Subject: Re: CCL:Reduced Mass

From: "Jens Spanget-Larsen" <[email-masked]>
Date: Thu, 13 Apr 2000 17:01:54 +0100

Dear Brian Space:

> In Gaussian output how is the reduced mass defined?

Let the r'th normal mode vector of unit length be given as

        _                   1/2
  Q  = >_ c   q  ,    q  = m    x
   r    i  ir  i        i   i    i

where the sum is over the 3N mass-weighted atomic displacement coordinates  q.  
m  are the corresponding atomic masses in AMU, and x the cartesian displacement 
coordinates (in Angstrom).  The "reduced mass" M in AMU may then be obtained as 

              _  2   -1
  M  = 1 / [ >_ c   m  ]
   r          i  ir  i

The "normal coordinates" printed by Gaussian apparently correspond to 
cartesian vectors (in Angstrom) normalized to unit length; in order to obtain 
the proper length of this vector, the printed coefficients  d  must be 
multiplied by the inverse square root of the reduced mass:

             -1/2  printed
  d   <---  M     d
   ir        r     ir

The proper cartesian displacement vector is then obtained as

        _
  X  = >_ d   x 
   r    i  ir  i

The coefficients c and d are related by 

             -1/2
  d   = c   m
   ir    ir  i

and we have the following relation

               -1/2
  |X | = |Q | M
    r      r   r

The inverse square root of the reduced mass is simply the length of the 
cartesian displacement vector X for unit displacement along normal mode Q.

Yours, Jens >--<

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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]
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