Subject: Summary of responses Re: Vibrational query

From: "Adrian Stevens" <[email-masked]>
Date: Tue, 19 Mar 1996 15:28:54 +0000

Dear all,

I'd like to thank everyone who responded to my original query concerning the
accuracy of calculated normal modes of vibration and also appologise for the
length of time that it has taken to post the summary of responses back to
the CCL.  The replies have proved most helpful towards the current research,
which is focused on the use of normal modes as the basis for a structural
descriptor that can be applied in QSAR-type applications.

For anyone that is interested in finding out further details of this research,
a paper by Prof. Laurie Phillips and PhD thesis by Dave Turner should be
published in the near future and provide the most detailed accounts.  Alter-
natively, I'm hoping to eventually put a web page onto the net, that should
give a general introduction and overview of the concepts applied.  I must add
that it is currently in the early stages of development and may take some time
to be completed - my own PhD thesis currently occupies all spare time. If
interested parties could mail me directly, then I'll get in touch at the
appropriate time.

Thanks to:

Attila Berces <[email-masked]>
Jon Erickson <[email-masked]>
Alan Shusterman <[email-masked]>
David A. Tilbrook <[email-masked]>
Edgardo Garcia <[email-masked]>
Aldert Westra Hoekzema <[email-masked]>

Cheers,

Adrian.

=========================

Original message follows:

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?

============================

Summary of responses follow:

1)

From:    Attila Berces <[email-masked]>
Date:    Fri Mar  1,  3:44pm -0500
To:      [email-masked]
Cc:
Subject: vibrations

Hello Adrian,
For the E2u mode of benzene, which is 1494 cm-1 experimentally, the simplest
local density funtional method gives 1462 cm-1. Close enough? As far as
benzene goes, the B2u mode of 1150 cm-1 is the worst by theoretical method,
because this is the dissociation coordinates into 2 HCCH units. Even that is
within the magic 5%, you are expecting.
A detailed study on benzene:
Berces and Ziegler, J. Chem. Phys. 98, 1993, p4793
Berces and Ziegler, J. Phys. Chem. 98, 1995, p11417.
For transition metal complexes:
J. Phys. Chem. 98, 1994, 1584
J. Phys. Chem. 98, 1994, 13233

> 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.

Any error in quantum chemistry comes either from the model ( i.e. harmonic
approximation) or the correlation effect. It looks like harmonic approximation
works pretty well except for high frequency stretches. Therefore, only
correlation effect is left to blame.

The problem in frequency calculations comes from the fact that error in
stretches and bendings is not the same. Therefore, the order between stretches
and bends of similar frequency may be switched or they mix too much or too
little. Look at the first reference for such examples.  Pulay and cowork worked
out a scheme for correcting force constant systematically by different scaling
factors for stretches, bends etc. These scaling factors are transferable to  a
certain extent and give not only very good eigenvalues but also good
eigenvectors. Lately in Chem. Phys Letters there was a paper on frequencies of
porphyrine.

Attila

2)

From:    [email-masked] <[email-masked]>
Date:    Fri Mar  1,  4:04pm -0500
To:      [email-masked]
Cc:
Subject: semi-empirical vibrational frequencies

Adrian,

I did some work comparing AM1 vibrational frequencies with experimental
values (JOC, 1995, 60, 1626) and they appeared to be ~18% off for C=O
stretching. Stewart found this to be the case, as well (J. Comp. Chem.
1991, 12, 948). Not much better for HF/6-31G*, off by ~10% (In Hehre,
An Initio Molecular Orbital Theory, 1986, Wiley).

Jon Erickson
DowElanco CAMD
[email-masked]

3)

From: [email-masked] (Alan Shusterman)
Date: 01 Mar 96 11:54:15 PST
To: [email-masked]
Cc:
Subject: Re: CCL:M:Errors in Vibrational mode calcs...

--- You wrote:
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.
--- end of quoted material ---
Confirm!

The HF wavefunction dissociates incorrectly, i.e., it keeps electrons paired up
and delocalized in the bond that is being stretched.  The electrons in this
bond really want to localize on each atom, i.e., correlate their motions.
Therefore, the HF energy surface rises too rapidly as the bond is stretched,
and this steep surface yields stretching frequencies that are too high.

The simplest workaround is to scale ab initio HF frequencies, i.e., multiply
them by 0.89.  This is not a perfect fix because not all vibrations are equally
affected by correlation, but the resulting numbers are usually pretty good.

Alan Shusterman
Department of Chemistry
Reed College
Portland, OR 97202

4)

From: [email-masked] (David A. Tilbrook)
Date: Sun, 03 Mar 1996 01:12:11 +0000
To: Adrian Stevens <stevensa>
Cc:
Subject: Re: CCL:M:Errors in Vibrational mode calcs...

>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!).

I'll run the calculation myself Adrian and will try and see what I get. Are
you 'scaling'
for frequencies by say 0.9 to give correction for the harmonic approximation?

>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?

Keep in touch about your work

Regards

David Tilbrook

5)

From: edgardo garcia <[email-masked]>
Date: Mon, 4 Mar 1996 14:39:58 -0300 (GRNLNDST)
To: Adrian Stevens <stevensa>
Cc:
Subject: Re: CCL:M:Errors in Vibrational mode calcs...

Hi Adrian,

I also experienced errors of +/- 50cm-1 with AM1 freq. calc.
on organic molecules with up to 100 atoms.  I would
say that:

1. In general the accuracy of freq. predicctions go down in
   the direction : bonds > angles > torsions
   Also for torsions you will have populations of conformers that
   will show different freq.
2. Semiempirical methods are not parametrized for freq. so you
   can't really expect them to be good, they can be erratic.
3. In any HF method the curvatures on the hyperenergy surface are sharpper
   than if elec. correlation is included leading to higger freq. for
   bonds.
4. In most methods a harmonic oscilator approximation is used to get the
   freq. from the energy results, the anharmonicity shoud lower the
   frequencies.
5. Maybe taking in account the 0th point virbrational energy will also
   lower the frequencies ?

Points 3 to 5 are the ones responsible for the general correction
factor of 0.8 - 0.95 usually found.
About DFM I don't have a clue. They certaily shoud result in higer
freq. because of points 4 & 5, also they don't include all
electron correlations. But, why they show erratic results relative
to experiment ?

Best regards,

Dr. Edgardo Garcia
Universidade de Brasilia
Brasilia DF Brazil

6)

From: [email-masked] (Aldert Westra Hoekzema)
Date: Wed, 6 Mar 96 11:28:03 +0100
To: "Adrian Stevens" <stevensa>
Cc:
Subject: Re:  CCL:M:Errors in Vibrational mode calcs...

Hi Adrian,

First of all I am not familiar with benzene frequencies, but have
done a lot of frequency calculations on normal alkanes, including
HF, MPx, CISD and DFT (B3PW91) levels of theory (6-31g** basis set).
Roughly speaking, there are two main sources of error in the
calculated as compared to experimental frequencies:
a. the efffect that you suggested, namely the lack of correlation.
As a result the curvature (and force contstant) in the well is too
large and frequency will be too high.  Improving the correlation
treatment reduces this error, in my calculations DFT turned out to
be the "best" (indeed, frequencies within the 5% you mentioned).
b. the use of the harmonic approximation.  There is not much one can
do about this error (I do not know about programs that calculate
anharmonic frequencies).  In general stretching modes suffer mostly
from the use of the harmonic approximation.  Perhaps experimental
information from overtones can help to estimate this error.

Hope this is clear and helpfull.
Please send me a summary of the responses you get.

Bye, Aldert

-- 
------------------------------------------------------
         Adrian Stevens  Research Associate 

Centre for Molecular Design, University of Portsmouth,
c/o SSRIU, Halpern House, 1/2 Hampshire Terrace, 
Portsmouth, Hampshire, UK, PO1 2QF.

Voice: +44 (0) 1705 843623 Fax: +44 (0) 1705 843722
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