NOON — A non-orthogonal localised orbital order-N method Original Research Article

We present the implementation of an orbital-based linear scaling method for total energy calculations within a Tight-Binding approach. Our scheme explicitly incorporates charge self-consistency for both single- and multiple-species systems and uses non-orthogonal basis sets to construct non-orthogonal orbitals. The energy functional of Kim et al. [Phys. Rev. B 52 (1995) 1640] is minimised within a hierarchical iteration scheme for wave functions and the Lagrangian parameter. A number of safeguard mechanisms are applied to stabilise the algorithms on both levels. Compared to exact diagonalisations using extended states we reproduce the total energy typically within 100 meV when localizing wave functions within second neighbours and within 30 meV when including third neighbours. The charge transfer effects and related energies for self-consistent-charge corrections are reproduced accurately.