Subject: SUMMARY Charge Equilibration

From: "J. Fleischhauer" <[email-masked]>
Date: Wed, 10 Jan 1996 18:09:36 GMT+1

Dear CClers,
Some time ago I posted a question concerning the <charge 
equilibration> (QEq) of Rappe and Goddard. Thanks to all who replayed
I received the following  answers :

=====================================================================
My original question :

Dear Netters

In our approach to describe charge influences in Force Field 
calculations, we want to try the an empirical method so called 
<charge equilibration> (QEq), described in 
A. K. Rappe, W. A. Goddard, J. Phys. Chem., 95, 3358, 1991.
This method is also available in the commercial CERIUS2 package.

Our problem is that there is no detailed description of the 
algorithm. 
Does anybody knows other sources of information dealing with the 
charge equilibration algorithm?

Especially we can't find an mathematical expression used for the 
calculation of the coulomb potential between center A and B = Jab(R). 

The Problem is the following :
The simple coulomb expression between unit charges on center A and B 
separated by the distance R is :

(14)                     Jab(R) = 14.4 / R

14.4    conversion factor, R in Angstroem, Jab in eV

Equation (14) is no longer valid for atoms with overlapping charge 
distributions (e.g. mostly bonded atoms). For R = 0 (14) leads to an 
infinite value whereas Jab(R=0) should reach a finite value Jaa 
instead. Like described in the reference, they use a shielding 
corrections to (14). The shielding to (14) will be quite large for 
bonded atoms (small R). The shielding correction to (14) were 
described in terms of a coulomb integral between atomic densities 
witch are expressed in form of slater orbitals. (eq.15)

(15)              Phi_slater = Nn * r power( n-1 ) * exp(-zeta*r) 

Nn      normalisation Constant
n       long periodic row
zeta    Slater Exponent
r       distance

The diatomic Coulomb integral Jab is evaluated exactly.

Our question :

1) Witch is the correct mathematical expression to describe the 
   coulomb interaction Jab(R) to get a potential with a finite 
   value for R=0 ?

==================================================================
First answer:

> Dear Juergen,
> I don't have the reference at hand. but what I think they did is 
> just integrating the expression.
> Also take a look the following reference:
> | AUTHOR: Rick, S. W.; Stuart, S. J.; Berne, B. J.
> | TITLE: Dynamical fluctuating charge force fields: Application to
> |              liquid water
> | JOURNAL NAME: The Journal of chemical physics.
> |     VOL, ISSUE: Volume 101, Number 7
> |     PAGES: 6141
> | YEAR: 1994
> They used the Rappe & Goddard approach and did what I said above 
> (eqn 2.11, in the rick et al 
> article)
> Hope this helps,
> Paul van Maaren

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

In the above article they describe the form of the coulomb overlap 
integral as follows :

Jab(r) = INT dri drj |SQR(Phi_slater_ni(ri) )| * 1 / (ri -rj -r) * 
                     |SQR(Phi_slater_nj(rj) )|
                     
ni, nj      principal quantum number eg. H = 1, O = 2 .. 
INT         means integral 
Phi_slater_ni, Phi_slater_nj see  above Phi_slater

The problem is now the mathematical solution of the integral. 
Does anybody knows it  ??????????????????? 

==================================================================
Second answer:

> Hi!
> I would be interested in the summary to your request. I tried 
> implementing this algorithm on 
> my own several years ago, but ran into many problems. Most annoying 
> is that certain atomic 
> parameters were not included in the paper and have never been 
> published in the literature ( as of > that time!).
> Good Luck!
> Gustavo A. Mercier, Jr. M.D.-Ph.D.

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

Indeed, I found in the CCL archive the following question, but 
without any answer :
>From the CCL Archive :

Date: Sun, 13 Jun 1993 08:38:16 -0400 (EDT)
From: Gustavo Mercier 
Subject: Goddard's Modified Mulliken - Pauling electronegativities 
To: [email-masked]
Message-Id: <[email-masked]>

Hi, Netters!
Does any body know the reference for the Mulliken - Pauling 
electonegativities as Modified by Rappe and Goddard for the 
construction of charges using the Charge Equilibration Method?
The Charge Equilibration Method generates charges for MM/MD 
simulations that depend on the atomic geometry without having to 
perform QM computations. Ref: Rappe and Goddard (1991) J. Phys. Chem. 
95, 3358-3363. In this paper they refer to a modified set of 
electronegativities necessary for the computations (see ref. 9, Rappe 
and Goddard Generalized Mulliken -Pauling Electronegativities. I. 
Main Group Elements (Groups 1, 13-17). J. Phys. Chem., submitted for 
publication.). A subsequent paper describing their UFF potential 
(UFF=Universal force field; ref: Rappe et. al. (1992) JACS 114, 10024-
10035), also makes reference to the GMP electronegativities, but 
again states "submitted for publication". I cannot find the reference 
in SCI. 
Was it ever published? 

Gus Mercier,jr

It is interesting to know, that the < 1991 Annual Report of the 
Materials & Molecular Simulation Center from Beckman Institute, 
California Institute of Technology > refers 

3) G. H. Miller, N. Karasawa and W. A. Goddard III. Charge 
   Equilibration for Crystals, to be submitted

4) a) Rappe and Goddard III , Generalized Mulliken -Pauling 
      Electronegativities. I. Main Group Elements. J. Phys. 
      Chem., submitted for publication.) and  
   b) Rappe and Goddard III , Generalized Mulliken -Pauling 
      Electronegativities. II. Transition  Metals, Lanthaanides,
      Actinides, and Groups 2, 12, and 18 ,  J. Phys. Chem., 
      submitted for publication.)
      
The Director and one of the authors of the report is W. A. Goddard 
III.

An extensive search in the CA database for this articles or any other 
publication of the authors and the charge equilibration algorithm was 
without a hit. It seems the above references where never published. 
This means that only parameter for 16 elements were published (A. K. 
Rappe, W. A. Goddard, J. Phys. Chem., 95, 3358, 1991.)
So I wrote an E- Mail request to W. A. Goddard III., more than 2 
months ago, dealing with our problems with the charge equilibration 
algorithm but there was no responce.

I wrote that charge equilibration is also available in the commercial 
CERIUS2 and POLYGRAF software packages. In the case of CERIUS2, there 
is a parameter file in /home/msi/cerius2_dir/res/CHARGE/QEq_neutral . 
(cerius_dir depends on the version , may be cerius2_1.6.2) 
If you are a CERIUS2 user it would be nice to have a look to the 
file, it contains parameters for all elements of the periodic system. 
In the case of POLYGRAF there should be a equal one.

J. Fleischhauer

======================================================================
Third answer

> I am also interested in implementing this method.  Would you please 
> send me a copy of any replies you receive.  
> Thank you,
> Patrick Walters

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

Any further comments are welcome

Thanks,
    
    Juergen Fleischhauer

_________________________________________________

Dipl. Chem. Juergen Fleischhauer

Technical University Clausthal
Dept. of Technical Chemistry
Erzstr. 18
D-38678 Clausthal Zellerfeld
Germany

Tel.    : 05323-72-2647
Fax.    : 05323-72-3655
E-Mail  : [email-masked]
__________________________________________________