Translations of fields represented by spherical-harmonic expansions for molecular calculations

Steinborn, E. Otto; Filter, Eckhard

doi:10.1007/bf00963465

Cited by 48 publications

(8 citation statements)

References 7 publications

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“…269 -270], many authors had quite a few problems with the determination of explicit expressions for the coefficients of the expansion of Gegenbauer polynomials in terms of Legendre polynomials. Also Steinborn and Filter constructed very messy expressions for these coefficients which are restricted to certain superscripts of the Gegenbauer polynomial [181,Section 3]. This is somewhat strange because already at that time a much more convenient expression for these expansion coefficients had been available in the mathematical literature.…”

Section: The Transformation Of One-range To Two-range Addition Theoremsmentioning

confidence: 99%

On the mathematical nature of Guseinov’s rearranged one-range addition theorems for Slater-type functions

Weniger

2011

J Math Chem

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Starting from one-range addition theorems for Slater-type functions, which are expansion in terms of complete and orthonormal functions based on the generalized Laguerre polynomials, Guseinov constructed addition theorems that are expansions in terms of Slater-type functions with a common scaling parameter and integral principal quantum numbers. This was accomplished by expressing the complete and orthonormal Laguerre-type functions as finite linear combinations of Slater-type functions and by rearranging the order of the nested summations. Essentially, this corresponds to the transformation of a Laguerre expansion, which in general only converges in the mean, to a power series, which converges pointwise. Such a transformation is not necessarily legitimate, and this contribution discusses in detail the difference between truncated expansions and the infinite series that result in the absence of truncation.

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Section: The Transformation Of One-range To Two-range Addition Theoremsmentioning

confidence: 99%

On the mathematical nature of Guseinov’s rearranged one-range addition theorems for Slater-type functions

Weniger

2011

J Math Chem

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Section: The Gegenbauer Addition Theorem Of Reduced Bessel Functionsmentioning

confidence: 99%

The strange history of B functions or how theoretical chemists and mathematicians do (not) interact

Weniger

2009

Int J of Quantum Chemistry

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B functions are a class of relatively complicated exponentially decaying basis functions. Because the molecular multicenter integrals of the much simpler Slater-type functions are notoriously difficult, it is not at all obvious why B functions should offer any advantages. However, B functions have Fourier transforms of exceptional simplicity, which greatly simplifies many of their molecular multicenter integrals. This article discusses the historical development of B functions from the perspective of the interaction between mathematics and theoretical chemistry, which traditionally has not been very good. Nevertheless, future progress in theoretical chemistry depends very much on a fertile interaction with neighboring disciplines.

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“…The Fourier transform approach uses the B ‐functions with a compact Fourier transform introduced by Shavitt 21 and developed for molecular calculations by Steinborn and Filter and coworkers 22–24. Weniger has pointed out that all the ETOs may be related mathematically to B ‐functions defined as follows 2: with the reduced Bessel functions of half‐integer order, $\hat{k}$ n +1/2 (α r ).…”

Section: Strategy For Molecular Structure Calculations Over Etosmentioning

confidence: 99%

“…The Fourier transform approach was used by Prosser and Blanchard in 1962 26 for the evaluation of two‐center integrals and applied to multi‐center integrals over B ‐functions by Filter and Steinborn in 1978 22. Related work was carried out by Szondy 27.…”

Section: Strategy For Molecular Structure Calculations Over Etosmentioning

confidence: 99%

Choice of atomic orbitals to evaluate sensitive properties of molecules: An example of NMR chemical shifts

Hoggan¹

2004

Int J of Quantum Chemistry

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Now ab initio or density functional theory (DFT) molecular property calculations over a Slater-type orbital basis are available in several software packages. In this work, the relative merits of various exponential-type orbitals (ETOs) are investigated for solving problems of interest to nuclear magnetic resonance (NMR), while showing how they are related mathematically. The preferred ETOs will be shown to be the hydrogenic orbitals and similar Coulomb Sturmians. Slater-type functions (STFs) will be compared with them, and suitable equivalent (seldom used) combinations given. The correct shielding of the nucleus, resulting from radial factors of hydrogenic orbitals, is finally shown to be essential in the evaluation of precise nuclear shielding tensors for NMR spectroscopy of molecules using ab initio or DFT methods.

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Translations of fields represented by spherical-harmonic expansions for molecular calculations

Cited by 48 publications

References 7 publications

On the mathematical nature of Guseinov’s rearranged one-range addition theorems for Slater-type functions

On the mathematical nature of Guseinov’s rearranged one-range addition theorems for Slater-type functions

The strange history of B functions or how theoretical chemists and mathematicians do (not) interact

Choice of atomic orbitals to evaluate sensitive properties of molecules: An example of NMR chemical shifts

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