On the Quantum-Mechanical Calculation of the Cohesive Energy of Molecules and Crystals. Part II. Treatment of the Alkali Metals with Numerical Applications to Sodium

In Part I, an expression for the cohesive energy of a crystal was derived in the case the wave function for the ground state is approximated by a single Slater determinant of Bloch spin orbitals, formed by linear combination of the atomic spin orbital associated with the self-consistent fields with exchange for the free constitutents. By using the new idea of ``combined atomic orbitals,'' all energy terms were reduced to only atomic two-center integrals, which could be evaluated by numerical integration. This method is here applied to the calculation of the cohesive energy of the alkali metals, where, due to the crystal symmetry, the combined atomic orbitals for the valence electrons are almost pure s-functions. It is shown that the conventional method, taking only the interaction between nearest neighbors into account, is entirely insufficient and that it is necessary to consider even bonding, overlapping, and electronic repulsion effects between neighbors of a rather high order. Numerical applications, including interactions between neighbors up to the order nine, are carried out for metallic sodium, giving the cohesive energy 24.7 kcal/mol and the interatomic distance 3.69A, in good agreement with the experimental values 26 kcal/mol and 3.67A, respectively. Except for the values of the fundamental constants e, m, h, ···, no empirical data are used.