Roothaan equations

The Roothaan equations are a representation of the Hartree-Fock equation in a non orthonormal basis set which can be of Gaussian-type or Slater-type. It applies to closed-shell molecules or atoms where all molecular orbitals or atomic orbitals, respectively, are doubly occupied. This is generally called Restricted Hartree-Fock theory.

The method was developed independently by Clemens C. J. Roothaan and George G. Hall in 1951, and is thus sometimes called the "Roothaan-Hall equations". [ Frank Jensen, Introduction to Computational Chemistry, John Wiley and Sons, 1999, pg 65 - 69, ISBN 0 471 98055 ] [ C. C. J. Roothaan, Reviews of Modern Physics, 23, 69, (1951) ] [ G. G. Hall, Proceedings of the Royal Society, London, A205, 541, (1951) ] The Roothaan equations can be written in a form resembling generalized eigenvalue problem, although they are not a standard eigenvalue problem because they are nonlinear:

:$mathbf\{F\}\; mathbf\{C\}\; =\; mathbf\{S\}\; mathbf\{C\}\; mathbf\{epsilon\}$

Where F is the so-called Fock matrix (which depends on the coefficients C due to electron-electron interactions), C is a matrix of coefficients, S is the overlap matrix of the basis functions, and $epsilon$ is the (diagonal, by convention) matrix of orbital energies. In the case of an orthonormalised basis set the overlap matrix, S, reduces to the identity matrix. These equations are essentially a special case of a Galerkin method applied to the Hartree-Fock equation using a particular basis set.

External links

* http://www.cachesoftware.com/mopac/Mopac2002manual/node443.html
* http://www.physik.unizh.ch/~sam/diss/node8.html

ee also

* Hartree-Fock

References