Subject: IR INTENSITIES

From: "E. Lewars" <[email-masked]>
Date: Sat, 27 Feb 1999 19:36:14 -0500 (EST)

1999 Feb 26

I have a question about calculating the relative intensities of IR vibrations.
Let me say at the outset that my interest here is to *illustrate* in a simple
way how intensities can be calc from the change in dipole moment
accompanying the normal-mode vibration; I know there are sophisticated
algorithms for calculating the intensity of IR bands. I just want to show
how, in principle, one might get relative intensities in a conceptually
simple way.

The intensity of a normal-mode vibration is approximately

                         I = k(dm/dq)**2

where
     k is a proportionality constant (we are interested in _relative_
     intensities)
     m = dipole moment
     q = a geometric parameter like bond length

Approximating the derivative as the ratio of finite increments enables us
to readily calculate relative intensities for the single mode of diatomic
molecules:

                       I = k(delta m/delta q)**2

Thus for H-F and HCl, using HF/6-31G* calcs:
    H-F   r(0.9109=r-equil), m = 1.9719 D; r(0.9209), m = 1.9897
         I = k(0.0178/0.01)**2 = 3.17k

    H-Cl  r(1.2662=r-equil), m = 1.5017 D; r(1.2762), m = 1.5081
         I = k(0.0064/0.01)**2 = 0.41k

   Intensity ratio, I(HF)/I(HCl) = 3.17/0.41 = 7.7

 A calc using Gaussian 98 gives an intensity ratio of 141.5/24.3 = 5.8
 Fine.
-------------
QUESTION:
Suppose we have, say H2O, and want to calc the relative intensities of
the asym and the sym stretching modes. In principle we can distort the geom
a little (as for H-F and H-Cl, above) and calc the change in dipole moment,
delta m. But what do we take as delta q when there is not just *one* simple
geometric parameter like r=(H--X)?  I suppose either q is composite, or the
expression for I has several terms.

                   O
                 /    \
               H       H

          Thanks
            E. Lewars
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