Three-centre two-electron Coulomb and hybrid integrals evaluated using nonlinear<i>D</i>- and barD-transformations

Safouhi, Hassan; Hoggan, Philip E.

doi:10.1088/0305-4470/32/34/307

Cited by 25 publications

(24 citation statements)

References 44 publications

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“…Therefore, new numerical integration techniques are required. It is shown in previous work 30–32 that the nonlinear D transformation of Sidi 33, 34 can be applied for improving convergence of the semi‐infinite integrals that occur in (21) and (22).…”

Section: Analytical and Numerical Evaluation Of Molecular Multicentermentioning

confidence: 99%

Highly accurate numerical results for three‐center nuclear attraction and two‐electron Coulomb and exchange integrals over Slater‐type functions

Safouhi

2004

Int J of Quantum Chemistry

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ABSTRACT:The present work focuses on the recent progress in nonlinear transformation methods for improving the convergence of highly oscillatory integrals and in their applications for an efficient and rapid numerical evaluation of molecular electronic integrals over Slater-type functions (STFs). The nonlinear D transformation, which is probably the most effective general approach for increasing the rate of convergence of semi-infinite oscillatory integrals, is presented. Molecular integrals over STFs are expressed as finite linear combinations of integrals over B functions. The basis set of B functions is suitable to apply the Fourier transform method, which led to analytic expressions, involving highly oscillatory functions, for molecular integrals. Efficient algorithms based on the D transformation are now developed for a numerical evaluation of molecular integrals over STFs. Numerical results that we obtained with linear and nonlinear molecules, and which are in agreement with those obtained using existing codes (Alchemy, STOP, and ADGGSTNGINT), show that the algorithms described in this work are relevant.

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Section: Analytical and Numerical Evaluation Of Molecular Multicentermentioning

confidence: 99%

Highly accurate numerical results for three‐center nuclear attraction and two‐electron Coulomb and exchange integrals over Slater‐type functions

Safouhi

2004

Int J of Quantum Chemistry

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“…(6) for I (2) and in the companion formulas for the other I (k) appear in a common, four-element structure: first, …”

Section: The Radial Termmentioning

confidence: 99%

“…here has been recent renewed interest in molecular integrals with exponential-type orbitals [1][2][3][4][5][6][7], including the use of techniques to accelerate convergence. Accordingly, we present an analysis of a class of Slater-type orbital (STO) molecular integrals, the (2-2) three-center electronelectron repulsion integrals that contain two bicentric electron distributions that share one center in common.…”

mentioning

confidence: 99%

On the computation of (2‐2) three‐center Slater‐type orbital integrals of 1/r₁₂ using Fourier‐transform‐based analytical formulas

Antolovic

Silverstone

2004

Int J of Quantum Chemistry

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ABSTRACT:We describe a computational scheme devised for using Fouriertransform-based analytic formulas for three-center integrals of r 12 Ϫ1 , wherein each electron is described by a two-center product of Slater-type orbitals. The asymptotic behavior of the auxiliary functions, which are related to modified spherical Bessel functions and to exponential integrals, is investigated, and recursive computational schemes are derived that are shown to be numerically stable for high summation indices and large internuclear distances.

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“…(29), (31), (33) and (35). We showed that FĨ ,s (x), FK ,s (x), and FH ,s (x) satisfy fourth-order linear differential equations of the form required to apply the D and D transformations [34,36,37]. The integrand FJ ,s,t (x) satisfies a sixth-order linear differential equation of the form required to apply the D and D transformations [35,37].…”

Section: Nonlinear D and D Transformationsmentioning

confidence: 99%

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

Safouhi¹,

Hoggan²

2000

Int. J. Quantum Chem.

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Three-centre two-electron Coulomb and hybrid integrals evaluated using nonlinearD- and barD-transformations

Cited by 25 publications

References 44 publications

Highly accurate numerical results for three‐center nuclear attraction and two‐electron Coulomb and exchange integrals over Slater‐type functions

Highly accurate numerical results for three‐center nuclear attraction and two‐electron Coulomb and exchange integrals over Slater‐type functions

On the computation of (2‐2) three‐center Slater‐type orbital integrals of 1/r₁₂ using Fourier‐transform‐based analytical formulas

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

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Three-centre two-electron Coulomb and hybrid integrals evaluated using nonlinearD- and barD-transformations

Cited by 25 publications

References 44 publications

Highly accurate numerical results for three‐center nuclear attraction and two‐electron Coulomb and exchange integrals over Slater‐type functions

Highly accurate numerical results for three‐center nuclear attraction and two‐electron Coulomb and exchange integrals over Slater‐type functions

On the computation of (2‐2) three‐center Slater‐type orbital integrals of 1/r12 using Fourier‐transform‐based analytical formulas

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

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On the computation of (2‐2) three‐center Slater‐type orbital integrals of 1/r₁₂ using Fourier‐transform‐based analytical formulas