Hartree Fock

Hartree Fock is a quantum method for calculation of molecules. It estimates the system wave function by a slater determinant of the molecular wave functions.

For an $$N$$ electron system, a Slater determinant may be written as:

$$ \Psi(\mathbf{q}_1,\mathbf{q}_2,\ldots,\mathbf{q}_N) = \frac{1}{\sqrt{N!}}\left\vert \begin{array}{c c c c} \psi_1(\mathbf{q}_1) & \psi_2(\mathbf{q}_1) & \ldots & \psi_N(\mathbf{q}_1) \\ \psi_1(\mathbf{q}_2) & \psi_2(\mathbf{q}_2) & \ldots & \psi_N(\mathbf{q}_2) \\ \vdots & \vdots & ~ & \vdots \\ \psi_1(\mathbf{q}_N) & \psi_2(\mathbf{q}_N) & \ldots & \psi_N(\mathbf{q}_N) \end{array} \right\vert $$

where $$\psi_i(\mathbf{q}_j)$$ denotes an orthonormal one-electron wave function or molecular spin-orbital (MO) and $$\mathbf{q}_j$$ the electronic spatial and spin coordinates. ...

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