Many-electron systems Hartree-Fock and correlated treatments

3 Many-electron systems Hartree-Fock and correlated treatments 

The Hartree-Fock (HF) orbitals p, can be shown to satisfy a Schrodinger-type eigenvalue equation 

The Fock operator F for an atomic or molecular system is a modified one-electron Hamiltonian (cf. Eq. (1.9b)), 

As usual, the Hartree-Fock model can be corrected with perturbation theory (e.g., the Mpller-Plesset [MP] method29) and/or variational techniques (e.g., the configuration-interaction [Cl] method30) to account for electron-correlation effects. The electron density p(r) = N f P 2 d3 2... d3r can generally be expressed as 

Let us examine the fluoride ion (F ), for which variational 6-311++G calculations give 

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