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- W3202675072 abstract "Abstract B functions B n , l m ( α , r ) are comparatively complicated functions. Nevertheless, their multicenter integrals are frequently substantially simpler than those of other exponentially decaying functions as for example Slater-type functions. This is a consequence of their exceptionally simple Fourier transform. The order n of a B function is usually assumed to be an integer, but it is possible to replace n ∈ N 0 by a nonintegral ν satisfying ν + 1 / 2 ∉ Z . Nonlinear orders increase the flexibility of B functions in variational calculations, but they make integral evaluation more difficult. For example, two-range addition theorems for B functions with nonintegral orders can be constructed, but their application in multicenter integrals is clearly more difficult than the application of their integral order counterparts. Convolution integrals for overlap and Coulomb integrals with integral orders are remarkably simple and therefore computationally attractive. In some cases, expressions for integrals of B functions with nonintegral orders can be obtained by substituting n → ν + 1/2 in the corresponding expressions with integral orders. However, in some practically important cases, explicit expressions for multicenter integrals with nonintegral orders cannot be constructed. In particular, complicated multicenter integrals, whose evaluation requires multidimensional quadrature in combination with powerful nonlinear convergence acceleration techniques, cannot be done in the case of B functions with nonintegral orders." @default.
- W3202675072 created "2021-10-11" @default.
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- W3202675072 date "2021-01-01" @default.
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- W3202675072 title "Are B functions with nonintegral orders a computationally useful basis set?" @default.
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- W3202675072 doi "https://doi.org/10.1016/bs.aiq.2021.06.002" @default.
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