Subject: Re: CCL:Development of new Force Fields

From: [email-masked] (Ming-Jing Hwang)
Date: Tue, 3 May 94 08:42:58 -0700

Frank Jensen wrote:

>...Why not simply select say, a Morse potential
>instead? The Taylor expression contains four parameter 
>(r0 and a,b,c), the Morse only three. ...

One reason, a practical one, to use power series instead of Morse function 
is to make parameterization easier when using quantum mechanical energy data.  
With a power series the entire energy function (i.e. force field) becomes 
linear with respect to the force field parameters (force constants) which 
are being sought, when reference values (bond and angle references) and 
nonbond parameters are held fixed.  The parameters (k1, k2, k3, etc.) can 
then be solved analytically with one matrix operation.  New bond and angle 
references can be projected from the linear force constants (k1) just solved, 
and optimal references (the so called "natural" bond lengths and bond 
angles of the hypothetical "unperturbed" state on the hypersurface of the 
training set molecules) can be obtained within a few iterations (when all 
the linear force constants vanish or are essentially zero).  This advantage of 
using the linear-least-squares fitting is lost if a Morse potential
is used.  Note also there is no structure minimization during the 
paramterization since the data fitted are direct energy surface properties 
(configurational energy differences, and energy 1st and 2nd derivatives, 
etc. from ab initio calculations) and not the geometric parameters 
(equilibrium bonds, angles, and torsions) or vibrational frequencies 
commonly used in the traditional methods.  This facilitates automation 
of many parts of the parameterization procedures in the derivation 
of CFF93 force field.  Efficient fitting procedures make it
possible to use large amount of quantum mechanical data to fit detailed
(Class II) force fields and obtain reliable results.

Ming-Jing Hwang
[email-masked]