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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 |
| I. I. Guseinov |
| Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University, Canakkale, Turkey |
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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 zα -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.
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Received: 06 January 2012
Revised: 13 February 2012
Accepted manuscript online:
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PACS:
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31.10.+z
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(Theory of electronic structure, electronic transitions, and chemical binding)
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31.15.-p
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(Calculations and mathematical techniques in atomic and molecular physics)
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02.70.-c
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(Computational techniques; simulations)
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Corresponding Authors:
I. I. Guseinov
E-mail: isguseinov@yahoo.com
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Cite this article:
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 2012 Chin. Phys. B 21 093101
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