where ⟨ψ FC i | is the i-th electronic state at the FC geometry and |ψ dist j ⟩ is the j-th state at the distorted geometry. It is now tempting to assume that any state at the distorted geometry can be described as a linear combination of the states at the FC geometry and vice versa. From this assumption it follows that the overlap matrix needs to be orthogonal, which can be demonstrated by employing the resolution of identity: