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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. These equations are essentially a special case of a
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In contrast to the
Hartree–Fock equations - which are integro-differential equations - the Roothaan–Hall equations have a matrix-form. Therefore, they can be solved using standard techniques.
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Hall, G. G. (1951). "The
Molecular Orbital Theory of Chemical Valency. VIII. A Method of Calculating Ionization Potentials".
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104:{\displaystyle \mathbf {F} \mathbf {C} =\mathbf {S} \mathbf {C} \mathbf {\epsilon } }
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applied to the
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