Roothaan equations

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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 the early 1950s, and are thus sometimes called the Roothaan-Hall equations. The Roothaan equations can be written in the form of generalized eigenvalue problem

[\mathbf \mathbf = \mathbf \mathbf \mathbf]

Where F is the so-called Fock matrix, 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.

External links

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

Roothaan equations

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See also