Subject: Summary: Frequencies calculated at different levels of theory

From: "Emadeddin Tajkhorshid" <[email-masked]>
Date: Mon, 8 Jun 1998 10:50:10 -0700

Dear all

Last week, I posted a question about the use of frequencies to judge about the
accuracy of geometries. Thanx to anybody who responded to my question. Speciall
thanx to Prof. Shusterman who, to my eyes, gave the exact answer to my
question.
I also beleive that we may not generally use the closeness of the frequencies
to experimental values as a measure of the accuracy of geometries. However,
there are different opinions among the answers I received.

Here are the summary of the answers I got from the community.
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Question:
Can we decide on the basis of the closeness of the frequencies obtaiened at one
level to judge about the accuracy of the geometrical parameters calculated in
that model?
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The answer to this question is no.

The most widely understood example of this is the performance of the
Hartree-Fock model which can give very accurate geometries for a wide range of
molecules. The accuracy of these predictions is somewhat basis set dependent
(and better basis sets are not always more accurate).

The interesting thing is that the Hartree-Fock model always gives poor
vibrational frequencies regardless of the basis set, although the errors depend
on the type of vibration (larger errors are seen for stretching vibrations).

The explanation for this paradoxical behavior, good geometries + poor
frequencies, is that the latter depends on information derived from several
geometries and correlation errors are geometry dependent. Therefore, minima on
the Hartree-Fock energy surface may occupy nearly the same positions as the
minima on the true surface, but the curvature around the minima on these
surfaces can be substantially different.

Alan

-----------
Alan Shusterman
Department of Chemistry
Reed College
Portland, OR
www.reed.edu/~alan

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There is an excellent review by Scott and Radom in either J. Phys. Chem or
J. Chem. Phys. from a year or so ago that compares levels of theory on
vibrational frequencies.  Also, Hehre (I think) was an author of a book a
few years ago comparing Ab Initio with experimental properties.

Hope that helps.

Darren Andrews.

PostGraduate Student,
School of Chemistry,
University of Leeds,
Leeds.
LS2 9JT.
England.

[email-masked]

Tel: 0113 233 6594.
Fax: 0113 233 6565.

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I believe that yes, you can draw this conclusion. At least for DFT, it has
been shown that the reference geometry is more important for accurate
frequencies and force constants than the actual flavor of DFT used. Cf.,
e.g., A. Bérces ("Berces" if your mailing program can't read the "é"
character) and T. Ziegler, in: Topics in Current Chemistry, Vol. 182, R. F.
Nalewajski (ed.), Springer-Verlag, Berlin, 1996; (same authors), Topics in
Curr. Chem. 1996, 182, 41. Besides, it is also possible to calculate
vibrational frequencies at any given reference geometry, even if it is not
the stationary point at that particular level of theory. This is, however,
not possible to do with the Gaussian program. Cf., e.g., the same
references, but also others by A. Bérces as well as: P. Pulay et al. JACS
1979, 101, 2550; G. Fogarasi et al. JACS 1992, 114, 8191.

I hope this helps a little ... In any case, I am interested in your summary.

Best regards, Georg

--
==============================================================
Dr. Georg Schreckenbach           Tel:     (USA)-505-667 7605
Theoretical Chemistry T-12        FAX:     (USA)-505-665 3909
M.S. B268, Los Alamos National      E-mail:  [email-masked]
Laboratory, Los Alamos, New Mexico, 87545, USA
Internet:    http://www.t12.lanl.gov/~schrecke/
==============================================================

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Well, this is a big problem. Let me start this way. The consistency of
the results (bond lengths, frequencies etc) from a particular method is
not preserved. Some cases even at HF/4-31G produce very accurate distance
(eg Li-H) - but in general this method is not satisfactory. DFT generally
slightly overestimate bond lengths, again it is not true for all type of
molecules. I do not have any ready ref. on comparison of dft and other
methods but sure there are more than 10-15 papers. Now in your case it
shows DFT (again which coorelation and exchange functional are used,
B3LYP is generally good but not good for transition metal) yields
frequencies close
to expt. So for this particular system distances are accurate. And you
can say for the similar kind of molecule it will be acurate. Please check
the scale factor of DFT method.

Tapas Kar, Ph. D
Asst. Scientist
Department of Chemistry
Southern Illinois University at Carbondale
Illinois 62901-4409

Fax: (618) 453 6408
Tel: (618) 453 6433
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-- 
Emad
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E. Tajkhorshid				
German Cancer Research Center; DKFZ             Tel: +49 6221 42 2340
Dept. Molecular Biophysics (H0200)              FAX: +49 6221 42 2333
P.O.Box 101949			   
69009 Heidelberg, Germany     Email: [email-masked] 
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* "Never express yourself more clearly than you think." -Niels Bohr *
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