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Momentum distribution in molecular systems

Part V. Momentum distribution and the shape of the Compton line for CH4, C2H6, C2H4 and C2H2

Published online by Cambridge University Press:  24 October 2008

W. E. Duncanson  and
C. A. Coulson
W. E. Duncanson
Affiliation:
University CollegeLondonc/o University College of North WalesBangor
C. A. Coulson
Affiliation:
University CollegeDundee
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Extract

Theoretical calculations on the mean radial momentum distribution of the electrons are made for the molecules CH4, C2H6, C2H4 and C2H2; from these distributions the profiles of the Compton line are deduced. It is assumed that each electron acts as a single scattering centre so that the mean radial distribution for the molecule is just the sum of the various “partial distributions” for each electron separately. The electrons are supposed to be paired together in the formation of localized bonds, and the contributions from each type of bond have to be separately determined. When superposed, these give the momentum distribution for the whole molecule. Such distributions are similar in shape, but the peak value of the momentum curves moves to higher values of p as the C—C bond becomes more saturated.

A comparison of the various partial distributions for C2H4 shows that the C—H bond is an important factor in the momentum distribution of such molecules. In other hydrocarbon molecules, we may presume that the proportion of C—H bonds will be very significant in determining the breadth of the momentum distribution curve, and hence of the width of the Compton line; in fact the half-width of the Compton line decreases both with an increase in the number of the C—H bonds, and with increased saturation of the C—C bonds.

In the only case where experimental results are available, CH4, the discrepancy between theory and experiment amounts to about 30%. Reasons for this discrepancy are discussed; in part the discrepancy may be attributed to the approximations used in the wave functions; but reasons are given for supposing that in part also it arises from an incorrect interpretation of the experimental results.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 37 , Issue 4 , October 1941 , pp. 406 - 421
Copyright
Copyright © Cambridge Philosophical Society 1941

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References

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