The introduction of orthogonality constraints in basis set calculations

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Abstract
The authors considers the introduction of orthogonality conditions in frozen-core Hartree-Fock calculations using basis-set expansions in which the orbitals are constrained to be orthogonal to core orbitals of the same symmetry. They find that such a constraint usually leads to a non-Hermitian eigenvalue problem. However, they show that for arbitrary core orbitals the eigenvalues are all real and that the required eigenvectors are orthogonal. The result is not restricted to Hartree-Fock calculations but also applies, for example, to model-potential calculations in which the orbitals for some reason should be orthogonal to a set of suitable core orbitals. If the core orbitals are chosen to be eigenfunctions of the Hamiltonian then the resulting matrix is Hermitian and has zero eigenvalues corresponding to the core orbitals. The authors also show how the problem may be transformed into a Hermitian matrix eigenvalue problem which is convenient for computational purposes.

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