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Molecules with tetrahedral and octahedral symmetry

II. Energy calculations and molecular constants for methane, silane and germane

Published online by Cambridge University Press:  24 October 2008

R. A. Ballinger  and
N. H. March
R. A. Ballinger
Affiliation:
Department of PhysicsThe UniversitySheffield
N. H. March
Affiliation:
Department of PhysicsThe UniversitySheffield
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Abstract

Detailed energy calculations for CH4, SiH4 and GeH4 have been carried out using the Thomas-Fermi approximation together with a nuclear field which is averaged over all orientations about the central nucleus. The energy, including exchange, has been calculated using the unmodified Thomas-Fermi electron densities as variation functions, and in this way bond lengths and force constants for the three molecules have been obtained. The effect of exchange is very marked, agreement with experiment being quite reasonable when it is included in this way.

In order to test the accuracy of this procedure, a scale factor has been introduced and used as a variational parameter. In this refined approximation, calculations have been made for SiH4, thus enabling improved charge distributions to be obtained. Energy curves are also presented for this molecule, showing separately the variations of kinetic, potential and exchange energies with internuclear distance. It is shown that whilst the scale factor has an appreciable effect on the separate energy curves, the total energy is virtually unchanged.

Finally, the reason why the exchange energy is of considerable importance in the theory is briefly discussed, and some observations are made concerning the rather abnormal bonding in GeH4.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 3 , July 1955 , pp. 504 - 516
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

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