Stochastic Generalized Active Space Self-Consistent Field: Theory and Application

Abstract

An algorithm to perform stochastic generalized active space calculations, Stochastic-GAS, is presented, that uses the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver. Stochastic-GAS allows the construction and stochastic optimization of preselected truncated configuration interaction wave functions, either to reduce the computational costs of large active space wave function optimizations, or to probe the role of specific electron correlation pathways. As for the conventional GAS procedure, the preselection of the truncated wave function is based on the selection of multiple active subspaces while imposing restrictions on the interspace excitations. Both local and cumulative minimum and maximum occupation number constraints are supported by Stochastic-GAS. The occupation number constraints are efficiently encoded in precomputed probability distributions, using the precomputed heat bath algorithm, which removes nearly all runtime overhead of GAS. This strategy effectively allows the FCIQMC dynamics to a priori exclude electronic configurations that are not allowed by GAS restrictions. Stochastic-GAS reduced density matrices are stochastically sampled, allowing orbital relaxations via Stochastic-GASSCF, and direct evaluation of properties that can be extracted from density matrices, such as the spin expectation value. Three test case applications have been chosen to demonstrate the flexibility of Stochastic-GAS: (a) the Stochastic-GASSCF [5•(6, 6)] optimization of a stack of five benzene molecules, that shows the applicability of Stochastic-GAS toward fragment-based chemical systems; (b) an uncontracted stochastic MRCISD calculation that correlates 96 electrons and 159 molecular orbitals, and uses a large (32, 34) active space reference wave function for an Fe(II)-porphyrin model system, showing how GAS can be applied to systematically recover dynamic electron correlation, and how in the specific case of the Fe(II)-porphyrin dynamic correlation further differentially stabilizes the 3 E g over the 5 A 1g spin state; (c) the study of an Fe 4 S 4 cluster's spin-ladder energetics via highly truncated stochastic-GAS [4•(5, 5)] wave functions, where we show how GAS can be applied to understand the competing spin-exchange and charge-transfer correlating mechanisms in stabilizing different spin-states.

FCIQMC-Tailored Distinguishable Cluster Approach: Open-Shell Systems

“… 48 In a recent study, Stochastic-MRCISD calculations have shown further evidence of a correlation-induced differential stabilization of the 3 E g state over the 5 A 1g . 49 In this work, we focus on the quintet–triplet spin gap Δ E = E Q – E T , which is estimated to be in a range of a few kcal/mol.…”

“…These orbitals have also been used in other works of ours and are described there in greater detail. 48 , 49 , 104 , 105 …”

“… Spin gaps (Δ E = E Q – E T ) of the Fe(II)-porphyrin over different active spaces. a Stochastic-MRCISD (6.8 kcal/mol) corresponds to a calculation correlating 96 electrons in 159 molecular orbitals, using CAS(32,34) as the reference wave function, ref ( 49 ). b Our previous best estimate from a subtractive embedding scheme, ref ( 105 ).…”

Multiconfiguration Pair-Density Functional Theory Calculations of Iron(II) Porphyrin: Effects of Hybrid Pair-Density Functionals and Expanded RAS and DMRG Active Spaces on Spin-State Orderings

“…The electronic structural description of iron porphyrins is also of fundamental interest, as these systems are prototypical of large, strongly correlated systems where determining the spin-state ordering is still challenging. For even the simplest, unfunctionalized iron­(II) porphyrin (FeP), the ordering of the lowest lying spin states is still being studied with recently developed, sophisticated electronic structure methods. − …”

Full configuration interaction quantum Monte Carlo for coupled electron--boson systems and infinite spaces

“…This has proven a successful means of sampling one-and two-body RDMs in fermionic systems for a diversity of applications, e.g. molecular properties [112,113], MCSCF orbital optimisations [59,[114][115][116] and contributions from internally contracted perturbers in multireference perturbation theories [117,118]. However, this approach makes an approximation that the set of configurational pairs, (i, j) with non-zero coefficient product which contribute to the RDMs of interest (Γ-connections) is equal to the set of (i, j) pairs connected by a non-zero Hamiltonian matrix element (H-connections).…”