Fourier transform of a two-center product of exponential-type orbitals. Application to one- and two-electron multicenter integrals

Trivedi, Harit P.; Steinborn, E. Otto

doi:10.1103/physreva.27.670

Cited by 127 publications

(92 citation statements)

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“…Whereas the Fourier transform of a two-center product of GTOS is rather simple (being itself mainly a Gaussian), the Fourier transform of a two-center product of ETOS is a *Dedicated to Professor K. Ruedenberg on the occasion of his 70th birthday. has proven to be a very successful method to obtain both compact analytical expressions and efficient numerical programs for the evaluation of the Fourier transform of a two-center product of ETOS. As a generalization of earlier work for STOS [4,13-151, Trivedi and Steinborn [5] derived a compact one-dimensional integral representation for the Fourier transform of a two-center product of B functions, valid for all quantum numbers and capable of an angular momentum decomposition [5]. The B functions [16] are the ETOS with the most simple Fourier transform [17].…”

Section: Introductionmentioning

confidence: 99%

Improved quadrature methods for the Fourier transform of a two‐center product of exponential‐type basis functions

Homeier

Steinborn

1992

Int J of Quantum Chemistry

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The numerical properties of a one-dimensional integral representation [H. P. Trivedi and E. 0. Steinborn, Phys. Rev. A 27, 670 (19S3)] for the Fourier transform of a two-center product of certain exponential-type orbitals (ETOS), the B functions [E. Filter and E. 0. Steinborn, Phys. Rev. A 18, 1 (1978)], are examined. These functions span the space of ETOS. Hence, molecular integrals for other ETOS, like the more common Slater-type orbitals, may be found as finite linear combinations of integrals with B functions. The main advantage of B functions is the simplicity of their Fourier transform that makes the derivation of relatively simple general formulas for molecular integrals with the Fourier transform method possible. The integrand of the integral representation mentioned above shows sharp peaks, making, in the cases of highly asymmetric charge distributions and/or large momentum vectors, usual quadrature methods rather slow. New quadrature schemes are presented that utilize Mobius-transformation-based quadrature rules. These rules are well suited for the numerical quadrature of functions possessing a sharp peak at or near one boundary of integration [H. H. H. Homeier and E. 0. Steinborn, J. Comput. Phys. 87, 61 (1990)l. Numerical results are presented that illustrate the fact that the new quadrature schemes are much more efficient than are automatic quadrature routines.

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Section: Introductionmentioning

confidence: 99%

Improved quadrature methods for the Fourier transform of a two‐center product of exponential‐type basis functions

Homeier

Steinborn

1992

Int J of Quantum Chemistry

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“…Equation (11) led to analytical expressions for all molecular multi-center integrals over B functions or STFs [Grotendorst & Steinborn (1988); Safouhi (2001a); Trivedi & Steinborn (1983)]. …”

Section: Fourier Transform In Molecular Multi-center Integrals Calculmentioning

confidence: 99%

“…In [Trivedi & Steinborn (1983)], the Fourier transform method is used in combination with equation (6) to derive analytic expressions for the following integrals:…”

Section: Fourier Transform In Molecular Multi-center Integrals Calculmentioning

confidence: 99%

“…Moreover, the Fourier transforms of STFs, of hydrogen eigenfunctions, or of other functions based on the generalized Laguerre polynomials can all be expressed as finite linear combinations of Fourier transforms of B functions [Weniger (1985); Weniger & Steinborn (1983b)]. The basis set of B functions is well adapted to the Fourier transform method [Geller (1962); Grotendorst & Steinborn (1988); Prosser & Blanchard (1962); Trivedi & Steinborn (1983)], which allowed analytic expressions to be developed for molecular multi-center integrals over B functions [Grotendorst & Steinborn (1988); Trivedi & Steinborn (1983)]. …”

Section: Introductionmentioning

confidence: 99%

“…Using the analytic expression (11) obtained by Trivedi and Steinborn [Trivedi & Steinborn (1983)] for the integrals over r j involved in equation (42) and equation (43), one can derive the following analytic expression for the integrals BÎ αβ 23 [Berlu & Safouhi (2008)]:…”

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See 2 more Smart Citations

Fourier Transformation Method for Computing NMR Integrals over Exponential Type Functions

Safouhi¹

2012

Fourier Transform - Materials Analysis

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Calculation of the one-electron two-center integrals over Slater-type orbitals by means of the ellipsoidal coordinates method

Mekelleche

Baba-Ahmed

1997

Int. J. Quant. Chem.

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A method for the calculation of one-electron two-center integrals is described. Using an ellipsoidal coordinate system, both the overlap, kinetic energy, and nuclear attraction integrals are expressed in terms of the so-called sigma function w introduced by Baba-Ahmed et al. A. Baba-Ahmed and J. Gayoso, Int. J. Quant. Chem. 23, Ž .Ž .x 71 1983 , Eq. 51 and which is easily programmed for a computer. The present investigation offers an advantage in that general formulas are derived which facilitate computation of the overlap and related two-center integrals over all Slater-type orbitals Ž . STOs with eventual nonintegral values of the principal quantum number. The proposed w algorithm permits to avoid the procedure of interpolation A. Baba-Ahmed and J.Ž .x Gayoso, Theor. Chim. Acta, 62, 507 1983 , Eqs. 11᎐14 used to overcome the difficulty introduced by the presence of nonintegral quantum numbers. Finally, numerical aspects of the proposed algorithm are analyzed and comparisons with other approaches are given.

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Fourier transform of a two-center product of exponential-type orbitals. Application to one- and two-electron multicenter integrals

Cited by 127 publications

References 20 publications

Improved quadrature methods for the Fourier transform of a two‐center product of exponential‐type basis functions

Improved quadrature methods for the Fourier transform of a two‐center product of exponential‐type basis functions

Fourier Transformation Method for Computing NMR Integrals over Exponential Type Functions

Calculation of the one-electron two-center integrals over Slater-type orbitals by means of the ellipsoidal coordinates method

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