Orbital Optimization in Selected Configuration Interaction Methods

Abstract

We study several approaches to orbital optimization in selected configuration interaction plus perturbation theory (SCI+PT) methods, and test them on the ground and excited states of three molecules using the semistochastic heatbath configuration interaction (SHCI) method. We discuss the ways in which the orbital optimization problem in SCI resembles and differs from that in multi-configurational self-consistent field (MCSCF). Starting from natural orbitals, these approaches divide into three classes of optimization methods according to how they treat coupling between configuration interaction (CI) coefficients and orbital parameters, namely uncoupled, fully coupled, and quasi-fully coupled methods. We demonstrate that taking the coupling into account is crucial for fast convergence and recommend two quasi-fully coupled methods for such applications: accelerated diagonal Newton and Broyden-Fletcher-Goldfarb-Shanno (BFGS).

$\mathbb{i}$CAS: Imposed Automatic Selection and Localization of Complete Active Spaces

“…(4) The size of CAS grows combinatorially with respect to n o and n e , to name just the major ones. While the combinatorial complexity can be alleviated to a large extent by imposing certain restrictions on the occupation patterns so as to a priori reduce the space size [15][16][17][18][19][20][21][22][23][24][25][26][27] or by using some highly efficient posteriori selection schemes as the CI solver, [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] the first three issues pertinent to orbital selection and optimization are more delicate. Although the selection of active orbitals can be automated by using, e.g, occupation numbers of NOs, [1][2][3][4]45,46 information entropies, [47][48][49] machine learning, 50 subspace projection, [51][52][53] stepwise testing, 54 etc., the so-constructed CAS cannot be guaranteed to be the same for all geometries of c...…”

iCISCF: An Iterative Configuration Interaction-based Multiconfigurational Self-consistent Field Theory for Large Active Spaces

“…In particular, some of these [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] have been adapted to CASSCF, enabling much larger CASSCF calculations. The present work aims to combine the iterative configuration interaction (iCI) approach 29 with CASSCF, leading to iCISCF as a new member of the staticdynamic-static (SDS) 30 family of methods (SDSPT2, 30,31 SDSCI, 29,30 iCI, 29 iCIPT2, 12,32 iVI (iterative vector interaction), 33,34 iCAS (imposed automatic selection and localization of active orbitals), 35 and iOI (iterative orbital interaction) 36 ).…”