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Half‐numerical evaluation of pseudopotential integrals
Author(s) -
FloresMoreno Roberto,
AlvarezMendez Rodrigo J.,
Vela Alberto,
Köster Andreas M.
Publication year - 2006
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.20410
Subject(s) - slater integrals , order of integration (calculus) , numerical integration , mathematics , cartesian coordinate system , quadrature (astronomy) , gaussian , scheme (mathematics) , pseudopotential , gaussian quadrature , numerical analysis , volume integral , trigonometric integral , mathematical analysis , nyström method , trigonometric functions , physics , geometry , quantum mechanics , integral equation , optics
A half‐numeric algorithm for the evaluation of effective core potential integrals over Cartesian Gaussian functions is described. Local and semilocal integrals are separated into two‐dimensional angular and one‐dimensional radial integrals. The angular integrals are evaluated analytically using a general approach that has no limitation for the l ‐quantum number. The radial integrals are calculated by an adaptive one‐dimensional numerical quadrature. For the semilocal radial part a pretabulation scheme is used. This pretabulation simplifies the handling of radial integrals, makes their calculation much faster, and allows their easy reuse for different integrals within a given shell combination. The implementation of this new algorithm is described and its performance is analyzed. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 1009–1019, 2006