Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations

Article

关键词: SHAPE TRUNCATION FUNCTIONS;    NUMERICAL-INTEGRATION;    VOLUME;    EQUATION;    ENERGY;    ATOMS;    ALGORITHM;    SURFACE;    SCHEME;   

DOI  :  10.1103/PhysRevB.84.045105

来源: SCIE

【 摘 要 】

A numerically efficient, accurate, and easily implemented integration scheme over convex Voronoi polyhedra (VP) is presented for use in ab initio electronic-structure calculations. We combine a weighted Voronoi tessellation with isoparametric integration via Gauss-Legendre quadratures to provide rapidly convergent VP integrals for a variety of integrands, including those with a Coulomb singularity. We showcase the capability of our approach by first applying it to an analytic charge-density model achieving machine-precision accuracy with expected convergence properties in milliseconds. For contrast, we compare our results to those using shape-functions and show our approach is greater than 10(5) times faster and 10(7) times more accurate. A weighted Voronoi tessellation also allows for a physics-based partitioning of space that guarantees convex, space-filling VP while reflecting accurate atomic size and site charges, as we show within KKR methods applied to Fe-Pd alloys.

【 授权许可】

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