I.4. Hartree–Fock approximation. The Hartree–Fock approximation is a simple yet important model for understanding electron–electron interaction...

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

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