Sampling diffusive transition paths

Abstract

The authors address the problem of sampling double-ended diffusive paths. The ensemble of paths is expressed using a symmetric version of the Onsager-Machlup formula, which only requires evaluation of the force field and which, upon direct time discretization, gives rise to a symmetric integrator that is accurate to second order. Efficiently sampling this ensemble requires avoiding the well-known stiffness problem associated with the sampling of infinitesimal Brownian increments of the path, as well as a different type of stiffness associated with the sampling of the coarse features of long paths. The fine-feature sampling stiffness is eliminated with the use of the fast sampling algorithm, and the coarse-feature sampling stiffness is avoided by introducing the sliding and sampling ͑S&S͒ algorithm. A key feature of the S&S algorithm is that it enables massively parallel computers to sample diffusive trajectories that are long in time. The authors use the algorithm to sample the transition path ensemble for the structural interconversion of the 38-atom Lennard-Jones cluster at low temperature.

Simulating structural transitions by direct transition current sampling: The example of LJ38

“…The study of the equilibrium thermodynamics of this system required more elaborate algorithms such as parallel tempering, [28][29][30] basin-sampling techniques, 31 Wang-Landau approaches, 32 or path-sampling methods. 19,33,34 More recently, the dynamical transitions between the two basins have been studied following various approaches. The interconversion rates between the FCC and ICO structures have been computed using discrete path sampling.…”

“…39 The authors thus developed a two-ended approach which manages to successfully locate reaction paths between the two basins: they started from a straight trial trajectory linking the two minima, and obtained convergence towards trajectories of energies similar to those obtained in the discrete path sampling approach. 33 Although the authors point out the lack of ergodicity in the sampling within their approach and the sensitivity on the "discretization" of the trajectories, this is nevertheless a progress and the main drawback remains the high computational cost (the work needed 10 5 h of central processing unit (cpu) time) to obtain such converged trajectories. In contrast, the simulations we present below required less than 10 2 h of cpu time.…”

Flux-correlation approach to characterizing reaction pathways in quantum systems: a study of condensed-phase proton-coupled electron transfer

“…The role of numerical simulations in this effort is particularly important for systems that exhibit multiple, competing reactive pathways. The characterization of reactive pathways in classical systems has been greatly advanced by the development of methods for rare event sampling [1][2][3][4][5][6] . However, the corresponding tools for quantum systems [7][8][9][10][11] are less developed, despite significant demand for understanding reactive charge and energy transfer pathways in complex quantum systems.…”

Improved transition path sampling methods for simulation of rare events

“…20 A central question is now the extent to which our findings for a 2D free energy surface apply to complex, three-dimensional systems such as pro-teins and glasses. For complex systems, however, that reaction coordinate is seldom known; in fact TPS is particularly advantageous when all else fails, i.e., when little, if anything, is known about the transition coordinate.…”