Application of a new Tight-Binding method for transition metals: Manganese

A new tight-binding total energy method, which has been shown to accurately predict ground state properties of transition and noble metals, is applied to Manganese, the element with the most complex ground state structure among the d metals. We show that the tight-binding method correctly predicts the ground state structure of Mn, and offers some insight into the magnetic properties of this state. (Submitted to Europhysics Letters) Most elements in the periodic table crystallize in the fcc, bcc, hcp and diamond structures. Among the few exceptions is Manganese, which has an equilibrium structure, denoted α-Mn, which contains 29 atoms in the unit cell [1]. First principles total energy methods, such as the full-potential Linearized Augmented Plane Wave (LAPW) method [2,3] are not very efficient in such systems, especially since the α-Mn phase has five internal parameters which must be adjusted to minimize the total energy in order to calculate the correct structure at each volume. Calculation of elastic constants, phonon frequencies, surface energies, vacancy formation energies, and other properties require even more computational effort. A reliable approximate method, based on first-principles results, is necessary for efficient computational study of complicated crystals such as Manganese. In a recent paper, Sigalas and Papaconstantopoulos [4] introduced the idea that the energy bands of Augmented Plane Wave (APW) calculations for cubic structures at different volumes can be fit to a non-orthogonal tight-binding (TB) Hamiltonian whose matrix elements are functions of the distance between pairs of atoms. The sum of eigenvalues resulting from the above TB Hamiltonian, together with a pair potential, were used to fit the total energies of the APW calculation, thus obtaining an interpolation formula that was employed to calculate the total energy for non-cubic structures. This procedure was applied to calculate the elastic constants of Pd, Ir, Au, Rh and Ta, which showed fairly good agreement