Surrogate Hessian accelerated structural optimization for stochastic electronic structure theories

Abstract

We present an efficient energy-based method for structural optimization with stochastic electronic structure theories, such as diffusion quantum Monte Carlo (DMC). This method is based on robust line-search energy minimization in reduced parameter space, exploiting approximate but accurate Hessian information from a surrogate theory, such as density functional theory. The surrogate theory is also used to characterize the potential energy surface, allowing for simple but reliable ways to maximize statistical efficiency while retaining controllable accuracy. We demonstrate the method by finding the minimum DMC energy structures of the selected flake-like aromatic molecules, such as benzene, coronene, and ovalene, represented by 2, 6, and 19 structural parameters, respectively. In each case, the energy minimum is found within two parallel line-search iterations. The method is near-optimal for a line-search technique and suitable for a broad range of applications. It is easily generalized to any electronic structure method where forces and stresses are still under active development and implementation, such as diffusion Monte Carlo, auxiliary-field Monte Carlo, and stochastic configuration interaction, as well as deterministic approaches such as the random-phase approximation. Accurate and efficient means of geometry optimization could shed light on a broad class of materials and molecules, showing high sensitivity of induced properties to structural variables.

Machine Learning Diffusion Monte Carlo Forces

“…This work thus illustrates the powerful role that machine learning could serve in not only accelerating but also providing key quantities like forces from stochastic and other techniques (e.g., RPA) that do not directly provide them. It also adds to the growing body of work leveraging a range of surrogate methods − to accelerate and extend the reach of stochastic methods.…”

A linear surrogate for optimising functions of an orthogonal matrix with applications in wave function theory

“…Therefore, we can achieve a considerable speedup if we construct an approximate function that is fast to evaluate -this is the idea of surrogate optimization. Recently, this idea has attracted some interest in chemistry, with research emphasis particularly on using machine learning to do geometry optimization [1][2][3][4] . There are also applications in experimental design [5] , predicting molecular properties [6] and calculating the electronic structure [7,8] .…”

A Quantum Monte Carlo Study of the Structural, Energetic, and Magnetic Properties of Two-Dimensional H and T Phase VSe2

“…15 Due to the fact that T-and H-VSe 2 have structural parameters that are coupled to their electronic and magnetic properties, it makes it difficult to produce conclusive results that rely solely on DFT or DFT+U. For this reason, we employed our recently developed energy-based surrogate Hessian method for structural optimization with stochastic electronic structure theories (such as DMC) 22 to obtain the geometric structure of T-and H-VSe 2 with DMC accuracy, resulting in high-accuracy bond lengths that resolve previous functional-dependent structural discrepancies. After obtaining an accurate geometry for both structures, we constructed a phase diagram between T-and H-VSe 2 using DMC-calculated energies and obtained accurate magnetic properties of each structure.…”

“…To alleviate the uncertainty in DFT methods, more sophisticated methods can be used such as diffusion Monte Carlo (DMC) . DMC is a correlated, many-body electronic structure method that has been demonstrated to have success for the electronic and magnetic properties of a variety of bulk and 2D systems. − This method has a weaker dependence on the starting density functional and U parameter and can successfully achieve results with an accuracy beyond the DFT+ U …”