Linear system-size scaling methods for electronic-structure calculations

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Abstract
We describe a method for performing electronic-structure calculations of the total energy and interatomic forces which scales linearly with system size. An energy functional is introduced which possesses a global minimum for which (1) electronic wave functions are orthonormal and (2) the correct electronic ground-state energy is obtained. Linear scaling is then obtained by introducing a spatially truncated Wannier-like representation for the electronic states. The effects of this representation are studied in detail. Molecular-dynamics simulations using an orthogonal tight-binding basis and ab initio local-orbital density-functional methods are presented. We study both Car-Parrinello and conjugate-gradient molecular-dynamics schemes and discuss practical methods for dynamical simulation. A detailed connection between our method and the density matrix approach of Daw [Phys. Rev. B 47, 10 895 (1993)] and Li, Nunes, and Vanderbilt, [Phys. Rev. B 47, 10 891 (1993)] is also provided.