Subject: single vs double differencing in numerical calcn of Hessian

From: <[email-masked]>
Date: Tue, 13 Jun 1995 10:48:28 -0500 (CDT)

Fellow CCLers:

	As part of his research into the calculation of the vibrational spectra
of transition metal complexes, one of my students is looking into the
differences between single and double differencing.  In both cases, the energy
hessian is calculated (using the Iowa State version of GAMESS) numerically by
displacing the symmetry unique atoms a small amount along the Cartesian axes.

In single differencing, the displacements are along the positive x,y, & z axes,
while in double differencing the diaplcements are along the positive and
negative Cartesian axes.

It seems to us from our reading that the general concencus is that there is
little change (for example, in calculated frequencies or derived thermodyanmic
quantities) in one versus the other and thus making it impractical to 
employ double differencing which takes roughly twice as long.  However, we
have yet to find a systematic study of this question for either main group or
transition metal complexes.

Any references to pertinent work would be most appreciated.

Sincerely,

Tom Cundari
Associate Professor of Chemistry

P.S.  We are using effective core potentials and are thus limited to 
	numerical methods for hessian calculation.
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Thomas R. Cundari                           Address from 3/15/95 -> ca. August:
Asst. Professor of Chemistry                Prof. Tom Cundari
Computational Inorganic Chemistry Lab       Visiting Scientist
University of Memphis                       Cornell Theory Center
Memphis, TN 38152                           520 Engineering & Theory Center Bldg
phone: 901-678-2629                         Cornell University
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e-mail: [email-masked]             phone: (607)254-8686
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http://www.memst.edu/chemistry/umchem.html  fax: (607)254-8888
					    e-mail: same as always
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