Subject: CCL:G:reduced mass

From: "Jens Spanget-Larsen" <[email-masked]>
Date: Thu, 29 Oct 1998 09:24:36 +0100

Eun Joo Lee:

> I would like to know how the gaussian program calculate the
> reduced mass when you submit the job for frequency calculation of molecule.
> I wonder how 3n-6 # of reduced mass is calculated instead of 3n # of reduced
> mass.(n is number of atoms)
> It could be very simple question, but still it puzzles me.

The normal vibrational modes are defined by a set of orthonormal 
vectors
        _           _      1/2
  Q  = >_ c   q  = >_ c   m    x
   r    i  ir  i    i  ir  i    i

where  q  are the massweighted atomic displacement coordinates,  m  
are the atomic masses and  x  are the cartesian displabcement 
coordinates.  The reduced mass for normal mode  r  is defined by

            _  2   -1
  M  = 1/( >_ c   m   )
   r        i  ir  i

The inverse square root of M is simply the length of the cartesian 
displacement vector X for unit displacement along normal coordinate 
Q:
              -1/2
 |X | = |Q | M
   r      r   r

The cartesian displacement vectors printed by Gaussain are normalized 
to unit length = 1 angstrom.  The proper length is obtained by 
multiplication of the printed coordinates by the inverse square root 
of the reduced mass.

Yours, Jens >--<
                             
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
JENS SPANGET-LARSEN         Phone:  +45 4674 2000  (RUC)
Department of Chemistry             +45 4674 2710  (direct)
Roskilde University (RUC)   Fax:    +45 4674 3011 
P.O.Box 260                 E-Mail: [email-masked]
DK-4000 Roskilde, Denmark   http://www.rub.ruc.dk/dis/chem/psos/
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=