Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy

Abstract

We introduce a new procedure for iterative selection of determinant spaces capable of describing highly correlated systems. This adaptive configuration interaction (ACI) determines an optimal basis by an iterative procedure in which the determinant space is expanded and coarse grained until self-consistency. Two importance criteria control the selection process and tune the ACI to a user-defined level of accuracy. The ACI is shown to yield potential energy curves of N2 with nearly constant errors, and it predicts singlet-triplet splittings of acenes up to decacene that are in good agreement with the density matrix renormalization group.

The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges

“…In the heath-bath CI theory introduced by Urmigar and co-workers, 6,7 the screening is based on the magnitude of the CI matrix elements. Other options include comparisons with a reduced-size calculation, as in the projective CI of Evangelista 8 and in the selected CI scheme by Head-Gordon and co-workers, 9 or are based on an n-body expansion of the correlation energy, as investigated by Zimmermann and co-workers 10,11 and by Gauss and co-workers. 12,13 These developments need to be put into the context of two relatively new and highly efficient approaches to solve the full CI (or complete active space CI) problem.…”

Excitation variance matching with limited configuration interaction expansions in variational Monte Carlo

“…The use and development of CI-based theories continues today [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] despite their central shortcoming of having to choose between being size-inconsistent (in truncated forms) or having a cost that scales factorially with system size (in full (FCI) or complete active space (CAS) forms). Indeed, many researchers are willing to live with this flaw in light of the stability and robustness that arise from CI's variational nature and straightforward systematic improvability.…”

“…[30] Like Evangelista's "guaranteed accuracy" measure, [11] σ 2 is a direct measure of wave function accuracy. By varying different states' sCI expansion lengths so that they are of equal accuracy as measured by σ 2 , we will show that effective error cancellation and accuracies in the range of 0.1 or 0.2 eV can be achieved even for very short sCI expansions.…”

Orbital optimisation in the perfect pairing hierarchy: applications to full-valence calculations on linear polyacenes

“…This has been recently been exploited in various stochastic and adaptive approaches to FCI and CAS-SCF [19][20][21][22][23][24][25][26][27][28][29][30][31], which have made quasi-FCI calculations feasible on much larger systems than before. For instance, ref.…”

“…Famously, DMRG calculations have been used to show that the larger linear polyacenes exhibit strong correlation for their π electrons [55]. Other approaches used have included density functional theory [56][57][58][59][60][61], multiconfiguration pair-density functional theory [62], projected Hartree-Fock theory [63], the random phase approximation [64], configuration interaction [60] (CI), adaptive CI [27], GW theory [65], variational two-electron reduced density matrix (VRDM) theory [66][67][68][69], Møller-Plesset perturbation theory [61,[70][71][72][73], spin-flip methods [74,75], CAS-SCF [53,59,71,72,76] as well as restricted-active space self-consistent field theory [77], valence bond [78] and CC valence bond (CCVB) theory [79,80], CC theory [70][71][72]80] and multireference averaged quadratic CC theory [81,82], an algebraic diagrammatic construction scheme [83], as well as PPH methods with approximate orbitals [50].…”