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

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 3Eg over the 5A1g spin
state; (c) the study of an Fe4S4 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.