β ⟩ for α ̸ = β ∈ P in Eq. (3). These elements are no longer trivial when interactions between different states are significant. This is known as the diagonal approximation (which is different from the "diagonal approximation" in CASPT2-D 9 ), and is obvious from the structure of the first term in Eq. ( ) and P . In XMS, the diagonal approximation in Ĥ0 is removed: