Approximating a Wavefunction as an Unconstrained Sum of Slater Determinants

TL;DR

This paper introduces a novel method for approximating multiparticle wavefunctions as unconstrained sums of Slater determinants, aiming for more efficient representations and deeper understanding of wavefunction structure.

Contribution

It presents a constraint-free approach using integral formulations and separated representations, improving computational efficiency and insight over existing methods.

Findings

Method achieves competitive computational complexity

Allows unconstrained sum of determinants for better efficiency

Provides new insights into wavefunction structure

Abstract

The wavefunction for the multiparticle Schr\"odinger equation is a function of many variables and satisfies an antisymmetry condition, so it is natural to approximate it as a sum of Slater determinants. Many current methods do so, but they impose additional structural constraints on the determinants, such as orthogonality between orbitals or an excitation pattern. We present a method without any such constraints, by which we hope to obtain much more efficient expansions, and insight into the inherent structure of the wavefunction. We use an integral formulation of the problem, a Green's function iteration, and a fitting procedure based on the computational paradigm of separated representations. The core procedure is the construction and solution of a matrix-integral system derived from antisymmetric inner products involving the potential operators. We show how to construct and solve this system with computational complexity competitive with current methods.