Publication

Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo

Example showing energy surface approximation for benzene, displaying the Gaussian process method with N(0, 2) eV noise added to the AIREBO force field. Blue circle points are chosen at the first iterations, red x points are chosen at the second iteration, and green star points are chosen at the third iteration. At each iteration, the sampled range of bond lengths is focused and the search domain for each iteration is displayed on the xy-plane.

Citation

R Archibald, Jaron T Krogel, Paul RC Kent, "Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo", The Journal of chemical physics, 149(16), 2018.

Abstract

Optimization of atomic coordinates and lattice parameters remains a significant challenge to the wide use of stochastic electronic structure methods such as quantum Monte Carlo (QMC). Measurements of the forces and stress tensor by these methods contain statistical errors, challenging conventional gradient-based numerical optimization methods that assume deterministic results. Additionally, forces are not yet available for some methods, wavefunctions, and basis sets and when available may be expensive to compute to sufficiently high statistical accuracy near energy minima, where the energy surfaces are flat. Here, we explore the use of Gaussian process based techniques to sample the energy surfaces and reduce sensitivity to the statistical nature of the problem. We utilize Latin hypercube sampling, with the number of sampled energy points scaling quadratically with the number of optimized parameters. We show these techniques may be successfully applied to systems consisting of tens of parameters, demonstrating QMC optimization of a benzene molecule starting from a randomly perturbed, broken symmetry geometry.

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