ORTHOGONALITY CONSTRAINTS IN FINITE BASIS-SET CALCULATIONS

The orthogonality-constrained one-body eigenvalue problem is formulated for complete, finite-dimensional spaces in terms of projection operators that partition the space into two orthogonal subspaces, one containing the constraints and one containing the desired solutions. We derive a Hermitian operator, associated with the Hamiltonian, having eigenvectors that are correspondingly partitioned, each subset of the eigenvectors providing a basis for one of the subspaces. This Hermitian operator advantageously replaces a non-Hermitian operator that was proposed in recent work of this group. The non-zero spectrum of the two operators is demonstrably the same, and the occurrence of null eigenvalues is clarified through characterization of the associated eigenvectors. The deviation from zero of these eigenvalues (apart from numerical inaccuracies) is related directly to the normalization of the constraint vectors. The formalism is extended to the case of non-orthonormal primitive basis sets, and a numerical application is carried out using B-spline functions.