Calculation of multicentre nuclear attraction integrals over Slater-type orbitals using unsymmetrical one-range addition theorems

doi:10.1088/1674-1056/19/4/043101

中国物理B ›› 2010, Vol. 19 ›› Issue (4): 43101-043101.doi: 10.1088/1674-1056/19/4/043101

Calculation of multicentre nuclear attraction integrals over Slater-type orbitals using unsymmetrical one-range addition theorems

Israfil I. Guseinov¹, N. Seckin Gorgun², Nimet Zaim²

(1)Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University, Çanakkale, Turkey; (2)Department of Physics, Faculty of Arts and Sciences, Trakya University, Edirne, Turkey

收稿日期:2009-05-25 修回日期:2009-07-27 出版日期:2010-04-15 发布日期:2010-04-15

Calculation of multicentre nuclear attraction integrals over Slater-type orbitals using unsymmetrical one-range addition theorems

Israfil I. Guseinov^a), N. Seckin Gorgun^b), and Nimet Zaim^b)

^a Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University, ?anakkale, Turkey; ^b Department of Physics, Faculty of Arts and Sciences, Trakya University, Edirne, Turkey

Received:2009-05-25 Revised:2009-07-27 Online:2010-04-15 Published:2010-04-15

摘要/Abstract

摘要： Using the unsymmetrical one-range addition theorems introduced by one of the authors with the help of complete orthonormal sets of $\varPsi ^\alpha $-exponential type orbitals ($\alpha = 1,0, - 1, - 2,...)$, this paper presents the sets of series expansion relations for multicentre nuclear attraction integrals over Slater-type orbitals arising in Hartree--Fock--Roothaan equations for molecules. The final results are expressed through multicentre charge density expansion coefficients and basic integrals. The convergence of the series is tested by calculating concrete cases for arbitrary values of parameters of orbitals.

Abstract: Using the unsymmetrical one-range addition theorems introduced by one of the authors with the help of complete orthonormal sets of $\varPsi ^\alpha $-exponential type orbitals ($\alpha = 1,0, - 1, - 2,...)$, this paper presents the sets of series expansion relations for multicentre nuclear attraction integrals over Slater-type orbitals arising in Hartree--Fock--Roothaan equations for molecules. The final results are expressed through multicentre charge density expansion coefficients and basic integrals. The convergence of the series is tested by calculating concrete cases for arbitrary values of parameters of orbitals.

Key words: Slater-type orbitals, nuclear attraction integrals, Hartree--Fock--Roothaan equations, unsymmetrical one-range addition theorems

中图分类号: (Self-consistent-field methods)

31.15.xr

Israfil I. Guseinov, N. Seckin Gorgun, Nimet Zaim. Calculation of multicentre nuclear attraction integrals over Slater-type orbitals using unsymmetrical one-range addition theorems[J]. 中国物理B, 2010, 19(4): 43101-043101.

Israfil I. Guseinov, N. Seckin Gorgun, and Nimet Zaim. Calculation of multicentre nuclear attraction integrals over Slater-type orbitals using unsymmetrical one-range addition theorems[J]. Chin. Phys. B, 2010, 19(4): 43101-043101.

参考文献 12

[1]	Roothaan C C J 1951 Rev. Mod. Phys. 23 69
[2]	Roothaan C C J 1960 Rev. Mod. Phys. 32 179
[3]	Levine I N 2000 Quantum Chemistry 5th ed. (NJ: Prentice Hall)
[4]	Boys S F 1955 Proc. Roy. Soc. Lond. A 200 542
[5]	Kato T 1957 Commun. Pure Appl. Math. 10 151
[6]	Agmon S 1982 Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of $N$-Body Schr?dinger Operators} (Princeton: Princeton University Press)
[7]	Guseinov I I 2008 J. Theor. Comput. Chem. 7 257
[8]	Guseinov I I 2002 Int. J. Quantum Chem. 90 114
[9]	Gradshteyn I S and Ryzhik I M 1980 Tables of Integrals, Sums, Series and Products 4th ed. (New York: Academic Press)
[10]	Guseinov I I 1970 J. Phys. B 3 1399
[11]	Condon E U and Shortley G H 1970 Theory of Atomic Spectra (Cambridge: Cambridge University Press)
[12]	Guseinov I I 2007 J. Math. Chem. 42 415

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Calculation of multicentre nuclear attraction integrals over Slater-type orbitals using unsymmetrical one-range addition theorems

Calculation of multicentre nuclear attraction integrals over Slater-type orbitals using unsymmetrical one-range addition theorems

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