A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals
International Journal of Computational and Theoretical Chemistry
Volume 3, Issue 1, January 2015, Pages: 1-5
Received: Feb. 23, 2015;
Accepted: Apr. 3, 2015;
Published: Apr. 14, 2015
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Dale J. Igram, Center for Computational Nanoscience, Department of Physics and Astronomy, Ball State University, Muncie, USA
Jason W. Ribblett, Department of Chemistry, Ball State University, Muncie, USA
Eric R. Hedin, Center for Computational Nanoscience, Department of Physics and Astronomy, Ball State University, Muncie, USA
Yong S. Joe, Center for Computational Nanoscience, Department of Physics and Astronomy, Ball State University, Muncie, USA
In molecular orbital theory, the bond integral parameter k is used to calculate the bond integral β for different molecular structures. The bond integral parameter k, which represents the ratio of bond integrals between two atoms of a diatomic molecule, is a function of the bond length. This parameter is usually obtained empirically; however, it will be shown that k can be determined analytically by utilizing the overlap integral S. k will be calculated for different atomic orbital combinations (ss,pp) of σ and π interactions as a function of bond length for a carbon-carbon diatomic molecule. The results, which are represented graphically, indicate that different atomic orbitals in different interactions can have the same, or very close to the same, k values. The graphs reveal some significant features for the different atomic orbital combinations with respect to magnitude and profile, as well as illustrate good agreement with experimental results, which validates the utilization of the overlap integral calculation method for the determination of the bond integral parameter k.
Dale J. Igram,
Jason W. Ribblett,
Eric R. Hedin,
Yong S. Joe,
A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals, International Journal of Computational and Theoretical Chemistry.
Vol. 3, No. 1,
2015, pp. 1-5.
A. Streitwieser, ‘Molecular Orbital Theory for Organic Chemists’, John Wiley & Sons, Inc., New York, New York, 1961.
P. O’D. Offenhartz, ‘Atomic and Molecular Orbital Theory’, McGraw-Hill Inc., New York, New York, 1970.
J.Lowe and K.A. Peterson, ‘Quantum Chemistry’, 3rdedn, Elsevier Academic Press, Burlington, Massachusetts, 2006.
D.J. Igram, Master of Science Thesis, Ball State University, 2014.
R.S. Mulliken, Journal of Physical Chemistry, vol. 56, 1952, pp. 295.
M. Orchin, R.S. Macomber, A. Pinhas, and R.M. Wilson, ‘The Vocabulary and Concepts of Organic Chemistry’, John Wiley & Sons, Inc., New York, New York, 2005.
J. Daintith, ‘Oxford Dictionary of Chemistry’, Oxford University Press, New York, New York, 2004.
R.S. Mulliken, C.A. Rieke, D. Orloff, and H. Orloff, Journal of Chemical Physics, vol. 17, 1949, pp. 1248.
N. Rosen, Physical Review, vol. 38, 1931, pp. 255.
K.K. Irikura, Journal of Physical Chemistry Reference Data, Vol. 36, No. 2, 2007, pp. 389.
F. Kamijo, Astronomical Society of Japan, vol. 12, 1960, pp. 420.
B.H. Bransden and C.J. Joachain, ‘Introduction to Quantum Mechanics’, Longman Scientific & Technical, Copublished in the United States with John Wiley & Sons, Inc., New York, New York, 1989.
R.L. Liboff, ‘Introductory Quantum Mechanics’, Addison Wesley, San Francisco, California, 2003.
E. Clementi, American Astronomical Society provided by the NASA Astrophysics Data System, 1960, pp. 898.