The zero-order CASPT Hamiltonian

To set up a size-extensive perturbation theory, the zero-order Hamiltonian must be additively separable. We shall here show that, for multiplicatively separable zero-order wave functions, the CASSCF Fock operator and the zero-order energy are both additively separable but that the presence of projection operators nevertheless makes the zero-order CASPT Hamiltonian H ... 

Fig. 14.12. The block-diagonal structure of the zero-order CASPT Hamiltonian matrix.

Comparing (14.7.15) and (14.7.16), we find that Hqab is not equal to Hoa + Hob- A similar argument would show that the zero-order CASPT Hamiltonian (14.7.8) is not additively separable. 

The nonseparable contributions to the zero-order CASPT Hamiltonian (14.7.15) then vanish and Hoab becomes separable ... 

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