Phys 498CQM Lecture # 7

Outline: Hartree-Fock Theory for Atoms

1. Continue discussion of solving 1-d Schr. Eq. by "shooting" method
   
2. Continue discussion of derivation of Hartree-Fock equations
   • Equations in the 2-electron case
   • Equations in the many-electron case
   • Meaning of eigenvalues - Koopman's theorem
   • Gap for adding vs subtracting particles
3. Solution of Restricted Hartree-Fock equations for spherical atoms
   • Closed shells, and with one more or one less electron, are spherical
   • Restricted HF (equal orbitals for up and down spin) apppropriate only for cases with paired spins (Closed Shell systems)
     • Regular or log grids?
     • Numerical solution of radial equations
   • For other cases, one can let the spin be unrestricted but still make the spherical approximation for the spacial potential (Spin unrestricted)
   • Full unrestricted case
     • Expressions for exchange and Hartree potentials in general case
     • Consequences
     • Self-Consistency in potential and wavefunctions
     • Starting guess - hydrogenic orbitals
   • Programs written by T. J. Wilkens
   • Examples of solutions: H, He, Li, Be, B, Ne.