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.

Related Topics:
Hartree-Fock - Basis set - Gaussian-type - Slater-type

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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 Roothaan equations can be written in the form of generalized eigenvalue problem

Related Topics:
Clemens Roothaan - George G. Hall - Generalized eigenvalue problem

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:mathbf{F} mathbf{C} = mathbf{S} mathbf{C} mathbf{epsilon}

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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.

Related Topics:
Fock matrix - Overlap matrix

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