Re: AMBER: Jarzinsky relationship

From: Adrian Roitberg <>
Date: Mon, 05 May 2008 11:13:51 -0400

The computed work is OF COURSE dependent on the velocity ! It must be,
or the whole apparatus of thermodynamics break down.

At infinitely slow pulling velocity, the work is exactly equal to the
free energy for the process.
For ANY finite velocity there is dissipative work, and its value
increases in a non-trivial way with the pulling speed.

The application of the Jarzinsky relationship is supposed to fix that.
There are tons of references, but you can try reading:

"Free Energy calculations with non-equilibrium methods. Applications of
the Jarzynski Relationship”. Hui Xiong, Alejandro Cresp, Marcelo Marti,
Dario Estrin and Adrian E. Roitberg. Theoretical Chemistry Accounts.
106(1-3): 338-346 (2006)

You will need to run MANY independent simulations pre-equilibrated with
a restraint at the original distance. Then you do an exponential average
of the work (at the proper temperature).

Please make sure you applied bugfix.32 to the amber 9 code if you are
pulling more than 100 angstroms.


PS: for ULTRA experts, there is a correction one can do to the whole
Jarsynki relationship, defined by Szabo and Hummer in PNAS around 200)
or 2001. Do not touch if you are not really familiar with the process
already !

E.M. wrote:
> Hello A
> I am scared....that means that the computed work is dependent on the
> velocity applied
> which sounds strange to me....there should be a way to factor out the
> work done by
> the biasing force.
> I ran various tests and it turns out that the higher the rate of motion
> of the force,
> the higher the work I get, . . . Is that correct?.
> The free energies I am computing should be flat at the end, but instead
> it looks as
> if the biasing work has to be subtracted.
> puzzled E.
> Adrian Roitberg wrote:
>> E.M. wrote:
>>> Hello,
>>> I am doing some pulling experiments using Jarzinsky's relationship,
>>> the output file using AMBER9 is something like
>>> x xo whatever work
>>> My question is, do I have to substract the biasing potential after I
>>> get the output
>>> or that is taking care of by the program?. I just want to make sure
>>> I understand
>>> what is going on here.
>>> Regards
>>> E.M.
>> Hi,
>> The 'wathever' in the list is the crucial factor, in fact it is the
>> only one one computes !
>> It is the external force applied by the external spring (as defined in
>> the input file). Basically, it is k*(x-x0)
>> Work is the integral of that force over the run, so there is no need
>> to subtract the biasing potential. The subtraction would be needed
>> only if work was computed from the spring energy, which is not.
>> a.
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                            Dr. Adrian E. Roitberg
                              Associate Professor
               Quantum Theory Project and Department of Chemistry
University of Florida                         PHONE 352 392-6972
P.O. Box 118435                               FAX   352 392-8722
Gainesville, FL 32611-8435                    Email
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Received on Wed May 07 2008 - 06:07:24 PDT
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