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Hartree-Fock Approximation

A method for approximating the solutions to the Schrödinger equation by assuming that electrons do not interact during the calculation.
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The statement of the theorem

The total wavefunction Ψ\Psi is approximated by a single Slater determinant formed from orthonormal single-particle orbitals ϕi\phi_i: Ψ=det⁡(ϕ1,…,ϕN)\Psi = \det(\phi_1, \dots, \phi_N). The resulting single-particle equations are solved variationally, leading to the Roothaan-Hall equations in the basis set representation: \n∑j=1N(Hij−SijE)cj=0\sum_{j=1}^{N} (\mathbf{H}_{ij} - \mathbf{S}_{ij} \mathbf{E}) c_{j} = 0 \nwhere H\mathbf{H} and S\mathbf{S} are the Fock and overlap matrices, respectively, and E\mathbf{E} is the matrix of orbital energies.