Energy Band Structure of Lithium by the Tight-Binding Method

The energy band structure of lithium has been calculated by the tight-binding method. The crystal potential used in the Hamiltonian is the "muffin-tin" version of the Seitz potential. Bloch functions are constructed from the $1s$, $2s$, and $2p$ Hartree-Fock functions of the free atom and are used to set up the secular equation for the energy of a given point in the Brillouin zone. The matrix elements may be expressed as the sums over the crystal lattice points of a series of multicenter integrals with varying distances between the centers of the two atomic orbitals. For the majority of the matrix elements, in order to achieve convergence, all the integrals for which the two centers are separated by less than six times the lattice constant must be included. The multicenter integrals are evaluated by the technique of Gaussian transformation and the method for computing the matrix elements of the potential energy is described. The calculated energies along the [100], [110], and [111] axes of the Brillouin zone agree well with those calculated by a Green's-function method, by a modified plane-wave method, and by the composite-wave variational method of Schlosser and Marcus.