The Roothaan equations are an extension of the Hartree-Fock model to molecular orbitals, and provide an approximation technique which can simplify computation. In particular, they generalise the method for an arbitrary basis set, which need not be orthonormalised.
The method was developed independently by Clemens Roothaan and George G. Hall in the early 1950s, and are thus sometimes called the Roothaan-Hall Equations. The method can be reduced to a form of the self-consistent field approach for molecular systems. In reduced form, the Roothaan Equations can be written:
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. For this reason, most implementations of these equations require such a basis, as a noticeable computational saving.
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See Also
Hartree-Fock
Computational chemistry