Page 58 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

A COUPLED MCSCF-PERTURBATION TREATMENT OF ELECTRONIC SPECTRA 43
is thus defined through the two sets namely by its matrix elements in the
space. If the determinants are built on orthogonal orbitals, equation (6) is
automatically fulfilled which ensures that equation (5) is also valid due to the definition of
. The matrix elements of are then easily calculated :

* for the P-P interaction :

* for the S-S interaction :

* for the S-P interaction :

With this choice for , equations (7) and (8) are automatically valid for the perturbation.
The only restriction is that we have to use orthogonal orbitals and Slater determinants rather
than Configuration State Functions (CSFs) as a basis for the perturbation. None of these
restrictions is constraining, however.

2.2. THE MOELLER-PLESSET PARTITION
A detailed study of the various possibilities in the choice of the partition to be used in
performing the perturbation falls outside the scope of the present contribution (see reference
[34]): here we will limit the discussion to the widely used Möller-Plesset partition [7] in
which the diagonal matrix elements are defined by :

where F is the usual Fock operator. For a multireference zeroth-order wavefunction,
equation (18) gives the usual expansion of the definition of the zeroth-order energy [35]:

This approach extends the usual MP single-reference approach and will be hereafter
referred to as "Barycentric Möller Plesset" (BMP) perturbation theory [35]. If the orbitals
used are of RHF or UHF type, a single reference BMP calculation is analogous to a MP2
or UMP2 calculation. However, as emphasized above, we only need to have orthogonal
orbitals, which means that the orbitals to be used are not necessarily those that diagonalize
a
the usual Fock operators for closed-shell system :