Unified treatment of one-range addition theorems for integer and non-integer n-STO, -GTO and -generalized exponential type orbitals with hyperbolic cosine in position, momentum and four-dimensional spaces

doi:10.1088/1674-1056/21/9/093101

中国物理B ›› 2012, Vol. 21 ›› Issue (9): 93101-093101.doi: 10.1088/1674-1056/21/9/093101

• ATOMIC AND MOLECULAR PHYSICS • 上一篇下一篇

Unified treatment of one-range addition theorems for integer and non-integer n-STO, -GTO and -generalized exponential type orbitals with hyperbolic cosine in position, momentum and four-dimensional spaces

I. I. Guseinov

Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University, Canakkale, Turkey

收稿日期:2012-01-06 修回日期:2012-02-13 出版日期:2012-08-01 发布日期:2012-08-01

Unified treatment of one-range addition theorems for integer and non-integer n-STO, -GTO and -generalized exponential type orbitals with hyperbolic cosine in position, momentum and four-dimensional spaces

I. I. Guseinov

Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University, Canakkale, Turkey

Received:2012-01-06 Revised:2012-02-13 Online:2012-08-01 Published:2012-08-01
Contact: I. I. Guseinov E-mail:isguseinov@yahoo.com

摘要/Abstract

摘要： The simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized exponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine (GETO HC, GMSO HC, and GHSH HC) in position, momentum and four-dimensional spaces, respectively. The final results are expressed in terms of one-range addition theorems of complete orthonormal sets of ψ ^α -exponential type orbitals, φ ^α -momentum space orbitals and z^α -hyperspherical harmonics. We notice that the one-range addition theorems for integer and noninteger n-Slater type orbitals and Gaussian type orbitals in position, momentum and four dimensional spaces are the special cases of GETO HC, GMSO HC, and GHSH HC. The theorems presented can be useful in the accurate study of electronic structure of atomic and molecular systems.

关键词: electronic structure, generalized exponential type orbitals, one-range addition theorems, Hartree-Fock-Roothaan equations

Abstract: The simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized exponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine (GETO HC, GMSO HC, and GHSH HC) in position, momentum and four-dimensional spaces, respectively. The final results are expressed in terms of one-range addition theorems of complete orthonormal sets of ψ ^α -exponential type orbitals, φ ^α -momentum space orbitals and z^α -hyperspherical harmonics. We notice that the one-range addition theorems for integer and noninteger n-Slater type orbitals and Gaussian type orbitals in position, momentum and four dimensional spaces are the special cases of GETO HC, GMSO HC, and GHSH HC. The theorems presented can be useful in the accurate study of electronic structure of atomic and molecular systems.

Key words: electronic structure, generalized exponential type orbitals, one-range addition theorems, Hartree-Fock-Roothaan equations

中图分类号: (Theory of electronic structure, electronic transitions, and chemical binding)

31.10.+z

31.15.-p (Calculations and mathematical techniques in atomic and molecular physics) 02.70.-c (Computational techniques; simulations)

I. I. Guseinov . Unified treatment of one-range addition theorems for integer and non-integer n-STO, -GTO and -generalized exponential type orbitals with hyperbolic cosine in position, momentum and four-dimensional spaces[J]. 中国物理B, 2012, 21(9): 93101-093101.

I. I. Guseinov. Unified treatment of one-range addition theorems for integer and non-integer n-STO, -GTO and -generalized exponential type orbitals with hyperbolic cosine in position, momentum and four-dimensional spaces[J]. Chin. Phys. B, 2012, 21(9): 93101-093101.

参考文献 21

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Unified treatment of one-range addition theorems for integer and non-integer n-STO, -GTO and -generalized exponential type orbitals with hyperbolic cosine in position, momentum and four-dimensional spaces

Unified treatment of one-range addition theorems for integer and non-integer n-STO, -GTO and -generalized exponential type orbitals with hyperbolic cosine in position, momentum and four-dimensional spaces

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