Subject: SUMMARY: QEq charges & applications

From: Didier MATHIEU <[email-masked]>
Date: Fri, 23 Jan 1998 10:54:17 +0100

Dear Dr. S. Shapiro & Bakowies,

Here are relevant responses to my inquiry about QEq charges and their
applications:

********  "Andrey Bliznyuk" <[email-masked]>

I spent some time trying to apply different versions of Qeq / PEOE 
methods. I even add some more parameters and tried to optimize them 
in order to reproduce charges, obtained from electroststaic potential 
calculations. Results been disappointing. I come to conclusion that 
you need many special atom types in order to get reasonable results. 
On the other hand, if you are ready to live with not very accurate 
potential (charges in that case may differ substantially, for example 
by 0.2 a.u.), these methods may be useful. 

> In this context, maybe it would be better to transfer atomic charges
> derived for chemical groups, between molecules showing the same
> chemical structures ? 

The main reason I was looking for QEq charges was that the results 
obtained from coventional MM calculations were unsutisfactory. 
 
> I don't know exactly how accurate atomic charges should be. I want
> to use them to derived molecular indexes, from averages of the
> electrostatic potential over molecular surfaces. For instance, I'd
> like to find relationships between sublimation enthalpy of molecular
> materials and such indexes. Because such empirical relations are not
> expected to be accurate maybe I could be satisfy with QEq charges

I guess, that it should work for you. 

********  "Smith JA (Jack)" <[email-masked]>

A simple idea I've been toying with is the use of Rappe's QEq scheme
(perhaps coupled with Landis' VALBOND scheme) together with a
variationally derived analytical Thomas-Fermi expression for the charge
density of charged atoms.  This generates a very quick, crude, but
surprisingly good electron density (a superposition of charged atom
densities) and a full electrostatic potential (in analytical form)
corresponding to the QEq charges.  It's fast enough to perform at an MD
timescale.

> I would be eager to know more about your "toy".
> 
I say 'toy' because I don't get much opportunity to actually work on
this stuff.

> > (perhaps coupled with Landis' VALBOND scheme) 
> 
> Do you please have any reference about this Landis'VALBOND scheme ?
> 
  The following was posted by Clark ([email-masked]) to
another list where VALBOND was being discussed (BTW, Dan Root now works
for MSI):

Published VALBOND work includes: 

'Valence Bond Concepts Applied to the Molecular Mechanics Description of
Molecular Shapes 1.  Application to Non-hypervalent Molecules of the
P-block.'  Daniel M. Root, Clark R. Landis, and Thomas Cleveland, J. Am.
Chem. Soc., 1993, 115, 4201-4209. 

'Valence Bond Concepts, Molecular Mechanics Computations, and Molecular
Shapes'  Clark R. Landis,  Advances in Molecular Structure Research,
Vol. 2,  Magdolna Hargittai and Istvan Hargittai, Editors,  JAI
Publishers, Inc.  New York, 1995. 

'Making Sense of the Shapes of Simple Metal Hydrides'  Clark R. Landis,
Thomas Cleveland, Timothy K. Firman,  J. Am. Chem. Soc.,  1995, 117,
1859-1860. 

'Regarding the Structure of W(CH3)6'  Clark R. Landis, Thomas Cleveland,
and Timothy K. Firman, Science, 1996, 272, 179. 

'Valence Bond Concepts Applied to the Molecular Mechanics Description of
Molecular Shapes.  2.  Applications to Hypervalent Molecules of the
P-Block', Tom Cleveland and Clark R. Landis, J. Am. Chem. Soc.,1996,
118, 6020-6031. 

'Steric Effects in the Cleavage of Dinitrogen by Molybdenum Triamide
Complexes', Konstantin Neyman, Jutta Hahn, Notker Rösch, and Clark R.
Landis, Inorganic Chemistry; 1997; 36; 3947-3951.  

> > variationally derived analytical Thomas-Fermi expression for the
> charge
> > density of charged atoms.  
> 
> Do you mean you solve the Euler equations for Thomas-Fermi under the
> constraint that atomic charges (defined in which way ?) should equal
> QEq
> charges ? 
> 
The analytical TF work actually dates back to that of Peter Csavinsky
[Phys Rev 166, 53 (1968); Phys Rev 8A, 1688 (1973)].  I use his
analytical expression (or some DZP-like extension of it) for the nuclear
screening function, separate out the pure Z/R term, and substitute a
QEq-adjusted N (N-q) for the number of electrons in the N*phi(x)/R term
(where phi is the screening function and x is the universal TF
coordinate).

> Or you simply modify the expression for the electrostatic potential
> according to such charges, but I cannot see how it can be done in a
> consistent way ?
> 
The potential would simply be

  Z/R - (Z-q)*phi(x)/R

where q is the partial charge adjustment (from QEq, for example) and
phi(x) is the universal (Z-dependent) screening function.  In my own
methodology, though, the screening function is refit dynamically to
match the GC-UHF Coulomb potential for each atom in a self-consistent
atoms-in-molecules approach.  This amounts to decomposing the molecular
UHF Coulomb potential (plus nuclear attraction) into a superposition of
atomic TF-like potentials.

> Finally, it seems you were interested mostly in the electron density,
> 
Actually I'm in a variety of aspects.  I just found that I could
generate a quick and dirty density (mainly for generating density
isosurfaces for visualization purposes) as a superposition of
charge-adjusted TF densities.  In TF theory, the potential is directly
related to the density, though.

> while I am only concerned - in a first approach - with the molecular
> electrostatic potential. Do you think the MEP derived for your TF
> density for charged atoms is better than the MEP obtained from the
> coulombic interaction with QEq charges ? 
> 
What this gives you is a screened potential at each atomic site instead
of point charges.  So it would be more like a density derived MEP.  I
don't know if would actually be any better in practice, but I'd think
it's worth a try.  Point charge models always bother me.  Atomic partial
charges (especially Mulliken type) also bother me.  Since QEq charges
are derived from matching chemical potentials between atoms (no
arbitrary basis partitioning) and the TF screening maps this to a
density, I feel much more comfortable with it.  However, I have no real
experience in trying to use these for real problems - it's still only a
'toy'.

> What do you mean by a
> "potential CORRESPONDING to QEq charges"... are they essentially the
> same ?
> 
No.  The TF (screened Coulomb) potential is not a point charge model.
The nuclear charge is localized (Z/R), but the electronic charge has
more of a Q*exp(R)/R behavior.  I suppose one could fit a point charge
model to the resulting potential, but why?

******** [email-masked] (Dirk Bakowies)

some time ago we have reported a semiempirical implementation of Rappe
and Goddard's QEq scheme. With MNDO type formulas for the two-center
integrals, we have calibrated the model to reproduce either Mulliken
or potential derived charges. It turns out that Mulliken charges are
easier reproduced (typically 0.05 e off) than potential derived charges
(0.1 e off). For standard organic molecules the scheme proved accurate
enough to be used in hybrid QM/MM calculations. It is my experience,
however, that subtle charge shifts due to electron delocalization
are not captured by the model.

See:
D. Bakowies, W. Thiel; J. Comp. Chem. 17 (1996) 87, JPC 100 (1996)
10580.

******** [email-masked]  (Narushi Goto)

Indeed I did some calculation using QEq to estimate IR/Raman
spectrum. As you already know, the frequencies are depend on
the accuracy of force field parameter. So in some case, I could
estimate frequencies and intensities with very high accuracy,
but in some case I could not.

Finally, in my opinion, QEq method is very good to calculate the
charges in a short time. Why don't you contact the Caltech Staff?

******** John McKelvey <[email-masked]>

A thought about the reliability of Qeq related to chemical shifts, etc:

The way I read the paper is that Qeq is built on the coulombic
interactions of
the CNDO Hamiltonian....

******** 
-- 
Didier MATHIEU
CEA - Le Ripault, BP 16
37260 Monts (France)
Tel. 33(0)2.47.34.41.85