Cluster decomposition of full configuration interaction wave functions: a tool for chemical interpretation of systems with strong correlation

TL;DR

This paper introduces a cluster decomposition method for analyzing FCI wave functions, enabling chemical interpretation of strongly correlated systems and guiding the development of scalable electronic structure models.

Contribution

The authors present a novel implementation of cluster decomposition analysis applicable to FCI and adaptive sampling CI wave functions, aiding interpretation and model development for complex molecules.

Findings

Cluster amplitudes decay rapidly with increasing rank in most systems.

Connected octuple excitations are significant in chromium dimer, indicating limitations of single-reference coupled-cluster methods.

The method provides insights into the convergence and importance of excitation manifolds in strongly correlated systems.

Abstract

Approximate full configuration interaction (FCI) calculations have recently become tractable for systems of unforeseen size thanks to stochastic and adaptive approximations to the exponentially scaling FCI problem. The result of an FCI calculation is a weighted set of electronic configurations, which can also be expressed in terms of excitations from a reference configuration. The excitation amplitudes contain information on the complexity of the electronic wave function, but this information is contaminated by contributions from disconnected excitations, i.e. those excitations that are just products of independent lower-level excitations. The unwanted contributions can be removed via a cluster decomposition procedure, making it possible to examine the importance of connected excitations in complicated multireference molecules which are outside the reach of conventional algorithms. We present an implementation of the cluster decomposition analysis and apply it to both true FCI wave functions, as well as wave functions generated from the adaptive sampling CI (ASCI) algorithm. The cluster decomposition is useful for interpreting calculations in chemical studies, as a diagnostic for the convergence of various excitation manifolds, as well as as a guidepost for polynomially scaling electronic structure models. Applications are presented for (i) the double dissociation of water, (ii) the carbon dimer, (iii) the {\pi} space of polyacenes, as well as (iv) the chromium dimer. While the cluster amplitudes exhibit rapid decay with increasing rank for the first three systems, even connected octuple excitations still appear important in Cr$_2$, suggesting that spin-restricted single-reference coupled-cluster approaches may not be tractable for some problems in transition metal chemistry.