Self-consistent order-Ndensity-functional calculations for very large systems

Abstract

We present a method to perform fully selfconsistent density-functional calculations, which scales linearly with the system size and which is well suited for very large systems. It uses strictly localized pseudoatomic orbitals as basis functions. The sparse Hamiltonian and overlap matrices are calculated with an O(N ) effort. The long range selfconsistent potential and its matrix elements are computed in a real-space grid. The other matrix elements are directly calculated and tabulated as a function of the interatomic distances. The computation of the total energy and atomic forces is also done in O(N ) operations using truncated, Wannier-like localized functions to describe the occupied states, and a band-energy functional which is iteratively minimized with no orthogonality constraints. We illustrate the method with several examples, including carbon and silicon supercells with up to 1000 Si atoms and supercells of β-C3N4. We apply the method to solve the existing controversy about the faceting of large icosahedral fullerenes by performing dynamical simulations on C60, C240, and C540.A large effort has been devoted in the last few years to develop approximate methods to solve the electronic structure of large systems with a computational cost proportional to its size. 1 Several approaches are now sufficiently accurate and robust to obtain reliable results for systems with thousands of atoms. So far, however, most of these schemes have been useful only with simple Hamiltonians, like empirical tight-binding models, which provide an ideal setting for order-N calculations. First-principles order-N calculations have been performed mainly in the non-selfconsistent Harris functional version 2 of the local density approximation (LDA) for electronic exchange and correlation (XC) using minimal bases. 1,3 Linear scaling algorithms in fully selfconsistent LDA have also been tried, 4 but the results are far from the linear scaling regime, due to the relatively small number of manageable atoms in those simulations. Hernandez et al. 5 have successfully produced LDA results in large silicon systems using a real-space grid method. The computational requirements that this kind of approach demands are, however, extremely large, and calculations must be performed in massive computational platforms.We have developed a selfconsistent density-functional formulation with linear scaling, capable of producing results for very large systems, whose computational demands are not overwhelmingly large, so that systems with many hundreds of atoms can be treated in modest computational platforms like workstations, and much larger systems can be treated in massive platforms. The method is based on the linear combination of atomic orbitals (LCAO) approximation as basis of expansion of the electronic states. Non-orthogonal LCAO bases are very efficient, reducing the number of variables dramatically, compared to plane-wave (PW) or real-space-grid approaches, so that larger systems can be studied. Also, LCAO can provide up to extremely accurate base...

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