Spherical tensor gradient operator method for integral rotation: A simple, efficient, and extendable alternative to Slater-Koster tables

The Journal of Chemical Physics vol. 129  p. 016102  DOI: 10.1063/1.2945897
PMID/PMCID: PMC2671661 Published: 2008-07-07 

Timothy J. Giese [ ] , Darrin M. York [ ]

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We present a novel alternative to the use of Slater–Koster tables for the efficient rotation and gradient evaluation of two-center integrals used in tight-binding Hamiltonian models. The method recasts the problem into an exact, yet implicit, basis representation through which the properties of the spherical tensor gradient operator are exploited. These properties provide a factor of 3 to 4 speedup in the evaluation of the integral gradients and afford a compact code structure that easily extends to high angular momentum without loss in efficiency. Thus, the present work is important in improving the performance of tight-binding models in molecular dynamics simulations and has particular use for methods that require the evaluation of two-center integrals that involve high angular momentum basis functions. These advances have a potential impact for the design of new tight-binding models that incorporate polarization or transition metal basis functions and methods based on electron density fitting of molecular fragments.