# FEP triangular bracket average

From: Mert Gür (gurmert_at_gmail.com)
Date: Sat Apr 26 2008 - 05:56:26 CDT

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:

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.*
**