Automatic State Interaction with Large Localized Active Spaces for Multimetallic Systems

The localized active space self consistent field (LASSCF) method factorizes a complete active space (CAS) wave function into an antisymmetrized product of localized active space wave function fragments. Correlation between fragments is then reintroduced through LAS state interaction (LASSI), in which the Hamiltonian is diagonalized in a model space of LAS states. However, the optimal procedure for defining the LAS fragments and LASSI model space is unknown. We here present an automated framework to explore systematically convergent sets of model spaces, which we call LASSI[$r$,$q$]. This method requires the user to select only $r$, the number of electron hops from one fragment to another and $q$, the number of fragment basis functions per Hilbert space, which converges to CASCI in the limit of $r,q\to\infty$. Numerical tests of this method on the tri-metal complexes [Fe(III)Al(III)Fe(II)($\mu_3$-O)]$^{6+}$ and [Fe(III)$_2$Fe(II)($\mu_3$-O)]$^{6+}$ show efficient convergence to the CASCI limit with 4-10 orders of magnitude fewer states.