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Propagators in Quantum Chemistry, 2nd Edition by Yngve Öhrn, Jan Linderberg

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Appendix C

Stability of Hartree-Fock Solutions

The many-electron Hamiltonian is expressed as

Image

where the Mulliken notation is used for the two-electron integrals. The Fock matrix then has the elements

Image

with Image an element of the 1-matrix, and the single-particle density operator Image. The tilde denotes operators relative the Hartree-Fock spin orbitals, i.e.,

Image

with Image and Image.

The average value of the Hamiltonian can be expressed in a number of ways

Image

Note that

Image

with

Image

Thus,

because

and because the trace of a ...

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