Core-valence separation in the spin-coupled wave function: A fully variational treatment based on a second-order constrained optimization procedure

Abstract

The theory of the spin-coupled (SC) wave function with core-valence separation, in which the core electrons are confined to a closed shell of doubly-occupied orbitals and the valence electrons are described with the complete set of features of the SC formalism, is developed to produce an efficient approach which makes possible its fully variational determination. The simultaneous optimization of the core orbitals, valence orbitals, and spin-coupling coefficients is achieved through a second-order nonlinear elimination constrained minimization algorithm which exhibits excellent convergence properties. It is no longer necessary to introduce an ad hoc preselection of core and valence orbitals−this is carried out by the minimization procedure itself which makes an optimum choice from a variational point of view. The only important item left to personal judgment is the selection of the number of core and valence electrons in the problem under investigation. Simplifications such as ‘‘freezing’’ of a part of the core orbitals are discussed alongside with the verification of the theoretical work and program code by emulating, under an appropriately modified set of constraints, the generalized valence-bond (GVB) wave function with perfect pairing and strong-orthogonality restrictions. It is demonstrated that it is possible, similar to the Hartree–Fock (HF) method, to transform the core orbitals into canonical form and to associate with each one of them an energetical quantity analogous to the HF orbital energy. The essential features of the approach are illustrated by a SC study of the process H2CO(1A1)→CH2(X̃ 3B1)+O(3P), involving the breaking of the C■O double bond. The results prove that only a fully variational SC wave function with core-valence separation is capable of providing a uniform description of the change in the physical properties of the system upon dissociation, which can be achieved by including in the SC part of the wave function just the four electrons immediately involved in the carbon–oxygen double bond.