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From: kynn ^%at%^ panix.com
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Date: Sat, 20 Nov 1999 10:14:07 -0500 (EST)
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To: CHEMISTRY&$at$&ccl.net
Subject: Restraining potentials for umbrella sampling





In all accounts of umbrella sampling I've seen, the restraining
potentials, when given, are invariably harmonic in the reaction
coordinate.  However, it would be computationally cheaper (specially
when the simulation method requires computing forces) to make this
potential flat in the region of interest.  I.e.,

		(x - x0)^2, if |x - x0| > h
	V(x) =
                h^2,        if |x - x0| <= h ;

This potential V is flat if the reaction coordinate x lies in the
interval [x0 - h, x0 + h], and grows quadratically otherwise.  (Linear
"walls" instead of quadratic ones lead to other problems, because they
don't penalize far-out conformations sufficiently unless one makes the
walls practically vertical; this would preclude even minor excursions
out of the window, which would be undesirable, since such excursions
may sometimes be necessary to adequately sample the desired window.)

Does anybody know of any serious drawback with the "flat-bottom"
scheme described above?

Thanks

KJ