Date: Tue, 11 Jun 2013 00:11:15 -0400
Hi Jason,
I am really sorry. I had a made a mistake. Here I am talking about WHAM and
not umbrella sampling. That was a bad mistake. I am really sorry. I have
attached the equation I am referring to (as a .png file). In this equation
rho(epsilon j) = optimum unbiased probability for bin j
Nw = number of windows
n subscript ij = number of snapshots in bin j that belong to window i
f subscript i = exp[beta*Fi]
Vi(epsilon j) = the harmonic potential of bin j with respect
to window i
So my question still is about calculating "Vi(epsilon j)"
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(epsilon j)"
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(epsilon j)".
I really appreciate your response. If you could advise me as to either it
is 1) or 2) or a different way that is used to calculate Vi(epsilon j)
, that would really help me. Because I am going to code this up.
Thank you very much
Sajeewa Dewage
On Mon, Jun 10, 2013 at 11:14 PM, Jason Swails <jason.swails.gmail.com>wrote:
> 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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(image/png attachment: wham1.png)
