Subject: Re: CCL:AM1 frequencies scaling

From: "Andy Holder" <[email-masked]>
Date: Tue, 27 May 1997 11:45:11 -0500

Netters,

Guiseppe Milano posed the following question a week or so ago:

> I would appreciate to receive information about scaling of AM1 frequencies 

I though I would reply as the author of two papers in this area:

J. Mol. Struct. (THEOCHEM);  1993, 281, 141  (AM1 results)
J. Mol. Struct. (THEOCHEM);  1997 in press.  (SAM1 results)

Unfortunately, things in the semiempirical world are not as simple as in the 
case of ab initio calculations in this area.  The AM1 paper above clearly 
showed that no single factor would solve the problem of scaling all 
vibrational types.  The errors for the different motions  was widely variable, 
although there were clear trends that were easily explainable by the relative 
simplicity of the semiempirical orbital descriptions.  A quite complex scheme 
of corrections was proposed in that paper.

The SAM1 paper basically says the same thing, although the error analysis has 
been greatly simplified, making adjustment of the vibrations to experimental 
results easier.  I have listed some selected data below to support this:

                                              Errors
Vib. Type    #Examples         SAM1      |SAM1|    AM1    |AM1|
-----------------------------------------------------------------
All             442            0.7%       9.0%     4.9%    9.6%
Str. (non-H)     69           14.0       15.7     14.9    18.2
Str. (C-H)      105           -2.6        3.8      4.4     4.5
Bends            75           -0.8       10.5      6.3    10.4
Rock/Wags       116            0.8        8.3      4.5     8.9
Defs.            66           -2.7        8.0     -1.8     7.8
Tors.            11          -20.4       21.2    -16.2    16.3

The take-home lessons:

1.  Only vibrational types that have signed and unsigned errors of the same  
    magnitude will likely benefit from adjustment.

2.  SAM1 non-H stretching modes can be scaled by multiplying by 0.86
    AM1 non-H stretching modes can be scaled by multiplying by 0.85

3.  SAM1 torsional modes can be scales by multiplying by 1.2563
    AM1 torsional modes can be scales by multiplying by 1.1933

4.  The TYPE of vibration must be identified before scaling.  This is best  
    done with vibrational animation graphics software.  I obviously used AMPAC  
    for all of these tasks.

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
                        KK         |          [email-masked]
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