Stochastic Difference-Dedicated Configuration Interaction for Magnetic Exchange in Large Active Spaces

The simulation of magnetic properties in strongly correlated systems remains a central challenge in electronic structure theory. The Difference-Dedicated Configuration Interaction (DDCI) method is widely regarded as a gold standard for computing magnetic exchange couplings, but its applicability is limited to small magnetic systems due to the steep growth of the configuration-interaction space with the number of correlated electrons and orbitals. Here, we introduce a stochastic formulation of DDCI based on Full Configuration Interaction Quantum Monte Carlo (FCIQMC) and the Generalized Active Space framework, which largely alleviates the computational bottleneck of conventional DDCI. The implementation is validated by comparison with conventional DDCI for the spin ladder of a trinuclear [Mn(IV)₃O₄]³⁺ cluster (S_local = 3/2). Using a small CAS(9,9) reference, DDCI fails to reproduce the spin-state energy differences defined by a two-parameter (J = -76, J' = -11 cm^-1) Heisenberg-Dirac-van Vleck Hamiltonian extracted from experimental measurements. In contrast, Stochastic-DDCI enables calculations with a much larger CAS(33,21) reference and reproduces the experimental spin ladder with remarkable accuracy, yielding deviations smaller than 33 cm^-1 with respect to the spin ladder extracted from the experimental measurements. This development extends DDCI methodologies to substantially larger active spaces and opens the door to the study of more complex magnetic systems.