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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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