Dual-Space-Operator Technique to Build Symmetry-Adapted Wave Functions. I. Molecules with Abelian Symmetry Group

A general method is described of building up open-shell multideterminant wave functions which are eigenfunctions of the spin operators $S^2$ and $S_z$. In the present case, that of a molecule with an Abelian symmetry group, the wave functions obtained are easily adapted for spatial symmetry. The matrix elements of the Hamiltonian are derived. The method gives a building up of the matrix elements of the irreducible representation [$n_1,n_2$] symmetric groups which, as far as the author knows, is original. While many of the specific results are not new, the author believes that the presentation which he used is both new and interesting. This method will be extended later to more general cases.