Chapter 5 Exact size consistency of multi - reference Møller - Plesset perturbation theory Practice

The size consistency of multi-reference Møller-Plesset perturbation theory as a function of the structure of the zeroth-order Hamiltonian is studied. In calculations it is shown that the choice of projection operators to define the zeroth-order Hamiltonian is crucial. In essence whenever such a projection operator can be written as the sum of projection operators onto particular subspaces, cross-product terms may appear in the zeroth-order Hamiltonian that spoil the size consistency. This problem may be solved using a separate projection operator for each subspace spanning an excitation level. In principle a zeroth-order Hamiltonian based on these projection operators results in a size consistent perturbation theory. However, it was found that some non-local spin recoupling effects remain. A new zeroth-order Hamiltonian formulated recently circumvents this problem and is shown to be exactly size consistent. Apart from the choice of projection operators, the orthogonalisation of the excited states is crucial also. It was found that modified Gramm-Schmidt in quadruple precision was not sufficient. A pivotted Householder QR factorisation (in double precision) offered the numerical stability needed to obtain size consistent results.