A Simplified Method of Computing the Cohesive Energies of Monovalent Metals

Abstract

A method is developed which, within the limits of the spherical cell approximation first presented by Wigner and Seitz, permits the evaluation of the cohesive energy, lattice constant, and compressibility of a monovalent metallic solid without the explicit computation of a central field for the atom. It is shown that empirical values of the first few $s$ and $p$ levels of the free atom can supply the relevant information usually obtained through the computation of a central field, so that a considerable simplification is possible. The method is applied to the calculation of the usual solid state parameters for the alkali metals, Na, K, and Rb. The results for Na compare very favorably with experiment as well as with those gained by previous workers. The K and Rb computations agree decidedly less well with experiment, but the values for K are appreciably better than those previously computed utilizing an explicit central field. The errors shown by the K and Rb computations are believed to be the inevitable consequence of any theory derived by replacing the effect of the core electrons by an equivalent central field rather than a result of any peculiarities inherent in the present approach.