234
Journal of Molecular Structure
Elsevier Publishing Company, Amsterdam. Printed in the Netherlands
SHORT COMMUNICATIONS
Some experiences with Watson's first order centrifugal distortion formula
We have applied Watson's first order, eight parameter centrifugal distortion
(CD) formula 1 to about 25 non-planar molecules and molecular species whose
spectra were arbitrarily selected from the literature. Several interesting features
which seem to be prevalent in this type of analysis are discussed below.
The molecules for which a least squares CDanalysis was carried out using a
computer program previously described2, were: allyl mercaptan3 (normal and
deuterated species), cis and skew butene-l 4, gauche and trans butyronitrile 5, 1,1difluoro-3-methylbutadiene6, 2,2-difluoro-l-methy1cyc1opropane 7, gauche and trans
ethyl formate8, trans fluoroacetyl fluoride9, 2-fluoropropene1 o, cis and gauche 3fluoropropenell, glycolaldehyde (normal2 and several deuterated12 species), phosphirane13, cis propionyl fluoride14, gauche and trans n-propyl fluoridels , and sulfur
tetrafluoride16. About 25 to 70 assigned transitions of high accuracy have been
reported for these molecules. The ratio between transitions and parameters thus
varies from about 3 to about 9, which are comparatively small numbers in a least
squares sense. The asymmetry parameter ,,17 varies from about 0.5 to about
-0.99, although most of the molecules are prolate asymmetrie tops.
Signifieant or almost signifieant values of all five CDconstants were obtained
for all moleeules having the absolute value oh less than 0.97. In faet, the eomputed
standard deviations of the CDconstants amount to only a few percent in most of
the eases studied. This is a very satisfaetory result considering the number and
types of transitions involved. Better CDconstants can undoubtedly be eomputed
for these moleeules when more transitions become available.
Our analysis reaffirms 18,19that accurate CDconstants are obtained as a result
of several faetors. The most important ones appear to be the following: As man y
transitions as possible should utilized. They should be take n from as many different
P-, Q-, and R- "families" as available. Transitions with large CD perturbations
(normally high J) are very important and should be employed if they can be assigned. The assignment of sueh transitions is often greatly facilitated using
preliminary poorly determined CDconstants obtained from low J transitions2, 12.
All eorrelation matrices revealed many large off-diagonal elements. The
largest of whieh were generally found between dK and dWK' and between dJK and
dWK' These two elements were for most molecules found to be very c10se to the
abs olute value of 1.0. We can see no easy way of reducing the many large offdiagonal elements substantially. This shows that it is generally very diffieult to
ob!ain unambiguous CDconstants from mierowave speetra alone.
Special difficulties were found for all of the above mentioned moleeules
J. Mol. Structure, 8 (1971) 234-235
SHOR T COMMUNICA
TIONS
235
which are very c\ose to a symmetri c top (K between -0.97 and -1.0). Highly illconditioned normal equations resulted for the eight parameter formulal for such
compounds, presurnably mainly as a result of the almost linear dependancy among
some of the operators of this expression. Our computations seem to indicate that
this formula is hard ly applicable for least squares fitting procedures when the ab.
solute value of K is greater than about 0.97 and the transitions are measured with
an accuracy of about 0.05 MHz.
Acknowledgement
Financial support from the Norwegian Research Council for Science and
Humanities is gratefully acknowledged.
Department of Chemistry,
The University of Oslo,
Blindern, Oslo 3 (Norway)
K.-M. MARSTOKK
HARALD MØLLENDAL
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Received December
10th, 1970
J. Mol. Structure, 8 (1971) 234-235