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

Steinborn, E. Otto; Filter, Eckhard

doi:10.1007/bf00963467

Cited by 111 publications

(32 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An expansion of a function in terms of Gegenbauer polynomials can be transformed into an expansion of the same function in a series Legendre polynomials. If these are expressed by spherical harmonics use can be made of orthogonality relations and other theorems supplied in the theory of angular momentum [55]. Hence, one has to be very careful if in a given EMM integrals with multicenter one, which replaces some physical coefficients and a new function, which contains radial integrals and spherical harmonics.…”

Section: Discussionmentioning

confidence: 99%

Calculation of electric multipole moment integrals with the different screening parameters via the Fourier transform method

Yükçü

Şenlik

Öztekin

2011

Int J of Quantum Chemistry

View full text Add to dashboard Cite

Three-center electric multipole moment integrals over Slater-type orbitals (STOs) can be evaluated by translating the orbitals on one center to the other and reducing the system to an expansion of two-center integrals. These are then evaluated using Fourier transforms. The resulting expression depends on the overlap integrals that can be evaluated with the greatest ease. They involve expressions for STO with different screening parameters that are known analytically. This work gives the overall expressions analytically in a compact form, based on Gegenbauer polynomials.

show abstract

Section: Discussionmentioning

confidence: 99%

Calculation of electric multipole moment integrals with the different screening parameters via the Fourier transform method

Yükçü

Şenlik

Öztekin

2011

Int J of Quantum Chemistry

View full text Add to dashboard Cite

show abstract

“…where the reduced Bessel functionk n−1/2 (ζ r) is defined by [4,5] k n−1/2 (ζ r) = 2 π (ζ r) n−1/2 K n−1/2 (ζ r)…”

Section: General Definitionsmentioning

confidence: 99%

“…Previous workers have defined its relationship to the Slater-type atomic orbital basis [5,7]. The advantage of B functions is that they possess a very compact analytical expression for their Fourier transform [8,9].…”

Section: Introductionmentioning

confidence: 99%

New method of rapid and accurate evaluation for multicenter bielectronic integrals over B functions

Safouhi¹,

Hoggan²

2000

Int. J. Quantum Chem.

View full text Add to dashboard Cite

“…These integrals, of which are required many millions even for the smallest molecules, are the only troubling computation in three‐center nuclear attraction integrals formulated over the physically better motivated exponential type functions (ETFs). In the present work, we use B functions 9–11 as a basis set of atomic orbitals, taking advantage of the exceptional simplicity of their Fourier transform 12, 13. These B functions are the most suitable when employing the Fourier transform method 14–17, which allowed analytic expressions to be developed for molecular multicenter integrals 16, 17.…”

Section: Introductionmentioning

confidence: 99%

The S and G transformations for computing three‐center nuclear attraction integrals

Slevinsky

Safouhi

2009

Int J of Quantum Chemistry

View full text Add to dashboard Cite

It is now well established that nonlinear transformations can be extremely useful in the case of oscillatory integrals. In previous work, we could show that the G transformation, which is not so well known among those interested in the numerical evaluation of highly oscillatory integrals, works very well for the extremely challenging integral called Twisted Tail. In this work, we demonstrate that these techniques also apply to three-center nuclear attraction integrals over exponential type functions. The accurate and rapid evaluation of these integrals is required in ab initio molecular structure calculations and density functional theory. Using a basis set of B functions and profiting from their relatively simple Fourier representation, these integrals are formulated as analytical expressions involving highly oscillatory spherical Bessel integral functions. In the present work, we implement two highly accurate algorithms for three-center nuclear attraction integrals. The first algorithm is based on the G transformation and the second is based on a combination of the S and G transformations. The application of these transformations is largely due to the properties of special functions that allow the computation of higher order derivatives of the integrands with exceptional simplicity. The numerical results illustrate the accuracy of these algorithms applied to three-center nuclear attraction integrals over exponential type functions with a miscellany of different parameters.

show abstract

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

Cited by 111 publications

References 13 publications

Calculation of electric multipole moment integrals with the different screening parameters via the Fourier transform method

Calculation of electric multipole moment integrals with the different screening parameters via the Fourier transform method

New method of rapid and accurate evaluation for multicenter bielectronic integrals over B functions

The S and G transformations for computing three‐center nuclear attraction integrals

Contact Info

Product

Resources

About