Page 194 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer
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HARTREE-FOCK MODEL TO THE LOWEST SINGLET AND TRIPLET EXCITED STATES 177
where is a Slater determinant in which an orbital is replaced by an one.
In this expression, the operator is the usual Fock operator of the Unrestricted
Hartree-Fock method [14]:
In this equation, the Mulliken notation for the repulsion integrals is used, that is:
and stands for the well known monoelectronic operator:
A similar operator as (8) can be written when a orbital is substituted by a virtual
one:
The calculation of the cross matrix elements (6) is somewhat more difficult, be-
cause the Slater Determinants involved in them are constructed with two sets of
non-orthonormal spinorbitals. This calculation, however, may be greatly simplified,
if the two sets are assumed to be corresponding, that is, if they fulfill the following
condition [14]:
As well known, this condition is not a restriction whenever the wavefunction is in-
variant under an unitary transformation [2].
Taking into account (12), the matrix elements (6), with their phase factor in (4), may
be written in the following way:
