Editing Hartree–Fock method (section)

== Numerical stability ==

[[Numerical stability]] can be a problem with this procedure and there are various ways of combatting this instability.  One of the most basic and generally applicable is called ''F-mixing'' or damping.  With F-mixing, once a single-electron wave function is calculated, it is not used directly.  Instead, some combination of that calculated wave function and the previous wave functions for that electron is used, the most common being a simple linear combination of the calculated and immediately preceding wave function.  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. In molecular calculations a similar approach is sometimes used by first calculating the wave function for a positive ion and then to use these orbitals as the starting point for the neutral molecule. Modern molecular Hartree–Fock computer programs use a variety of methods to ensure convergence of the Roothaan–Hall equations.