ORDER-N PROJECTION METHOD FOR FIRST-PRINCIPLES COMPUTATIONS OF ELECTRONIC QUANTITIES AND WANNIER FUNCTIONS

We present a generalized projection-based order-hi method which is app licable within nonorthogonal basis sets of spatially localized orbital s. The projection to the occupied subspace of a Hamiltonian, performed by means of a Chebyshev-polynomial representation of the density oper ator, allows the nonvariational computation of band-structure energies , density matrices, and forces for systems with nonvanishing gaps. Fur thermore, the explicit application of the density operator to local ba sis functions gives a powerful method for the calculation of Wannier-l ike functions without using eigenstates. In this paper, we investigate such functions within models of diamond and fourfold-coordinated amor phous carbon starting from bonding pairs of hybrid orbitals. The resul ting Wannier states are exponentially localized and show an ellipsoida l spatial dependence. These results are used to maximize the efficienc y of a linear-scaling orthonormalization scheme for truncated Wannier functions.