Place: Magnetic Tight Binding, Institute of Physics, London, UK
With the desire of having transferable tight-binding (TB) models based on ab-initio methods, the demands on TB models have substantially increased. Moreover, the limitations of the two-centre orthogonal Slater-Koster formalism have become evermore apparent. While "traditional" two-centre tight-binding approaches give qualitative agreement for structural stability within a significant portion of the periodic table, quantitative differences between alloy structures are much more difficult to predict. In addition, the predictive power of such models is considerably lower when they are applied to systems in which the coordination varies significantly from bulk solids. The transferability of the electronic structure at defects and surfaces is limited, due to the neglect of the environmental contributions which play a critical role in the electronic structure at interfaces. This has serious practical issues for TB simulations, as simulations of surfaces and defects are the exact problems for which simplified models of the electronic structure are necessary, as they involve simulation cells beyond the practical capability of ab-initio calculations.
In the present contribution, a number of steps towards environmental linear-scaling tight-binding methods are introduced. Firstly, we describe a "downfolding" approach by which an optimum minimal basis Hamiltonian can be determined directly from ab-initio calculation. In the second step, a non-orthogonal environmental tight-binding (ETB) model for Ni and Co is described in which the tightly-bound d orbitals and diffuse s orbitals are both included . In order to verify the ability of the model to describe a variety of local atomic arrangements, the model is applied to small metallic clusters which sample a large range of coordinations. A third step towards linear-scaling ETB simulations is to deal with the problem of the overlap matrix. We introduce a linear-scaling method for the evaluation of the screening matrix based on a Chebyshev expansion of the inverse of the overlap matrix. The method is applied to a number of realistic TB models, with a final brief discussion of the combination of the method with linear-scaling diagonalisation methods.