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

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 π 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.

A Combined Selected Configuration Interaction and Many-Body Treatment of Static and Dynamical Correlation in Oligoacenes

“…The oligoacenes have long been of fundamental interest to chemists due to their semiconducting and optical properties, [54][55][56][57][58][59][60][61][62][63][64] and theoreticians have been studying their singlet-triplet splittings and ground state electronic structures with particular attention to the disputed emergence of a stable, open-shell singlet ground state with increasing acene size. 12,22,54,[65][66][67][68][69][70][71][72][73][74][75][76] In characterizing the ground state, qualitatively different interpretations can arise depending on the degree dynamical correlation included, with recent studies suggesting that pure active-space methods tend to overestimate biradical character in these ground states. [74][75][76][77] An accurate theoretical characterization of the oligoacenes is complicated, however, by (i) strong correlation in the π/π * manifold, (ii) their size, prohibitive for many ab initio methods, and (iii) the large basis sets required for experimental comparisons.…”

Variational coupled cluster for ground and excited states

“…10] are equal to the cluster analysis of the CI coefficients. 86,[146][147][148] In their VCCD benchmark study, Van Voorhis and Head-Gordon 49 relied on the standard TCCD iterative procedure (where one computes an approximate diagonal Jacobian matrix based on the difference of the Fock matrix elements f q p ) to solve Eq. ( 9):…”

“…Regarding the starting values of the cluster amplitudes t, once again we have taken advantage of the FCI representation by obtaining these via a cluster analysis of the corresponding CI eigenvectors. 86,147…”

Reduced Density Matrix Cumulants: The Combinatorics of Size-Consistency and Generalized Normal Ordering

“…on each side of (5) gives a c amplitude as a polynomial in the t amplitudes. 38,39 In this second role, (5) solves our problem of additive separability for the configuration interaction and coupled cluster amplitudes. By the previous arguments, this is the one and only solution.…”