Seniority-based coupled cluster theory

Abstract

Doubly occupied configuration interaction (DOCI) with optimized orbitals often accurately describes strong correlations while working in a Hilbert space much smaller than that needed for full configuration interaction. However, the scaling of such calculations remains combinatorial with system size. Pair coupled cluster doubles (pCCD) is very successful in reproducing DOCI energetically, but can do so with low polynomial scaling (N(3), disregarding the two-electron integral transformation from atomic to molecular orbitals). We show here several examples illustrating the success of pCCD in reproducing both the DOCI energy and wave function and show how this success frequently comes about. What DOCI and pCCD lack are an effective treatment of dynamic correlations, which we here add by including higher-seniority cluster amplitudes which are excluded from pCCD. This frozen pair coupled cluster approach is comparable in cost to traditional closed-shell coupled cluster methods with results that are competitive for weakly correlated systems and often superior for the description of strongly correlated systems.

Benchmark of Dynamic Electron Correlation Models for Seniority-Zero Wave Functions and Their Application to Thermochemistry

“…[56] However, in order to predict spectroscopic constants and thermochemistry within chemical accuracy, we need to include dynamic correlation effects that go beyond the simple electron-pair model. This can be achieved a posteriori using PT approaches, [46,47] coupled cluster corrections, [50,51] or DFT-type methods. [54,55] In this work, we have extended the previously presented PT models with an AP1roG reference function and benchmarked those models against spectroscopic constants for multiply bonded diatomics and thermochemical data extrapolated to the basis set limit.…”

“…A different, computationally feasible approach suitable for strongly-correlated systems uses seniority-zero wavefunctions to describe the static/nondynamic part of the electron correlation en-ergy. [31][32][33][34][35][36][37][38][39][40][41][42][43][44] The missing dynamic electron correlation effects are included a posteriori in these ansätze using, for instance, many-body perturbation theory [45][46][47], coupled-cluster theory [48][49][50][51][52], extended random phase approximation [53], and density functional theory (DFT) corrections [54,55].…”

Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction

“…These density matrices are sparse and have a simple structure. [9] They can be used for expectation values, but perhaps more importantly for finding the appropriate set of orbitals. To accomplish this latter feat, one can introduce the antihermitian one-body operator…”

Communication: Configuration interaction combined with spin-projection for strongly correlated molecular electronic structures

“…[5][6][7][8][9][10][11][12][13][14][15][16] Among them, projected Hartree-Fock (PHF) stands on symmetrybreaking and restoration in the mean-field picture and delivers static correlations efficiently. 12,17 Scuseria et al have extended PHF to describe the residual dynamic correlations by sequentially updating and adding PHF wave functions based on approximate excited PHF states.…”