Last hour: Hartree-Fock Self-Consistent Field (HF-SCF) Method Approximations: WF=product of one-e- fcts (only true for separable Hamiltonian) Treat each electron in the average field of all other electrons Assume central effective fields HF-SCF radial functions are not H-like (because of potential from e-e repulsion), but are still labeled by quantum numbers n, ℓ (representing the nodal structure). Maintains idea of orbitals for each electron Set of orbitals with the same n  shell; set of orbitals with the same ℓ  subshell Filled shells and subshells yield a spherically symmetric probability density (Unsöld’s Theorem) EHF-SCF > Eexact (linear variation method!) HF-SCF is the basis for the buildup principle that determines the ordering of low energy configurations for multi-electron atoms. The energies of the 1-e- AO’s correspond approximately to the negative of the ionization energies of these electron, i.e., Ej is about the energy necessary to remove an electron from the orbital j (Koopmans’ Theorem).

Learning Goals for Chapter 20 – The Hartree-Fock SCF Method After this chapter, the related homework problems, and reading the relevant parts of the textbook, you should be able to: explain the challenges in solving the problem of determining energy levels of multielectron atoms; explain the approximations made in the Hartree-SCF method; qualitatively explain the strategy of the Hartree-SCF method; explain the meaning of “zeta” and “STO” in quantum chemistry terminology; qualitatively explain the difference betwee the Hartree-SCF method and the Hartree-Fock-SCF method; use simple linear variation theory to solve eigenvalue problems.

Atomic Structure and Term Values En increases with n at constant n, greater ℓ means more “circular” orbit  more screening of nuclear charge  Enℓ increases with ℓ order of orbitals depends on Z: e.g. 3d < 4s for Z < 7 3d > 4s for 7≤ Z ≤ 21 from I. Levine: Quantum Chemistry