Spin-Pure Stochastic-CASSCF via GUGA-FCIQMC Applied to Iron–Sulfur Clusters

In this work, we
demonstrate how to efficiently compute the one-
and two-body reduced density matrices within the spin-adapted full configuration interaction quantum Monte Carlo (FCIQMC) method,
which is based on the graphical unitary group approach (GUGA). This
allows us to use GUGA-FCIQMC as a spin-pure configuration interaction
(CI) eigensolver within the complete active space self-consistent
field (CASSCF) procedure and hence to stochastically treat active
spaces far larger than conventional CI solvers while variationally
relaxing orbitals for specific spin-pure states. We apply the method
to investigate the spin ladder in iron–sulfur dimer and tetramer
model systems. We demonstrate the importance of the orbital relaxation
by comparing the Heisenberg model magnetic coupling parameters from
the CASSCF procedure to those from a CI-only (CASCI) procedure based
on restricted open-shell Hartree–Fock orbitals. We show that
the orbital relaxation differentially stabilizes the lower-spin states,
thus enlarging the coupling parameters with respect to the values
predicted by ignoring orbital relaxation effects. Moreover, we find
that, while CASCI results are well fit by a simple bilinear Heisenberg
Hamiltonian, the CASSCF eigenvalues exhibit deviations that necessitate
the inclusion of biquadratic terms in the model Hamiltonian.