Subject: Errors in Vibrational mode calcs...

From: "Adrian Stevens" <[email-masked]>
Date: Fri, 1 Mar 1996 16:46:50 +0000

Dear all,

(Appol's. for the length of the mail message!)

I have a query with regard to the accuracy of calculated normal modes of
vibration (as for example, determined via semi-empirical methods)

A while back, there was some discussion on the list, of the calculation
of normal modes of vibration.  In particular, David Young (at Michigan
State University, [email-masked]) posted a short introduction to
the subject, titled 'Computational Modeling of Molecular Vibrations'
(see Sun, 13 Aug 1995 in the CCL archive for the full posting).  In it, he
highlighted that vibrational frequencies from semi-empirical calculations
tend to be qualitative in that bond stretches have high frequencies, bond
angle bending lower frequencies, torsions even lower, etc.  However, he also
pointed out that the actual values are often erratic.  When compared with
experiment, some values come close while others are either too low or too
high.  He also made mention that density-functional theory methods give
frequencies with this same erratic behavior, albeit, with a somewhat smaller
deviation from the experimental results.

I have certainly experienced such erratic behaviour in my current work.  I
started off initially, deciding to do a calibration test of the MOPAC software
against the experimentally observed values for benzene - a reasonable starting
point for any study is to check the accuracy of the model being applied.
Taking the whole task of actually trying to figure out which eigenvalue
corresponded to the c-c mode of 1485 cm-1 for an unsubstituted ring (in a
substituted ring, eg tolualdehyde, this is the ~1600 cm-1 peak), there was
no value to my mind, within an acceptable margin (it was pointed out to me,
that a value returned within *5%* of the experimental result is acceptable!).

It has been suggested to me, that the main reason for the deviation from
experiment is attributable (and this I'm told applies also to ab initio Hartree
Fock calculations) mainly to the intrinsic over-estimation of the electron-
electron repulsion terms in the Hartree-Fock approach (an electron correlation
effect?).  What I would really appreciate primarily, would be confirmation
or rejection of this statement, but idealy, an explanation of the underlying
reason, with possible work-arounds, corrections, etc.  It certainly puzzles
me, that DFT also returns this error, when it treats the electrons in such a
different fashion to Hartree-Fock?

If replies could be mailed to me directly ([email-masked]),
I'll post a summary of the responses to the net (hopefully, with out too
much delay on my part).

Thanks in advance to all who contribute.

Adrian.

-- 
-----------------------------------------------------------------
                          |    Centre for Molecular Design,
   Adrian Stevens         |    c/o SSRIU,
                          |    University of Portsmouth,
   Research Associate     |    Halpern House,
                          |    1/2 Hampshire Terrace,
                          |    Portsmouth,
                          |    Hampshire, UK, PO1 2QF.
-----------------------------------------------------------------
  Voice: +44 (0) 1705 843623   E-mail:  [email-masked]
-----------------------------------------------------------------