Hartree-Fock and Self-Consistent-Field Calculations

3 Hartree-Fock and Self-Consistent-Field Calculations 

The orbital approach to the problem of electronic structure reduces a many-electron problem to a corresponding number of one-electron problems. The Hartree-Fock solution represents the best attainable description of the electronic structure of a many-electron system in terms of the one-electron orbital approach. 

In the orbital description of electronic structure, the motion of each electron is determined by a spin-orbital, ut, a simple product of a space function fc and a spin function at 

By analogy with a system in which each electron moves independently of the others, the total wavefunction is taken to be a product of the one-electron spin orbitals, one for each electron in the system. To satisfy the additional restrictions of the Pauli principle, and simultaneously to allow for the indistinguishability of the electrons, an antisymmetrized sum of such product functions must be used to 

The energy of such a determinantal wavefunction, ( R), is obtained by the quantum mechanical averaging of the electronic Hamiltonian operator given in equation (6) 

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