Geminal embedding scheme for optimal atomic basis set construction in correlated calculations

TL;DR

This paper presents a novel embedding scheme to construct optimal, system-adaptive atomic basis sets for correlated electronic structure calculations, significantly reducing variational parameters and enabling efficient many-body wave function optimization.

Contribution

It introduces a geminal embedding scheme that systematically contracts primitive basis sets into geminal embedded orbitals, improving efficiency in correlated calculations.

Findings

Reduced number of variational parameters for target accuracy

Successful applications to water, cerium, and liquid hydrogen

Enhanced control over many-body wave function optimization

Abstract

We introduce an efficient method to construct optimal and system adaptive basis sets for use in electronic structure and quantum Monte Carlo calculations. The method is based on an embedding scheme in which a reference atom is singled out from its environment, while the entire system (atom and environment) is described by a Slater determinant or its antisymmetrized geminal power (AGP) extension. The embedding procedure described here allows for the systematic and consistent contraction of the primitive basis set into geminal embedded orbitals (GEOs), with a dramatic reduction of the number of variational parameters necessary to represent the many-body wave function, for a chosen target accuracy. Within the variational Monte Carlo method, the Slater or AGP part is determined by a variational minimization of the energy of the whole system in presence of a flexible and accurate Jastrow factor, representing most of the dynamical electronic correlation. The resulting GEO basis set opens the way for a fully controlled optimization of many-body wave functions in electronic structure calculation of bulk materials, namely, containing a large number of electrons and atoms. We present applications on the water molecule, the volume collapse transition in cerium, and the high-pressure liquid hydrogen.