Hartree-Fock

In computational physics and computational chemistry, the Hartree-Fock (HF) or self-consistent field (SCF) calculation scheme is a self-consistent iterative variational procedure to calculate the Slater determinant (or the molecular orbitals which it is made of) for which the expectation value of the electronic molecular Hamiltonian is minimum. Whilst it calculates the exchange energy exactly, it does not include the effect of electron correlation. The procedure is named after Douglas Hartree, who devised the self-consistent field method, and V. A. Fock, who demonstrated the rigour of Hartree's method and reformulated it into the matrix form used today. Expressed in a Slater-type or Gaussian-type basis set, the Hartree-Fock equation can be transformed into matrix form called Roothaan equations.

Numerical stability

Numerical stability can be a problem with this procedure- there are various ways of combating this instability. One of the most basic and generally applicable is called F-mixing. With F-mixing, once a single electron wavefunction is calculated it is not used directly. Instead, some combination of that calculated wavefunction and the previous wavefunctions for that electron is used - the most common being a simple linear combination of the calculated and immediately preceding wavefunction. A clever dodge, employed by Hartree, for atomic calculations was to increase the nuclear charge, thus pulling all the electrons closer together. As the system stabilised, this was gradually reduced to the correct charge.

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