Iterative Configuration Interaction with Selection

Abstract

Even when starting with a very poor initial guess, the iterative configuration interaction (iCI) approach [J. Chem. Theory Comput. 12, 1169] for strongly correlated electrons can converge from above to full CI (FCI) very quickly by constructing and diagonalizing a very small Hamiltonian matrix at each macro/micro-iteration. However, as a direct solver of the FCI problem, iCI scales exponentially with respect to the numbers of electrons and orbitals. The problem can be mitigated by observing that a vast number of configurations have little weights in the wave function and hence do not contribute discernibly to the correlation energy. The real questions are then (a) how to identify those important configurations as early as possible in the calculation and (b) how to account for the residual contributions of those unimportant configurations. It 1 arXiv:1911.12506v2 [physics.chem-ph] 6 Jan 2020is generally true that if a high-quality yet compact variational space can be determined for describing the static correlation, a low-order treatment of the residual dynamic correlation would then be sufficient. While this is common to all selected CI schemes, the 'iCI with selection' scheme presented here has the following distinctive features:(1) Full spin symmetry is always maintained by taking configuration state functions (CSF) as the many-electron basis. (2) Although the selection is performed on individual CSFs, it is orbital configurations (oCFG) that are used as the organizing units. (3) Given a coefficient pruning-threshold C min (which determines the size of the variational space for static correlation), the selection of important oCFGs/CSFs is performed iteratively until convergence. (4) At each iteration for the growth of the wave function, the first-order interacting space is decomposed into disjoint subspaces, so as to reduce memory requirement on one hand and facilitate parallelization on the other. (5) Upper bounds (which involve only two-electron integrals) for the interactions between doubly connected oCFG pairs are used to screen each first-order interacting subspace before the first-order coefficients of individual CSFs are evaluated. (6) Upon convergence of the static correlation for a given C min , dynamic correlation is estimated by using the state-specific Epstein-Nesbet second-order perturbation theory (PT2). The efficacy of the iCIPT2 scheme is demonstrated numerically by benchmark examples, including C 2 , O 2 , Cr 2 and C 6 H 6 .

QUESTDB: A database of highly accurate excitation energies for the electronic structure community

“…Originally developed in the late 1960s by Bender and Davidson 129 as well as Whitten and Hackmeyer, 130 new efficient SCI algorithms have resurfaced recently. Three examples are iCI, 151, 156–158 semistochastic heat‐bath CI, 116, 118–120, 141, 142 and configuration interaction using a perturbative selection made iteratively (CIPSI) 131, 135, 137, 159 . These flavors of SCI include a second‐order perturbative (PT2) correction which is key to estimate the “distance” to the FCI solution (see below).…”

High-level coupled-cluster energetics by merging moment expansions with selected configuration interaction

“…The selected CI schemes, which date back to the pioneering efforts in the late 1960s and early 1970s, [57][58][59][60] have recently regained significant interest, as their modern implementations have demonstrated the ability to capture the bulk of many-electron correlation effects in a computationally efficient manner using a conceptually straightforward linear wave function ansatz. [61][62][63][64][65][66][67][68][69][70][71][72][73] The selected CI model adopted in the CC(P ;Q) considerations reported in this work is the CI method using perturbative selection made iteratively (CIPSI), 59 as recently reformulated and further developed in Refs. 70 and 71.…”

The Ground State Electronic Energy of Benzene

“…[61][62][63][64][65][66][67] (SHCI), and iterative CI with selection[68][69][70][71] (iCI) methods all belong to a wider class of selected CI (SCI) methods,[96][97][98][99][100][101][102][103][104][105][106][107][108] which approximate the full linear expansion of the FCI wave function by selecting only important determinants in conjunction with perturbative corrections to account for any residual correlation. The FCI Quantum Monte Carlo[72][73][74][75] (FCIQMC) method offers another approach for sampling the wave function, namely, a stochastic QMC propagation of the wave function in the many-electron Hilbert space aimed at projecting out the FCI ground state.…”