Measuring Multi-Configurational Character by Orbital Entanglement

TL;DR

This paper introduces a new orbital-entanglement based diagnostic, $Z_{s(1)}$, to assess the multi-configurational character of wave functions, aiding the choice of quantum chemical methods.

Contribution

The paper presents a novel, cost-effective diagnostic based on orbital entanglement that reliably indicates multi-configurational character in wave functions.

Findings

$Z_{s(1)}$ diagnostic accurately distinguishes single- and multi-configurational wave functions.

It can be computed from partially converged DMRG wave functions.

The diagnostic is practical for routine quantum chemical applications.

Abstract

One of the most critical tasks at the very beginning of a quantum chemical investigation is the choice of either a multi- or single-configurational method. Naturally, many proposals exist to define a suitable diagnostic of the multi-configurational character for various types of wave functions in order to assist this crucial decision. Here, we present a new orbital-entanglement based multi-configurational diagnostic termed $Z_{s(1)}$. The correspondence of orbital entanglement and static (or nondynamic) electron correlation permits the definition of such a diagnostic. We chose our diagnostic to meet important requirements such as well-defined limits for pure single-configurational and multi-configurational wave functions. The $Z_{s(1)}$ diagnostic can be evaluated from a partially converged, but qualitatively correct, and therefore inexpensive density matrix renormalization group wave function as in our recently presented automated active orbital selection protocol. Its robustness and the fact that it can be evaluated at low cost make this diagnostic a practical tool for routine applications.