The many-electron Hamiltonian is expressed as
where the Mulliken notation is used for the two-electron integrals. The Fock matrix then has the elements
with an element of the 1-matrix, and the single-particle density operator . The tilde denotes operators relative the Hartree-Fock spin orbitals, i.e.,
with and .
The average value of the Hamiltonian can be expressed in a number of ways
and because the trace of a ...