Alternative Technique for the Constrained Variational Problem Based on an Asymptotic Projection Method: II. Applications to Open-Shell Self-Consistent Field Theory

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The problem of the orthogonality of the closed- and open-shell orbitals in self-constistent field (SCF) theory are reviewed. An easily implemented asymptotic projection method for talking orthogonality constraints into account is used to develop an alternative open-shell SCF approach for ground and excited states. Variational derivation of the open-shell Hartree-Fock equations is described which does not involve off-diagonal Lagrangian multipliers. The possibilities of designing a well-defined, open-shell many-body perturbation theory using the orbitals of the asymptotic projection method is demonstrated by means of calculations of ground and excited state energies using the different levels of approximation. We also focus on the development of alternative computational strategies capable of optimizing relatively small distributed basis sets with respect to the positions and exponents of the basis functions.