Are natural orbitals useful for generating an efficient expansion of the wave function?

TL;DR

This paper examines the effectiveness of natural orbitals in minimizing the difference between a wave function and its CI approximation, revealing their limitations and proposing methods to optimize orbital selection.

Contribution

It demonstrates that natural orbitals rarely yield the optimal basis for CI approximations, except in specific cases, and introduces a way to generate orbitals that minimize the wave function difference.

Findings

Natural orbitals often do not minimize the wave function difference.

In special cases, natural orbitals are optimal for CI expansions.

A method to generate orbitals that minimize the wave function difference is proposed.

Abstract

We investigate whether the natural orbitals (NOs) minimize $\lVert\Psi - \Phi\rVert^2$, where $\Psi$ is a wave function and $\Phi$ is a full configuration interaction (CI) approximation to $\Psi$ in a truncated basis. We will show that the NOs rarely provide the optimal orbitals for $\Phi$, except when (1) there are only two particles or (2) only one basis function is removed in the case of fermions. Further, we will show that the CI expansion coefficients of $\Psi$ and $\Phi$ are identical up to a global scaling factor and demonstrate how the NOs can be used to generate the orbitals that minimize $\lVert\Psi - \Phi\rVert^2$.