Adaptation of the molecular-orbital method to study the crystalline structure and shape of a monovalent metal: Application to lithium

An approximation, derived from the self-consistent-field-molecular-orbital method, which includes nuclear repulsion is proposed to study metallic structures of alkali atoms. The method allows the evaluation of the average energy per atom in the massive crystal and the loss of stability in various smaller samples according to their crystal lattice. The method was applied to lithium. Several atomic lattices, bcc, fcc, and pentagonal symmetry, were studied as a function of the number of atoms. The distance between nearest neighbors deduced from bond orders is identical for pentagonal and for fcc structures and bigger than the one for the bcc system. Surface energies were evaluated using the destabilization terms relative to the surface atoms. The relative stability of the crystalline lattices was investigated as a function of the number of atoms and of the spatial conformation of the structures. It appears that small-sized structures have an atomic lattice different from that of massive crystals. Thus, the bcc system becomes prefered only for structures having more than about ${10}^6$ atoms.