Computational Chemistry 4.17 - Fock Operator
Short lecture on the Fock operator in Hartree-Fock theory.
The Fock operator forms a pseudo-eigenvalue equation where the eigenfunction is a spin orbital and the eigenvalue is the orbital energy. The Fock operator consists of the one-electron core Hamiltonian operator plus the Coulomb potential and exchange potential, each of which is a sum of the Coulomb and exchange operators for all the other occupied spin orbitals, respectively. This is a pseudo-eigenvalue equation because the mean-field operator depends on the form of all the other spin orbitals in the molecule. A simplified representation of the Fock operator may be obtained by making use of the permutation operator, which exchanges the indices of electrons 1 and 2 wherever they are encountered when acted upon by the operator. For the current spin orbital, the Coulomb and exchange operators cancel out, thus we can include the current spin orbital as well in the sum over all other occupied orbitals.
Notes Slide: https://i.imgur.com/BsVQ3M3.png
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