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COUPLED HARTREE-FOCK APPROACH 283
zero-order orbitals. Taking the Hermitian product with an unoccupied in eq. (21)
one has
and left-multiplying by the ket and summing over k gives
where
is the Hartree-Fock propagator [10], [11] and the projector
is equivalent to the identity operator when acting on the subspace of virtual or-
bitals [7].
3. Solution of second-order CHF equation
We discuss a method to evaluate the second-order molecular orbitals appearing in eq.
(17) consistent with the first-order computational scheme outlined in the previous
section. In particular we take advantage of definition (30) to develop a compact
approach explicitly oriented to numerical applications.
The second-order CHF equation for the i-th occupied orbital is
where the orbitals satisfy the orthonormality condition to second order,
Taking in (32) the Hermitian product with and using eqs. (19), (21), and (22),
one finds
where the index j = i can be omitted in the sum, in the present case of real pertur-
bations, owing to eq. (27). Summing over i occupied, the last term in (34) vanishes.
