THE SIZE CONSISTENCY OF MULTIREFERENCE MOLLER-PLESSET PERTURBATION-THEORY

The size consistency of multi-reference Moller-Plesset perturbation th eory as a function of the structure of the zeroth-order Hamiltonian is studied. In calculations it is shown that the choice of projection op erators to define the zeroth-order Hamiltonian is crucial. In essence whenever such a projection operator can be written as the sum of proje ction operators onto particular subspaces, cross-product terms may app ear in the zeroth-order Hamiltonian that spoil the size consistency. T his problem may be solved using a separate projection operator for eac h subspace spanning an excitation level. In principle a zeroth-order H amiltonian based on these projection operators results in a size consi stent perturbation theory. However, it was found that some non-local s pin recoupling effects remain. A new zeroth-order Hamiltonian formulat ed recently circumvents this problem and is shown to be exactly size c onsistent. Apart from the choice of projection operators, the orthogon alization of the excited states is crucial also. It was found that mod ified Gramm-Schmidt in quadruple precision was not sufficient. A pivot ted Householder QR factorization (in double precision) offered the num erical stability needed to obtain size consistent results.