# Re: FEP triangular bracket average

From: Jerome Henin (jhenin_at_cmm.chem.upenn.edu)
Date: Sat Apr 26 2008 - 11:30:37 CDT

Mert,

As you say, no combination of energy values sampled from independent
simulations in states A and B will give you the average in state A
that is needed for FEP.

Instead, to evaluate the FEP average, both energy functions A and B
(or at least their difference) should be computed on-the-fly during a
single simulation in state A. The alchemical free energy feature of
NAMD does just that. Calculation of both potential energy functions is
made possible by providing a "hybrid" topology that describes two
chemical systems at once.

Best,
Jerome

On Sat, Apr 26, 2008 at 6:56 AM, Mert Gür <gurmert_at_gmail.com> wrote:
> Dear all,
>
> I have a problem understanding the theory of free energy perturbation
> method. I have read several papers and have also read the alchemical free
> energy perturbation tutorial.
>
> As explained very simply at this link:
>
> http://en.wikipedia.org/wiki/Free_energy_perturbation
>
> the triangular brackets denote an average over a simulation run for state A.
> In practice, one runs a normal simulation for state A, but each time a new
> configuration is accepted, the energy for state B is also computed.
> Let say I have run a simulation for state A in NAMD and a simulation for
> state B in NAMD.
> I now have energy values for each snapshot of A and B. So I actually have
> the distribution (probability) function for A and B seperately.
> If I havent understand it wrong, MD already gives me the Boltzman
> distribution so that I have just to take the simple average (sum/N) of any
> property I have recorded at N snapshots. By doing so I have the triangular
> bracket average.
> How do I perform the same for <E(A)-E(B)>A (definition given in the link).
> I mean do I simply subtract each energy value I record at each snapshot for
> B, from the energy value I recorded for A.
> If I do so I dont see how it becomes the average over a simulation run for
> state A.
>
> Thanks in advance,
>
> Mert Gur
> Computational Science and Engineering
> Koc University
> Istanbul/Turkey

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