OF THE MONTH Forces and Lattice Relaxations Calculated by aFull - Potential KKR - Green ' s Function

In this review we demonstrate that a recently developed full-potential KKR-Green's function method allows an eecient calculation of forces and lattice relaxations in transition metals. The forces can be readily evaluated by the ionic Hellmann-Feynman theorem, while the Green's functions for shifted positions can be obtained by angular momentum transformations. As applications we calculate the lattice relaxations around impurities in Cu and Al. Moreover, we show that the method allows to determine the phonon frequencies of transition metals from a single self-consistent calculation of the coupling constants in real space and present results for ferromagnetic Ni. The KKR method of electronic structure calculations, introduced by Korringa 1] and Kohn and Rostoker 2], is well known for its mathematical rigorousness and elegance. By taking advantage of multiple scattering theory, the method clearly separates the scattering properties of the single potentials from the geometrical structure of the system. Moreover, the size of the resulting algebraic equations is optimally small. On the other hand, the KKR theory is subtle and complex, so that even the evaluation of the free-space structure constants represents a problem in itself. Moreover, its numerical implementation for band-structure calculation is neither easy nor eecient. This has lead to the fact that the linear methods, like LMTO, ASW, and LAPW, received over the years considerably more attention.