Cellular Method and the Calculation of Molecular Wavefunctions. II. Application to the Alkali Molecules

The ``image method'' described in the preceding paper [H. S. Fricker and P. W. Anderson, J. Chem. Phys. 55, 5028 (1971)] is used to calculate valence orbitals in Li2, Na2, K2, and NaLi for a Wigner-Seitz cellular potential. The Green's functions are obtained by the quantum defect method. We discuss the problems involved in generating basis functions from point sources, and describe a simple, partly variational matching procedure which yields eigenvalues accurate to about 0.001 Ry and excellent wave-functions. Although the method is much simpler than a conventional self-consistent calculation, it gives, as in the metals, a good description of the binding: We obtain equilibrium distances to better than 10%, binding energies and vibration frequencies to within 30% and, with an empirical ``Coulomb integral,'' reasonable excitation energies. But the importance of short-range and angular correlations and the absence of a model comparable with the free electron theory of metals, makes it difficult to calculate the remaining interactions from first principles.