On Mon, Jun 10, 2013 at 2:25 PM, Sajeewa Pemasinghe <sajeewasp.gmail.com>wrote:
> Hi all,
>
> I have a question on umbrella sampling. The problem is in the calculation
> of "Vi(Xj)" i.e. the harmonic potential of window # i in bin # j.
> There may be more than one point in bin # j that belong to window # i. In
> such a case
>
>
> 1) do we calculate the harmonic potentials for each point in bin # j with
> respect to the center of the window # i and then add them together and call
> it "Vi(Xj)"
>
> OR
>
> 2) do we calculate the harmonic potential for the center of the bin # j
> with respect to the center of the window # i and call it "Vi(Xj)".
>
> I think the former is better. I would like to have your expert opinion on
> this matter.
>
I admit that the question itself confuses me. "Binning" is only part of
post-processing umbrella sampling results, but that is done as part of the
MBAR or WHAM analysis that you do to compute the final PMF. (Note that not
all methods for constructing the PMF require histograms or binning).
As far as setting up windows to carry out umbrella sampling simulations,
there is no 'binning'. Windows in umbrella sampling differ based on where
you put the center of the umbrella---there is no reference to what 'bin'
you are in.
To me, Vi(Xj) just means the energy of the conformation given by the
position vector 'j' in window 'i' (which is the Hamiltonian plus a harmonic
restraint centered at r_i on the reaction coordinate).
In umbrella sampling, the force exerted by the umbrella itself is
continuous, and evaluated according to the simple harmonic potential
k(x-x0)^2, where x0 is the center of the umbrella. The force due to the
umbrella is computed as the gradient of this function (x-x0 itself is a
vector quantity with both magnitude and direction, and so too is its
gradient).
Hopefully this either answers your question or helps in some way,
Jason
--
Jason M. Swails
Quantum Theory Project,
University of Florida
Ph.D. Candidate
352-392-4032
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Received on Mon Jun 10 2013 - 20:30:03 PDT
