Measuring Electron Correlation. The Impact of Symmetry and Orbital Transformations

TL;DR

This paper reviews measures of electron correlation across different theories, emphasizing the roles of symmetry, basis choice, and orbital transformations in understanding and reducing wavefunction complexity.

Contribution

It introduces a detailed analysis of how symmetry and basis choices influence electron correlation measures and wavefunction complexity in quantum chemistry.

Findings

Symmetry considerations can simplify wavefunction representations.

Choice of basis impacts the perceived extent of electron correlation.

Orbital rotations affect multireference character in molecular systems.

Abstract

In this perspective, the various measures of electron correlation used in wavefunction theory, density functional theory and quantum information theory are briefly reviewed. We then focus on a more traditional metric based on dominant weights in the full configuration solution and discuss its behaviour with respect to the choice of the $N$-electron and the one-electron basis. The impact of symmetry is discussed and we emphasize that the distinction between determinants, configuration state functions and configurations as reference functions is useful because the latter incorporate spin-coupling into the reference and should thus reduce the complexity of the wavefunction expansion. The corresponding notions of single determinant, single spin-coupling and single configuration wavefunctions are discussed and the effect of orbital rotations on the multireference character is reviewed by analysing a simple model system. In molecular systems, the extent of correlation effects should be limited by finite system size and in most cases the appropriate choices of one-electron and $N$-electron bases should be able to incorporate these into a low-complexity reference function, often a single configurational one.