Computational Chemistry 4.22 - Restricted Hartree-Fock
Short lecture on spin-restricted Hartree-Fock operators and energies.
Restricted Hartree-Fock (RHF) makes use of restricted Slater determinants to simplify the Hartree-Fock equations. The pairing of opposite-spin electrons in the same spatial orbital allows us to cut the number of necessary orbitals to consider in half. Additionally, we can integrate out the spin in our one-electron and two-electron integrals. This doesn't affect our one-electron core Hamiltonian integrals, or our two-electron Coulomb integrals, but it does cut the number of exchange integrals in half. The resulting expression allows us to describe the molecular energy in terms of twice a sum over half the orbitals for one-electron energy, and a full double sum over two-electron energy, where each term is twice a Coulomb integral subtracted by an exchange integral. Orbital energies simplify as well, with the two-electron term reducing to a sum over half as many orbitals of 2J-K.
Notes Slide: https://i.imgur.com/W6Al6ar.png
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