I.4. Hartree–Fock approximation. The Hartree–Fock approximationis a simple yet
important model for understanding electron–electron interaction incrystals.
(a) Derive the Hartree–Fock self-consistent field equations fromthe variational principle
using a Slater determinant of single-particle orbitals as a trialmany-electron
wavefunction.
(b) Consider the total electronic energy of a system (e.g. amolecule) in the Hartree–
Fock approximation. Calculate the change in the energy of thesystem if an
electron is promoted from an occupied ith orbital to an unoccupiedjth orbital,
assuming that the orbitals are unchanged after the excitation. Howis this excitation
energy related to the eigenvalues of the Hartree–Fock equations?This kind
of excitation is called a neutral excitation, which occurs forexample in a photoexcitation
process, since no electrons are added or removed from the system.The
result is known as Koopmans’ theorem.
