Improved accuracy and acceleration of variational order-N electronic-structure computations by projection techniques

We have performed minimizations of the order-N energy functional of Ordejon et al. [Phys. Rev. B 51, 1456 (1995)] in models of fourfold-coordinated am orphous carbon containing 512 and 4096 atoms using the first-principle loca l-orbital Hamiltonian of Sankey and Niklewski. The total time for performin g the minimization can be significantly reduced by directly projecting the initial functions to the occupied subspace of the Hamiltonian before applyi ng a conjugate-gradients minimization. In addition, the energies achieved i n the minimization can be significantly lowered by dynamically optimizing t he localization regions of the projected functions using a population rathe r than distance criterion. Furthermore, the projection method also provides an efficient scheme for the linear-scaling computation of the Fermi energy in semiconductors, which is needed for the computation of the projected fu nctions as well as for the evaluation of several other order-N functionals. [S0163-1829(98)01344-7].