Subject: IR INTENSITIES__SUMMARY;THANKS

From: "E. Lewars" <[email-masked]>
Date: Fri, 12 Mar 1999 18:04:42 -0500 (EST)

1999 March 12
               SUMMARY OF REPLIES TO Q ABOUT HOW TO CALC
          INTENSITY RATIO OF IR BANDS IN A SIMPLE WAY

 Hello, Thanks very much to all who replied to my question (below).
 Here is the summary of answers.
-------------

QUESTION:
>From E. Lewars:
Subject: Re: CCL:G:IR INTENSITIES
Date: Mon, 1 Mar 1999 15:21:12 +0300

>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
 ===========================
ANSWERS

#1

In your expression   I = k(dm/dq)**2 , the quantity q is not just a
geometrical parameter but it is a normal coordinate. So that, in your finite
difference approximation, you should use a normal coordinate vector as delta
q.

For example, in order to calculate the intensity of full-symmetric mode, you
should take a positive increments for both OH bond lengths. For asymmetric
mode, you should take +delta for one bond lengths, and simultaneously -delta
for another one. More exactly, you should use a realistic normal coordinate
vector received e.g. from hessian calculation.

Yours,
-S.
*******************************************************************
Dr. Stanislav K. Ignatov
Department of Chemistry, University of Nizhny Novgorod
23 Gagarin Avenue, Nizhny Novgorod 603600  Russia
Phone: +7-(831)-265-8035
Email: [email-masked]
http://quark.unn.runnet.ru
*******************************************************************
===========

#2
To: "E. Lewars" <[email-masked]>
Subject: RE: G:IR INTENSITIES
Date: Sun, 28 Feb 1999 02:27:10 +0100

Dear Prof. Lewars,

I would suggest to use linear combinations of bond distances. For the 
water example: 
asym. mode : +delta_r(O-H1)-delta_r(O-H2) 
sym. mode  : +delta_r(O-H1)+delta_r(O-H2) 
with abs(delta_r(O-H1)) = abs(delta_r(O-H1)). 

There will be a problem with bigger molecules since modes of equal symmetry tend
 to interact and spread over the whole molecule.

Stefan
______________________________________________________________________
Dr. Stefan Fau
Fachbereich Chemie, AK Frenking
Philipps-Universit\344t Marburg
35032 Marburg, Germany
[email-masked]
=========

#3
Date: Sun, 28 Feb 1999 11:26:38 -0800 (PST)
Subject: Re: CCL:G:IR INTENSITIES
To: [email-masked]

You need to refer to the classic, Wilson, Decius, and Cross,
Molecular Vibrations.  In the expression, d(mu)/dq, q is not a single
internal coordinate but a normal coordinate.  Cotton's book on group
theory gives a short discussion of how to obtain the normal coordinates.
I thought that Gaussian calculated them as well.
======

#4
                  1-MAR-1999 12:32:21.97
>From:  IN%"[email-masked]"  "Didier MATHIEU"
To:     IN%"[email-masked]"  "E. Lewars"
CC:     IN%"[email-masked]"
Subj:   CCL:IR INTENSITIES per.syst.& Berry phase

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
=================