Partial separability of the Schroedinger equation combined with a Jastrow factor

TL;DR

This paper introduces a novel computational scheme that separates electron-electron interactions from electron-nuclear dynamics using a partial separability approach combined with a Jastrow factor, improving accuracy for Coulombic systems.

Contribution

The work presents a new method for energy calculation in Coulomb systems by combining partial separability with a Jastrow correlation factor, applicable to small molecules and atoms.

Findings

Accurate energy estimates for H2, H3+, and Li systems.

Analytical forms derived for electron correlation effects.

Extension potential to larger atomic and molecular systems.

Abstract

Describing the Coulomb interactions between electrons in atomic or molecular systems is an important step to help us obtain accurate results for the different observables in the system. One convenient approach is to separate the dynamic electronic correlation, i.e., Coulomb electron-electron repulsion, from the motion of the electrons in the nuclei electric field. The wave function is written as the product of two terms, one accounting for the electron-electron interactions, which is symmetric under identical particle exchange; the other is antisymmetric and represents the dynamics and exchange of electrons within the nuclear electric field. In this work, we present a novel computational scheme based on this idea that leads to an expression of the energy as the sum of two terms. To illustrate the method, we look into few-body Coulombic systems, H2, H3+ and Li(1s2,2s), and discuss the possible extension to larger systems. A simple correlation factor, based on the Jastrow exponential term, is employed to represent the dynamics of the electron pairs leading to simple analytical forms and accurate results. We also present and illustrate a different approach with the Li atom based on the partial separability applied to a portion of the atom.