Computational Chemistry 4.16 - Coulomb and Exchange Operators
Short lecture on Coulomb and exchange operators 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 (electron kinetic energy plus electron-nuclear attraction to all nuclei) and the mean-field operator. The mean field operator consists of the Coulomb and exchange potential operators. Each of these operators is a sum of the Coulomb and exchange operator of all other occupied spin orbitals acting on the spin orbital, respectively. The Coulomb operator of a spin orbital represents the repulsion an electron at a point in space would experience due to the charge density of an electron in that spin orbital integrated over all space. The exchange operator does not have a similarly straightforward classical interpretation, and arises only due to quantum effects.
Notes Slide: https://i.imgur.com/N1oqgsg.png
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