The water vapor molecule

  • Darling B
  • Dennison D
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The problem of the vibration rotation spectrum of water vapor is treated
by means of the theory of semi-rigid polyatomic molecules developed
by Wilson and Howard. The potential energy is expanded as a power
series in the normal coordinates and involves three zeroth-order
constants, six first-order and six second-order constants. The positions
of the band centers are calculated and found to depend upon ten quantities,
Xi, Xik, and {γ} which are functions of the potential constants.
A new feature of the treatment is the recognition of a resonance
interaction between certain of the overtone bands which arises from
the near equality of v1 and v3. Eighteen band centers are known experimentally.
These serve to determine the Xi, Xik, {γ} and furnish eight
self-consistency checks which are very adequately satisfied. There
exists no discrepancy between the Raman and infrared spectra as reported
earlier. In order to obtain the geometric displacements corresponding
to each normal co-ordinate it is necessary to examine the spectrum
of D2O. This not only furnishes the required information but also
allows two independent checks upon the theory both of which turn
out to be in nearly perfect accord. The interaction between vibration
and rotation is considered and the effective moments of inertia are
calculated. These are functions of the normal frequencies and of
the first-order potential constants. It is shown that {Delta}=IC-IA-IB
depends only upon the normal frequencies and hence may be computed
at once. A comparison between the observed and predicted {Delta}
yields a very satisfactory agreement. The analysis of the rotational
structure made by Mecke is supplemented by taking account of the
rotational stretching. The resulting molecular constants fix the
valence angle to be 104\,^{\circ}31' and the O-H distance to be
0.9580A. From the effective moments of inertia the first-order potential
constants may be evaluated and these, together with Xik determine
the second-order potential constants. It is now possible to compute
the interaction constant {γ} and a comparison with the observed
{γ} again results most satisfactorily.

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  • Byron T. Darling

  • David M. Dennison

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