A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals

Dale J. Igram; Jason W. Ribblett; Eric R. Hedin; Yong S. Joe

doi:doi:10.11648/j.ijctc.20150301.11

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A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals

Dale J. Igram, Jason W. Ribblett, Eric R. Hedin, Yong S. Joe

Published in International Journal of Computational and Theoretical Chemistry (Volume 3, Issue 1)

Received: 23 February 2015 Accepted: 3 April 2015 Published: 14 April 2015

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Abstract

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.

Published in	International Journal of Computational and Theoretical Chemistry (Volume 3, Issue 1)
DOI	10.11648/j.ijctc.20150301.11
Page(s)	1-5
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Molecular Orbital Theory, Bond Integral, Overlap Integral, Atomic Orbitals, Carbon Dimer

References

[1]	A. Streitwieser, ‘Molecular Orbital Theory for Organic Chemists’, John Wiley & Sons, Inc., New York, New York, 1961.
[2]	P. O’D. Offenhartz, ‘Atomic and Molecular Orbital Theory’, McGraw-Hill Inc., New York, New York, 1970.
[3]	J.Lowe and K.A. Peterson, ‘Quantum Chemistry’, 3rdedn, Elsevier Academic Press, Burlington, Massachusetts, 2006.
[4]	D.J. Igram, Master of Science Thesis, Ball State University, 2014.
[5]	R.S. Mulliken, Journal of Physical Chemistry, vol. 56, 1952, pp. 295.
[6]	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.
[7]	J. Daintith, ‘Oxford Dictionary of Chemistry’, Oxford University Press, New York, New York, 2004.
[8]	R.S. Mulliken, C.A. Rieke, D. Orloff, and H. Orloff, Journal of Chemical Physics, vol. 17, 1949, pp. 1248.
[9]	N. Rosen, Physical Review, vol. 38, 1931, pp. 255.
[10]	K.K. Irikura, Journal of Physical Chemistry Reference Data, Vol. 36, No. 2, 2007, pp. 389.
[11]	F. Kamijo, Astronomical Society of Japan, vol. 12, 1960, pp. 420.
[12]	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.
[13]	R.L. Liboff, ‘Introductory Quantum Mechanics’, Addison Wesley, San Francisco, California, 2003.
[14]	E. Clementi, American Astronomical Society provided by the NASA Astrophysics Data System, 1960, pp. 898.

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APA Style

Dale J. Igram, Jason W. Ribblett, Eric R. Hedin, Yong S. Joe. (2015). A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals. International Journal of Computational and Theoretical Chemistry, 3(1), 1-5. https://doi.org/10.11648/j.ijctc.20150301.11

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ACS Style

Dale J. Igram; Jason W. Ribblett; Eric R. Hedin; Yong S. Joe. A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals. Int. J. Comput. Theor. Chem. 2015, 3(1), 1-5. doi: 10.11648/j.ijctc.20150301.11

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AMA Style

Dale J. Igram, Jason W. Ribblett, Eric R. Hedin, Yong S. Joe. A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals. Int J Comput Theor Chem. 2015;3(1):1-5. doi: 10.11648/j.ijctc.20150301.11

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@article{10.11648/j.ijctc.20150301.11,
  author = {Dale J. Igram and Jason W. Ribblett and Eric R. Hedin and Yong S. Joe},
  title = {A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals},
  journal = {International Journal of Computational and Theoretical Chemistry},
  volume = {3},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ijctc.20150301.11},
  url = {https://doi.org/10.11648/j.ijctc.20150301.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijctc.20150301.11},
  abstract = {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.},
 year = {2015}
}

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TY  - JOUR
T1  - A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals
AU  - Dale J. Igram
AU  - Jason W. Ribblett
AU  - Eric R. Hedin
AU  - Yong S. Joe
Y1  - 2015/04/14
PY  - 2015
N1  - https://doi.org/10.11648/j.ijctc.20150301.11
DO  - 10.11648/j.ijctc.20150301.11
T2  - International Journal of Computational and Theoretical Chemistry
JF  - International Journal of Computational and Theoretical Chemistry
JO  - International Journal of Computational and Theoretical Chemistry
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2376-7308
UR  - https://doi.org/10.11648/j.ijctc.20150301.11
AB  - 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.
VL  - 3
IS  - 1
ER  -

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Author Information

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

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Plain Text BibTeX RIS

APA Style

Dale J. Igram, Jason W. Ribblett, Eric R. Hedin, Yong S. Joe. (2015). A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals. International Journal of Computational and Theoretical Chemistry, 3(1), 1-5. https://doi.org/10.11648/j.ijctc.20150301.11

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ACS Style

Dale J. Igram; Jason W. Ribblett; Eric R. Hedin; Yong S. Joe. A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals. Int. J. Comput. Theor. Chem. 2015, 3(1), 1-5. doi: 10.11648/j.ijctc.20150301.11

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AMA Style

Dale J. Igram, Jason W. Ribblett, Eric R. Hedin, Yong S. Joe. A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals. Int J Comput Theor Chem. 2015;3(1):1-5. doi: 10.11648/j.ijctc.20150301.11

Copy | Download

@article{10.11648/j.ijctc.20150301.11,
  author = {Dale J. Igram and Jason W. Ribblett and Eric R. Hedin and Yong S. Joe},
  title = {A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals},
  journal = {International Journal of Computational and Theoretical Chemistry},
  volume = {3},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ijctc.20150301.11},
  url = {https://doi.org/10.11648/j.ijctc.20150301.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijctc.20150301.11},
  abstract = {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.},
 year = {2015}
}

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TY  - JOUR
T1  - A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals
AU  - Dale J. Igram
AU  - Jason W. Ribblett
AU  - Eric R. Hedin
AU  - Yong S. Joe
Y1  - 2015/04/14
PY  - 2015
N1  - https://doi.org/10.11648/j.ijctc.20150301.11
DO  - 10.11648/j.ijctc.20150301.11
T2  - International Journal of Computational and Theoretical Chemistry
JF  - International Journal of Computational and Theoretical Chemistry
JO  - International Journal of Computational and Theoretical Chemistry
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2376-7308
UR  - https://doi.org/10.11648/j.ijctc.20150301.11
AB  - 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.
VL  - 3
IS  - 1
ER  -

Copy | Download