Subject: Re: CCL:Fitting point charges to ESP with Spartan

From: Konrad Hinsen <[email-masked]>
Date: Mon, 4 Nov 96 09:35:49 +0100

> Do you have a reference or some corroborating evidence for your remarks
> regarding CHELPG?  Do you believe the same is true for CHELP?

Yes, there is no difference as far as the actual fitting procedure is
concerned. CHELP and CHELPG differ only in the selection of evaluation
points for the potential.

As for the potential instability, CHELP and CHELPG find the
least-squares fit by solving the so-called "normal equations". Any
text book on matrix computations or least-squares fitting will explain
in detail why this approach is unstable for all but trivial problems.
Essentially, the matrix describing the least-squares problem is
ill-conditioned, and forming the normal equations aggravates this
problem by effectively squaring the condition number. A much better
approach is to use singular value decomposition.

There was a paper in J. Comp. Chem. earlier this year (I think March)
that demonstrated the problem for charge fitting. I don't agree with
all its conclusions, but it clearly shows the risks of normal-equation
based solution schemes.
-- 
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Konrad Hinsen                          | E-Mail: [email-masked]
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