Subject: IR INTENSITIES per.syst.& Berry phase

From: Didier MATHIEU <[email-masked]>
Date: Mon, 01 Mar 1999 15:54:54 +0000

reply to E. Lewars + additional question

E. Lewars wrote:
> -------------
> 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.

As the distortion of a given mode q is given by the associated
eigenvector U, then I think "delta q" should be taken as the magnitude
(e.g. in Angstrom) of the distortion vector (delta q).U after conversion
from the mass-weighted cartesian coordinates Q to the standard cartesian
coordinates X.
In other words, (delta q).U is given e.g. in amu^(1/2).Anqstroms. Each
coordinate of this mass-weighted cartesian vector (delta q).U should be
divided by the square root of the mass of the associated atom. This
gives a new vector (delta x).X in angstroms, whose magnitude is (delta
x). 
Then, delta m is the difference between the dipole calculated on the
distorted geometry and the one calculated on the equilibrium geometry.
To be consistent with to diatomic case, it seems to me, although I
didn't studied to question in depth, that one should divide the
magnitude of delta m (in Angstroms) by the magnitude of the vector
(delta q).U in amu^(1/2).Angstroms, and then take the square of this
quantity to obtain the intensity in Debye^2.Angstrom^-2.amu^-1.

If this works, then such a scheme might be of practical value (instead
of chain-rule differentiation of (delta m)/(elta q)) in the following
context:
* normal modes are available 
* IR intensities are to be obtained from a higher theoretical level as
normal modes 
* one is only interested only in intensities in a restricted region of
the spectrum
Indeed, the IR intensities sought should be obtainable from a few dipole
moment calculations for geometries distorted according to the few
associated eigenvectors.

BTW, I have another question related to IR intensities, more specially
for periodic systems. 
It seems to me that some papers reported IR intensities for periodic
systems in a purely classic approach, using a parameterized model for
charge distribution (e.g. electro-optic parameters).
On the other hand, I have been told that calculation of IR intensities
of periodic systems should take into account the quantum "Berry Phase"
(I don't know what it is) to make up for the lack of a proper definition
of the "dipole moment" of such a system.
How can one reconcile this requirement for the Berry phase with
classical simulations for which no quantum concept is used ??

Thanks
-- 
Didier MATHIEU
CEA - Le Ripault, BP 16
37260 Monts (France)
Tel. 33(0)2.47.34.41.85