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Journal of Mathematical Chemistry

, Volume 43, Issue 3, pp 1024–1031 | Cite as

On the unified treatment of complete orthonormal sets of functions in coordinate, momentum, and four dimensional spaces and their expansion and one-range addition theorems

  • I. I. Guseinov
Article

The new formulas have been established for the expansion and one-range addition theorems for the complete orthonormal sets of functions in coordinate, momentum, and four-dimensional spaces. These theorems enable us to derive the formulas for the overlap integrals over STOS, Ψα-ETOs, Φα-MSOs, and Z α-HSHs which can be useful in the study of different quantum mechanical problems in both the theory and practice of calculations dealing with atoms, molecules, and solids when the coordinate, momentum or four-dimensional spaces employed. This work presents the development of our previous paper (I.I. Guseinov, J. Math. Chem., (2007) DOI:  10.1007/s10910-006-9154-1).

Keywords

one-range addition theorems exponential-type orbitals momentum space orbitals hyperspherical harmonics 

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References

  1. 1.
    I.I. Guseinov, J. Math. Chem. (2007) DOI:  10.1007/s10910-006-9154-1.
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    Guseinov I.I. (2002) Int. J. Quantum Chem. 90: 114CrossRefGoogle Scholar
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    Barnett M.P. (2002) Theor. Chem. Acc. 107: 241Google Scholar
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    Guseinov I.I. (2003) J. Chem. Phys. 119: 4614CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Physics, Faculty of Arts and SciencesOnsekiz Mart UniversityCanakkaleTurkey

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