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.

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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)