Stochastic determination of effective Hamiltonian for the full configuration interaction solution of quasi-degenerate electronic states

We propose a novel quantum Monte Carlo method in configuration space, which stochastically samples the contribution from a large secondary space to the effective Hamiltonian in the energy dependent partitioning of L\"owdin. The method treats quasi-degenerate electronic states on a target energy with bond dissociations and electronic excitations avoiding significant amount of the negative sign problem. The performance is tested with small model systems of H$_4$ and N$_2$ at various configurations with quasi-degeneracy.