Atomic clusters and nanoscale particles: From coarse-grained dynamics to optimized annealing schedules

Abstract

An adaptive method is presented to optimize schedules for the simulated annealing of clusters and nanoscale particles. The method, based on both molecular-dynamics simulations and a set of master equations, is applied to a model configuration space for which the exact optimal schedule can also be found. The adaptive method is demonstrably suitable for optimizing larger and more realistic systems than can be treated by an exact method, even one based on a statistical-sample master equation.

Dynamics and thermodynamics of supercooled liquids and glasses from a model energy landscape

“…In previous work we have investigated relaxation ͑of the total energy͒ in a number of atomic and molecular clusters using a master equation approach 100,101 following Kunz and co-workers. [9][10][11][12] Non-Arrhenius relaxation of the total potential energy has been observed for systems with multifunnel energy landscapes. 4,24,25 We have suggested that the apparent increasing activation energy with decreasing temperature is due to the system occupying lower-energy states within different funnels that can only transfer probability via their higher energy members.…”

Combining pressure and temperature control in dynamics on energy landscapes

“…Finally we design optimal schedules that maximize the probability to reach a particular basin of the energy landscape. For the last step, we employed similar techniques as have been used for the optimization of relaxation schedules on lumped complex energy landscapes in the past; examples are optimal schedules for global optimization algorithms [22,[43][44][45][46], or the dynamics on minimum+saddle point landscape models derived for atom clusters, with the goal to design an optimal simulated annealing schedule to reach the global minimum [47].…”

Markov state modeling and dynamical coarse-graining via discrete relaxation path sampling

“…In fact, the analysis of complex first order rate equations via a master equation (ME) 8 formulation has been widely used in other areas of molecular science for many decades. [9][10][11][12] Much of the recent work is based upon molecular dynamics (MD) simulations, whereas the ME framework was previously exploited using kinetic transition networks [13][14][15][16] based on geometry optimization and unimolecular rate theory. [9][10][11] In a nutshell, MSMs aim at coarse-graining the dynamics of the system via mapping it onto a continuous-time Markov jump process (MJP), that is, a process whose evolution involves memoryless jumps between discretized states representing various typical conformations of the original system.…”

“…[9][10][11][12] Much of the recent work is based upon molecular dynamics (MD) simulations, whereas the ME framework was previously exploited using kinetic transition networks [13][14][15][16] based on geometry optimization and unimolecular rate theory. [9][10][11] In a nutshell, MSMs aim at coarse-graining the dynamics of the system via mapping it onto a continuous-time Markov jump process (MJP), that is, a process whose evolution involves memoryless jumps between discretized states representing various typical conformations of the original system. That such a reduction is possible rests on the observation that most molecular systems display metastability: they do indeed stay trapped in specific regions of their conformational space for a) research@fackovec.net b) eve2@cims.nyu.edu c) dw34@cam.ac.uk long enough periods of time that they forget the memory of how they got there, then make a transition to another such region, etc.…”

“…This feature offers the possibility that if we somehow identify the states of the MSMs with these metastable regions, we should indeed be able to construct an MSM that is both accurate (i.e., such that the dynamics remains Markovian after projection on these states, which is not the case in general) and informative about the original dynamics. Previous ME applications to clusters, solids, and biomolecules exploited a natural coarse-graining in terms of local minima of the potential energy surface, [9][10][11][17][18][19] or suitably lumped sets of minima and transition states. [20][21][22][23] In practice, however, implementing this coarse-graining approach faces several difficulties.…”