An optimized initialization algorithm to ensure accuracy in quantum Monte Carlo calculations

Abstract

Quantum Monte Carlo (QMC) calculations require the generation of random electronic configurations with respect to a desired probability density, usually the square of the magnitude of the wavefunction. In most cases, the Metropolis algorithm is used to generate a sequence of configurations in a Markov chain. This method has an inherent equilibration phase, during which the configurations are not representative of the desired density and must be discarded. If statistics are gathered before the walkers have equilibrated, contamination by nonequilibrated configurations can greatly reduce the accuracy of the results. Because separate Markov chains must be equilibrated for the walkers on each processor, the use of a long equilibration phase has a profoundly detrimental effect on the efficiency of large parallel calculations. The stratified atomic walker initialization (STRAW) shortens the equilibration phase of QMC calculations by generating statistically independent electronic configurations in regions of high probability density. This ensures the accuracy of calculations by avoiding contamination by nonequilibrated configurations. Shortening the length of the equilibration phase also results in significant improvements in the efficiency of parallel calculations, which reduces the total computational run time. For example, using STRAW rather than a standard initialization method in 512 processor calculations reduces the amount of time needed to calculate the energy expectation value of a trial function for a molecule of the energetic material RDX to within 0.01 au by 33%.

Generalized valence bond wave functions in quantum Monte Carlo

“…The Cϩϩ source code is available online under the GNU public license. Starting with a script generated input file based on an SCF calculation and similar Jastrows, we use our own efficient algorithm 27 to initialize the walkers. We evaluate the local energy in all-electron updates, using the cusp replacement algorithm of Ma et al 28 We use VMC to optimize all CI coefficients and Jastrows by the method recommended by Toulouse and Umrigar, 8 with our modifications as outlined in Sec.…”

Quantum Monte Carlo and Related Approaches

“…The efficiency of various stages of QMC algorithms is constantly being improved. For example, a strategy for the generation of the ensemble of random walkers has been designed that shortens the equilibration phase of QMC simulations and reduces the total run time. Improved algorithms for updating trial wave functions , provide speed and storage savings that facilitate the treatment of large systems with multideterminant wave functions.…”