XMSCASPT2

XMSCASPT2 stands for Extended Multistate Complete Active Space Second-Order Perturbation Theory. It is a post–Hartree–Fock method designed to provide a balanced and accurate description of dynamic correlation for several electronic states simultaneously, particularly in photochemical and excited-state problems. By incorporating multiple states in a single perturbative treatment, XMSCASPT2 aims to yield reliable relative energies and smooth potential energy surfaces across avoided crossings and conical intersections.

The method starts from a state-averaged complete active space self-consistent field (SA-CASSCF) reference, which provides a common set of molecular orbitals for the chosen states. A rotation of the reference states is then performed to diagonalize the zeroth-order Hamiltonian within the subspace of the selected states. This state-rotation, or state-optimized basis, produces a rotated set of states in which the dynamic correlation corrections are applied consistently. The second-order perturbative corrections are calculated for these rotated states, and the resulting multi-state effective Hamiltonian is diagonalized to obtain excitation energies and state interactions. This procedure mitigates intruder-state problems and reduces numerical issues associated with strong state mixing.

Key advantages include a more robust treatment of near-degeneracies and conical intersections, improved stability against intruder states compared to standard MS-CASPT2, and a balanced description of ground and excited states. The method remains sensitive to the choice of active space and the number of states included, and it can be computationally demanding for large systems. XMSCASPT2 is widely used in quantum chemistry for exploring photochemical pathways and excited-state landscapes where accurate multi-state correlation is essential.