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Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework. I: Total energy calculation. (English) Zbl 1251.82008

It is known that the Kohn-Sham density functional theory is one of the most widely used electronic structure theories. In the present paper, a new discretization scheme is given that adaptively and systematically builds the rapid oscillations of the Kohn-Sham orbitals around the nuclei as well as environmental effects into the basis functions. In this scheme, the resulting basis functions are constructed adaptively and seamlessly from the atomic configuration in local domains, called elements. The basis functions are discontinuous at the boundary of the elements, and they form the basis set used in the discontinuous Galerkin (DG) framework. The flexibility of the DG framework allows the authors to employ these discontinuous basis functions to approximate the continuous Kohn-Sham orbitals. Moreover, they achieve high accuracy in the total energy calculation with a very small number (4–40) of basis functions per atom. The new method (i.e., the authors’ method) is implemented in parallel with a rather general data communication framework, and the current implementation is able to calculate the total energy for systems consisting of thousands of atoms. The authors also apply the DG algorithm to solve eigenvalue problems with oscillatory eigenfunctions, and the basis functions are constructed by solving auxiliary local problems numerically.

MSC:

82B10 Quantum equilibrium statistical mechanics (general)
82-08 Computational methods (statistical mechanics) (MSC2010)
35Q55 NLS equations (nonlinear Schrödinger equations)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65Z05 Applications to the sciences

Software:

lobpcg.m; SelInv
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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