We find that within local-density schemes for calculating the cohesive energy of simple metals greater sophistication in treating the atom is required. The outermost electron in, e.g., the sodium atom has an unpaired spin. For this and the many similar cases a generalization of the scheme to a spin-density-functional formalism is needed. Application of the local-spin-density approximation gives, e.g., the energy of the hydrogen atom within 1.6% of the exact value, while the local-density approximation is 10% off. The improvement is due to our use of a better model system, i.e., the spin-polarized electron liquid, in the local approximation. We elaborate on the factors leading to the smallness of the error, and we find that there is a systematic partial cancellation between too attractive and too repulsive contributions to the binding for valence electrons in hydrogen and similar atoms. When we extend Tong's calculation for sodium metal along these lines, we find the cohesive energy to lie within 4% of the experimental value. A similar improvement is found for lithium. The spin-density scheme should be a very useful practical method for a large range of applications, including the calculation of chemisorption and charge transfers.

• Received 18 March 1974

DOI:https://doi.org/10.1103/PhysRevB.10.1319