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Chin. Phys. B, 2012, Vol. 21(9): 093101    DOI: 10.1088/1674-1056/21/9/093101
ATOMIC AND MOLECULAR PHYSICS Prev   Next  

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
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.
Keywords:  electronic structure      generalized exponential type orbitals      one-range addition theorems      Hartree-Fock-Roothaan equations  
Received:  06 January 2012      Revised:  13 February 2012      Accepted manuscript online: 
PACS:  31.10.+z (Theory of electronic structure, electronic transitions, and chemical binding)  
  31.15.-p (Calculations and mathematical techniques in atomic and molecular physics)  
  02.70.-c (Computational techniques; simulations)  
Corresponding Authors:  I. I. Guseinov     E-mail:  isguseinov@yahoo.com

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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