The choice of a zeroth-order Hamiltonian for second-order perturbation theory with a complete active space self-consistent-field reference function

The choice of a zeroth-order Hamiltonian, Ĥ0, for second-order perturbation theory with a complete active space self-consistent-field (CASSCF) reference function is discussed in detail, in the context of the inclusion of the denominator shifts found to be important in recent single-reference high-spin open-shell theories and the formulation of a computationally efficient method. Using projection operators and second quantization algebra, an operator is constructed which consists of the complete active space Hamiltonian in the active space and the Mo/ller–Plesset zeroth-order Hamiltonian in the inactive and secondary spaces. This operator, designated CAS/A, has the reference as an eigenfunction without the necessity of projection, it naturally incorporates denominator shifts which appear in terms of active space Fock operators, it does not give rise to intruder states, and it costs little more than other CASSCF perturbation theories. The incorporation of the complete active space Hamiltonian introduces additional active space two-particle terms into the zeroth-order energies over the Fock operators, which may be regarded as an inconsistency. To achieve an approximate consistency, they may be removed or supplemented with other particle–particle and hole–hole terms. The results of test calculations indicate that supplementation is not advisable and that removal has only a modest effect. The test calculations are compared with other results and experiment, and support the effectiveness of the proposed CAS/A Ĥ0.