where Êpq is the one-electron spin-averaged excitation operator and f pq is the Fock matrix element, which is defined later. The definition of the zeroth-order Hamiltonian strongly affects the smoothness of the potential energy surface (PES). In particular, the invariance with respect to rotations of the reference wavefunction 9 is a desirable property for MRPTs and is essential for smooth PESs. By operating the projector P , the first term in Eq. ( ) can be explicitly written as