The Spherical Tensor Gradient Operator

Weniger, Ernst Joachim

doi:10.1135/cccc20051225

Cited by 31 publications

(48 citation statements)

References 127 publications

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“…solid-harmonics maximally lowers their angular momentum [17], and thus they are closed under differentiation. The solid-harmonic addition theorem extends the product rule of differentiation to these differential operators [16].…”

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confidence: 99%

Efficient quantum-chemical geometry optimization and the structure of large icosahedral fullerenes

Dunlap

Zope

2006

Chemical Physics Letters

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Geometry optimization is efficient using generalized Gaunt coefficients, which significantly limit the amount of cross differentiation for multi-center integrals of highangular-momentum solid-harmonic basis sets. The geometries of the most stable C 240 , C 540 , C 960 , C 1500 , and C 2160 icosahedral fullerenes are optimized using analytic densityfunctional theory (ADFT), which is parameterized to give the experimental geometry of C 60 . The calculations are all electron, the orbital basis set includes d functions and the exchange-correlation-potential basis set includes f functions. The largest calculation on C 2160 employed about 39000 basis functions.

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confidence: 99%

Efficient quantum-chemical geometry optimization and the structure of large icosahedral fullerenes

Dunlap

Zope

2006

Chemical Physics Letters

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“…In analogy, the differentials present in Eq. (13) are rewritten as (16) where ∇ Q is the gradient operator andẐ lm (∇ Q ) are the (real) spherical harmonic gradient operators [111]. Heuristically, they are obtained by taking an explicit expression for Z lm (r) and replacing all Cartesian coordinates with the corresponding differentials.…”

Section: A Generalised Mcmurchie-davidson Schemementioning

confidence: 99%

Calculation of Araki-Sucher correction for many-electron systems

2017

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In this paper we consider the evaluation of the Araki-Sucher correction for arbitrary many-electron atomic and molecular systems. This contribution appears in the leading order quantum electrodynamics corrections to the energy of a bound state. The conventional one-electron basis set of Gaussian-type orbitals (GTOs) is adopted; this leads to two-electron matrix elements which are evaluated with help of generalised the McMurchie-Davidson scheme. We also consider the convergence of the results towards the complete basis set. A rigorous analytic result for the convergence rate is obtained and verified by comparing with independent numerical values for the helium atom. Finally, we present a selection of numerical examples and compare our results with the available reference data for small systems. In contrast with other methods used for the evaluation of the Araki-Sucher correction, our method is not restricted to few-electron atoms or molecules. This is illustrated by calculations for several many-electron atoms and molecules.

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“…Detailed discussions of the mathematical properties of reduced Bessel functions and of their anisotropic generalizations can be found in ]. Furthermore, B functions have much more appealing properties applicable to multi-center integral problems, compared to other exponentially decaying functions [Filter & Steinborn (1978a;b); Steinborn & Filter (1975);Weniger (2005); Weniger & Steinborn (1983a)]. The multi-center molecular integrals over B functions can be computed much more easily than the corresponding integrals of other exponentially decaying functions.…”

Section: Introductionmentioning

confidence: 99%

Fourier Transformation Method for Computing NMR Integrals over Exponential Type Functions

Safouhi¹

2012

Fourier Transform - Materials Analysis

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The Spherical Tensor Gradient Operator

Cited by 31 publications

References 127 publications

Efficient quantum-chemical geometry optimization and the structure of large icosahedral fullerenes

Efficient quantum-chemical geometry optimization and the structure of large icosahedral fullerenes

Calculation of Araki-Sucher correction for many-electron systems

Fourier Transformation Method for Computing NMR Integrals over Exponential Type Functions

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