Ab initio Closed Shell Formalism

Ab initio Closed Shell Formalism.—The method for calculation of HF CO s in polymers and crystals at the ab initio level has been discussed many times 1-5 therefore, we repeat here only the basic expressions to allow a self-contained discussion of the procedures applied. We will work entirely in configuration space, writing down the many-electron crystal wavefunction as a Slater-deter- 

4 (a) J.-M. Andr6, in Electronic Structure of Polymers and Molecular Crystals , ed. J.-M. Andr6 and J. Ladik, Plenum Press, New York, 1975, p. 1 (6) J. Ladik, ibid, p. 23. 

Ladik and S. Suhai, in Molecular Interactions , ed. H. Ratajczak and W. J. Orville-Thomas, J. Wiley and Sons, New York, 1980, p. 151. 

N stands here for the number of elementary cells and yja(r) = Xa(r—Rj—Ra) is an AO centred in the cell j at Rj+Ra. Applying the non-relativistic electronic Hamiltonian (in atomic units) 

Here the atomic overlap integrals between the reference cell and cell j are defined by s t=iXa(f) x b(f)y and the corresponding Fock-matrix elements have the form 

---