Subject: SEMIEMPIRICAL FREQUENCY SCALING SUMMARY

From: elewars <[email-masked]>
Date: Sun, 21 May 2000 17:31:07 -0400

2000 May 20

Here is my summary of the answers to my question on semiempirical
vibrational freqs scaling factors.
I failed to remember that the "canonical reference" of Scott and Radom
also gives AM1 and PM3 factors (Table 10: AM1 0.9532; PM3 0.9761; these
are briefly discussed then shunted aside for a lengthy treatment of ab
initio and DFT freqs, which with their ZPEs are said to be more
accurate). Note that for AM1, PM3 and SAM1 a single correction factor
for the whole frequency range is not as good as for ab initio or DFT: I
think that if you are interested in C=O stretch, for example, it's
better to find 20 or so C=O compounds for which the freqs are
experimentally known, calculate the stretching freqs with AM1 or PM3,
then plot exp vs calc freqs and get the slope of the best-fit line
through the origin (exp=k calc). The resulting factor of about 0.85 is a
good way from the broad-range ca. 0.95 factor.

Thanks very much to all who responded (#1--#8, below).

EL
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The Question
2000 May 1

Hello,

I would appreciate it if someone could send me a ref for  AM1 and PM3
vibrational frequency scaling factors, i.e the numbers to multiply a
calculated IR frequency by to get (approximately) the observed,
experimental frequency ; I know these numbers are about 0.9.
If the scaling for SAM1 is available I would welcome getting that too.

(If anyone is interested, the canonical reference for ab initio and DFT
scaling factors--freqs and ZPEs-- is
A. P. Scott and L. Radom, J Phys Chem, 1996, 100, 16502-16513).

Thanks

E. Lewars
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The Answers

#1

Please see:  M. B. Coolidge, J. E. Marlin, and J. J. P. Stewart,
"Calculations of Molecular Vibrational
Frequencies Using Semiempirical Methods", J. Comp. Chem., 12, 948-952
(1991).

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#2
I am somewhat puzzled by your question:  According to "the canonical
reference" (i.e., Scott & Radom, Table 1) the IR frequency scaling
factors for
AM1 and PM3 are equal to 0.9532 and 0.9761, respectively.  The
corresponding
rms errors are quoted as 126 and 159 cm-1.

Yours, Jens >--<

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
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]
DK-4000 Roskilde, Denmark   http://www.rub.ruc.dk/dis/chem/psos/
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#3
Dear Professor Lewars,

        I may be able to help you if you just want a scaling factor. I
don't have
a reference, but the CCCDBD (http://srdata.nist.gov/cccbdb/) has a few
pages for playing around with vibrational frequency scaling factors.
Unfortunately it does not have the AM1 and PM3 data in the public
version.
In a month I hope to have another release which will allow users to
choose
a set of molecules and calculate a scaling factor for a much broader
selection of methods and basis sets, including AM1 and PM3. If there is
a
certain class of molecules in which you are interested I can query the
internal version here and return a scaling factor. For example, if I
choose
everything in the database with a CH bond and exclude radicals I get 65
species, 1124 vibrations and a factor of 0.9235 ± 0.0076 for AM1. For
PM3 I
get 68 species, 1171 vibrations and a factor of 0.9451 ± 0.0071. For all

the molecules with experimental vibrational frequencies in the CCCBDB I
get
AM1 224 species, 1834 vibrations, 0.9199 ± 0.0060
PM3 246 species, 1867 vibrations, 0.9435 ± 0.0058

Hope this is useful.

Russ Johnson
[email-masked]

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#4
You are in principle right about the values of ca. 0.9, but this is very

tentative. For example, you can take a look for sf's for some nitriles
in
my papers

V.A.Basiuk. IR spectra simulation as auxiliary tool for gas
chromatography/Fourier transform IR spectroscopy/mass spectrometry
identification of unknown compounds. 2. PM3, AM1, MNDO and MINDO3
simulations for simple nitriles/ Spectrochim. Acta A, 1999, 55, N14,
2771-2782.

V.A. Basiuk, R. Navarro-Gonzalez, Y. Benilan and F. Raulin. PM3, AM1,
MNDO
and MINDO3 semi-empirical IR spectra simulations for some nitriles of
interest for Titan's chemistry/ Spectrochim. Acta A, 2000, 56, N6,
1157-1165.

But from my experience with other classes of compounds, I can say that
sf's can vary significantly depending on the chemical structure.

Good luck!

***********************************************

Dr. Vladimir Basiuk
Instituto de Ciencias Nucleares
Universidad Nacional Autonoma de Mexico
Circuito Exterior C.U.
A. Postal 70-543
04510 Mexico, D.F., MEXICO

Tel:    (52) 56 16 27 97
        (52) 56 22 46 74
Fax:    (52) 56 16 22 33
email:  [email-masked]

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#5

Hi E. Lewars,

You asked:

>I would appreciate it if someone could send me a ref for  AM1 and PM3
>vibrational frequency scaling factors, i.e the numbers to multiply a
>calculated IR frequency by to get (approximately) the observed,
>experimental frequency ; I know these numbers are about 0.9.
>If the scaling for SAM1 is available I would welcome getting that too.

The reference you mentioned for ab initio and DFT scaling factors:

>(If anyone is interested, the canonical reference for ab initio and DFT

>scaling factors--freqs and ZPEs-- is
>A. P. Scott and L. Radom, J Phys Chem, 1996, 100, 16502-16513).

Is also the best source I know of for general PM3 scaling factors.  (If
you need
some Metal-Main group vibration information, try:  K. K. Stavrev, ZCPE
Bulletin
(1992).)

For AM1 and SAM1, though, Andy Holder has done the most thorough main
group studies.
Originally for AM1 vibrational frequencies:

 E. F. Healy & A. Holder, J. Mol. Struct. (Theochem), 281, 141-56
(1993).

And he has updated this information for SAM1, combining both sets of
comparisons in
:

 A. Holder & R. Dennington II, J. Mol. Struct. (Theochem)401, 207-18
(1997).

SAM1 is more accurate, (average signed error of only 0.7% vs 4.9% for
AM1), except
he identified systematic scaling factors for some different vibrational
modes:
specifically a scaling factor of 0.86 is required for non-H stretching
frequencies.

EC
---

Ernest Chamot
Chamot Laboratories, Inc.
530 E. Hillside Rd.
Naperville, Illinois 60540
(630)637-1559
[email-masked]
http://www.chamotlabs.com/cl
============
#6
Professor Lewars,

The correction you mention for stretching frequencies is about correct,
but
things are not as simple as they are for ab initio frequencies.  the
only way
to correct frequencies coherently is by type.  The same scaling factor
will
not apply to all types of vibrations.  The paper you mention is good for

AM1.  the following reference is for a similar study on SAM1.  As above,
I
don't know of a PM3 paper.

A.J. Holder* and R.D. Dennington II.  "An Evaluation of SAM1 Calculated
Vibrational Frequencies", THEOCHEM,, 401/3 (1997)  207-18.

Regards, Andy Holder

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UUUU  UUU MMM   MMKK KKKK   CCCC   |           ANDREW J. HOLDER
 UU    U   MM   MMK   K    CC  CC  | Assoc. Prof. of Comp./Org.
Chemistry
 UU    U   MMM M MK KK    CCC      |          Dept. of Chemistry
 UU    U   M MM  MK   KK   CC  CC  |  University of Missouri-Kansas City

  UUUUU   MMM M MMKK   KK   CCCC   |         Kansas City, MO  64110
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#7
Hello,

for AM1 and PM3 scaling factors (frequencies and force constants) see
for example:

Seeger, D. M., C. Korzeniewski, et al. (1991).
“Evaluation of Vibrational Force Fields Derived by Using Semiempirical
and Ab
Initio Methods.”
J. Phys. Chem. 95: 6871-6879.

Grunenberg, J. and R. Herges (1997).
“Calculation of Molecular Vibrations: Selective Scaling Factors for
Semiempirical
Force Constants.”
J. Comp. Chem.18: 2050-2059.

Greetings,
Jörg

--
Dr. Jörg Grunenberg, Org. Chemie, Hagenring 30, 38106 Braunschweig
email: [email-masked] phone: +49 531 391 5252
URL: http://www.tu-bs.de/institute/org-chem/grunenberg/grunenberg.html
=========
#8
Hi!
Could you send me a summary of the answers you received by now.
I am also extremely interested in calculated (both Ab Initio and
semiempirical) vibrational frequencies.

Best regards,

Vasile CHIS
--------------------------------------------------------------------
Dr. Vasile CHIS
"Babes-Bolyai" University
Department of Physics
1, Kogalniceanu
RO-3400 Cluj-Napoca
ROMANIA
Tel: +40 64 194315 / 5153
Fax: +40 64 191906
E-mail: [email-masked]
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