An efficient approach to ab initio Monte Carlo simulation

Abstract

We present a Nested Markov chain Monte Carlo (NMC) scheme for building equilibrium averages based on accurate potentials such as density functional theory.Metropolis sampling of a reference system, defined by an inexpensive but approximate potential, was used to substantially decorrelate configurations at which the potential of interest was evaluated, thereby dramatically reducing the number needed to build ensemble averages at a given level of precision. The efficiency of this procedure was maximized on-the-fly through variation of the reference system thermodynamic state (characterized here by its inverse temperature β 0 ), which was otherwise unconstrained. Local density approximation (LDA) results are presented for shocked states of argon at pressures from 4 to 60 GPa, where -depending on the quality of the reference system potential -acceptance probabilities were enhanced by factors of 1.2-28 relative to unoptimized NMC. The optimization procedure compensated strongly for reference potential shortcomings, as evidenced by significantly higher speedups when using a reference potential of lower quality. The efficiency of optimized NMC is shown to be competitive with that of standard ab initio molecular dynamics in the canonical ensemble.

Modelling of framework materials at multiple scales: current practices and open questions

“…However, while ab initio Monte Carlo simulations are possible, the large number of energy evaluations necessary make them relatively rare in the literature. [15,16] In the context of framework materials, Monte Carlo simulations are used at various scales. First, simulated annealing and biased Monte Carlo simulations are extensively used in the areas of structure solution and to localization of extra-framework ions and adsorbed species.…”

“…We note that the question of the 'level of description' applied to the systems (quantum chemistry versus empirical potentials) is relevant not only for MD but also for Monte Carlo simulations, which stochastically generate representative configurations of the system in a given thermodynamic ensemble, by the application of random moves weighted by the appropriate Boltzmann probabilities. However, while ab initio Monte Carlo simulations are possible, the large number of energy evaluations necessary make them relatively rare in the literature [15,16]. In the context of framework materials, Monte Carlo simulations are used at various scales.…”

First principles reactive simulation for equation of state prediction

“…Alone, swap and cluster moves only update a handful of atoms in between each costly QM calculation; to increase the efficiency we perform a long sequence of such moves via Nested MC (NMC). [45][46][47][48][49][50][51][52] Specifically, NMC simulates the system on an approximate reference potential (U 0 ) for a fixed number of moves. The "full" or DFT potential energy is then calculated at the end points of the chain.…”

“…We employ a Monte Carlo (MC) simulation scheme that uses a machine-learned (ML) reactive force-field, akin to those described above, as a reference potential to accelerate the simulation of reactive atomic systems while exactly retaining DFT level results. The ML potential is used in a nested Monte Carlo (NMC) [45][46][47][48][49][50][51][52] framework to propose a long chain of small moves that are then accepted or rejected in toto according to how well the ML potential predicts energy change. This scheme avoids having to compute the expensive DFT potential for every small update.…”

Direct coupling of first-principles calculations with replica exchange Monte Carlo sampling of ion disorder in solids

“…We note that when a moderately accurate but inexpensive potential is available for the system under study, MC simulation with such a potential can be "nested" between MC steps taken with DFT energies to speed up the sampling. The efficiency of this "nested Monte Carlo (NMC)" method [12,13] depends on the quality of the potential, and thus the method does not allow the user to fully escape from the difficulties mentioned above.…”