.