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.

Additional recommended knowledge

Recognize and detect the effects of electrostatic charges on your balance

Essential Laboratory Skills Guide

Weighing the right way

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. ^{[1] [2] [3]} The Roothaan equations can be written in the form of generalized eigenvalue problem

Where F is the so-called Fock matrix, C is a matrix of coefficients, S is the overlap matrix of the basis functions, and ε 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.

See also

• Hartree-Fock

References

1. ^ Frank Jensen, Introduction to Computational Chemistry, John Wiley and Sons, 1999, pg 65 - 69, ISBN 0 471 98055
2. ^ C. C. J. Roothaan, Reviews of Modern Physics, 23, 69, (1951)
3. ^ G. G. Hall, Proceedings of the Royal Society, London, A205, 541, (1951)