Atoms in Valence Bond. Method, implementation and application

The Atoms in Valence Bond (AiVB) approach is presented. The main goal was to develop a new and innovative approach, within the existing Valence Bond framework, to build and analyze the molecular VB wave function in terms of atoms and their atomic states, in a very user-friendly environment. The necessary theoretical tools, detailed implementation in TURTLE, an ab initio VB/VBSCF program and application are described. The procedure to build the molecular Atoms in ValenceBond (AiVB) wave function is not arbitrary, and is carried out by specifying the atomic states of the atoms in the different atomic AiVB structures. Presently the AiVB wave function is restricted to atomic orbitals from atomic Hartree-Fock calculations, but this is not a fundamental limitation. All possible projections of the atomic state, for each of the atoms, have to be included as separate VB structures. The AiVB approach extends the standard concept of VB structure, which is limited to a single spin-function, in order to realistically describe the atoms in their atomic states. The AiVB structure assumes a more general form where it is expressed as a sum of N-electron Slater determinants with a fixed expansion coefficients in front of each Slater determinant, which is not optimized variationally. The AiVB structures have a good quantum numbers S and Ms of the molecule considered. The Slater determinants will have different orbitals however the spin function may or may not be the same.