Re: Convergence of the Gram-Charlier expansion

From: Chris Chipot (chipot_at_ks.uiuc.edu)
Date: Sun Sep 30 2012 - 11:46:58 CDT

Khanlarkhani,

you can restate your free energy change,

as

where /g/(?/U/) is a Gaussian distribution and /H_n /(?/U/) are Hermite
polynomials.

The farthest you are from second-order perturbation theory, the slower the
convergence of your Gram-Charlier expansion.

As for the order, it is pretty much system dependent. Charging a van der
Waals particle will evidently be pretty quick.

Chris Chipot

On 9/30/12 5:34 PM, Ali Khanlarkhani wrote:
> The following sentence come from "ParseFEP Plugin, Version 1.5" manual:
> "Convergence of the Gram-Charlier expansion at a given order
> represents a relevant measure of how well-defined the probability
> distribution is."
> What does it mean? convergence at what order is good?
>
> Khanlarkhani

-- 
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Chris Chipot, Ph.D.
Theoretical and Computational Biophysics Group
Beckman Institute
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