Page 57 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

42 O. PARISEL AND Y. ELLINGER
which is the usual first order perturbation coefficient for in the first order correction to
the initial wavefunction . The first- and second-order corrections to the energy are in
that case:

We emphasize that the validity of equations (7) and (8) depends on that of equations (5)
and (6) which reflect the fact that expansion (2) is performed on the set of the eigenvectors
of
If, for example, we suppose that is the ground state electronic configuration of
interest and are Slater determinants built on a set of orthogonal orbitals then
equation (6) is automatically fulfilled.
Furthermore, if are eigenvectors of some one-electron operator such that:

equation (5) becomes also valid. An immediate application of these results is the usual MP2
theory for a set of RHF or UHF orbitals with taken as the Fock operator for the
polyelectronic system.

In the CIPSI theory, the reference is the zeroth order space S which consists in a set of
determinants Let then P be the perturbation space formed of Slater determinants
arising from all the single and double excitations relative to the Slater determinants included
in S for the description of We define the zeroth-order wavefunction as :

The expansion coefficients are determined variationally so that is one of the
eigenvectors of the restriction of H to the S space with eigenvalue

where defines the projection operator onto the S space. We now chose the zeroth-order
hamiltonian so that: