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Approximate full configuration interaction (FCI) calculations have recentlybecome tractable for systems of unforeseen size thanks to stochastic andadaptive approximations to the exponentially scaling FCI problem. The result ofan FCI calculation is a weighted set of electronic configurations, which canalso be expressed in terms of excitations from a reference configuration. Theexcitation amplitudes contain information on the complexity of the electronicwave function, but this information is contaminated by contributions fromdisconnected excitations, i.e. those excitations that are just products ofindependent lower-level excitations. The unwanted contributions can be removedvia a cluster decomposition procedure, making it possible to examine theimportance of connected excitations in complicated multireference moleculeswhich are outside the reach of conventional algorithms. We present animplementation of the cluster decomposition analysis and apply it to both trueFCI wave functions, as well as wave functions generated from the adaptivesampling CI (ASCI) algorithm. The cluster decomposition is useful forinterpreting calculations in chemical studies, as a diagnostic for theconvergence of various excitation manifolds, as well as as a guidepost forpolynomially scaling electronic structure models. Applications are presentedfor (i) the double dissociation of water, (ii) the carbon dimer, (iii) the{\pi} space of polyacenes, as well as (iv) the chromium dimer. While thecluster amplitudes exhibit rapid decay with increasing rank for the first threesystems, even connected octuple excitations still appear important in Cr$_2$,suggesting that spin-restricted single-reference coupled-cluster approaches maynot be tractable for some problems in transition metal chemistry.

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