Computational Chemistry 4.14 - Hartree-Fock Approximation

Short lecture on the Hartree-Fock approximation for the Hamiltonian operator of molecular systems.

Even after applying the Born-Oppenheimer approximation the molecular Schrodinger equation is still an N-body problem for all electrons due to the non-separable two-electron terms. One solution is to use the Hartree-Fock approximation to average the repulsion of electrons over the average position of all other electrons, rather than an explicit pairwise interaction. This allows the Hamiltonian to be expressed as a sum of one-electron operators and is finally separable. This would result in a straightforward eigenvalue equation, however the form of the mean-field operator depends on all of the other N-1 occupied spin orbitals, thus it is a non-linear pseudo-eigenvalue equation.

Notes Slide: https://i.imgur.com/Ky5DTD9.png

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