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From: Adrian Roitberg <roitberg.qtp.ufl.edu>

Date: Wed, 02 May 2007 09:26:30 +0200

James W wrote:

*> Dear all ,
*

*> #the reference : (http://en.wikipedia.org/wiki/Jarzynski_equality)
*

*> I confused the Jarzynski's equality . The equality is shown:
*

*> exp (-F/KT) = < exp (-W/KT) > .
*

*> &
*

*> F = < W > + ......
*

*> I used SMD module of CHARMM and obtained the reaction coordinates &
*

*> work ,like this :
*

*> ______________________________________________________
*

*> 57.00000 57.73576 -1471.51842 0.00000
*

*> 57.00093 57.34648 -691.10171 -1.00562
*

*> (RC) (WORK)
*

*> *RC : reaction coordinates
*

*> I wanted to obtain the " < W > " form my data . My method is :
*

*> 1. S = sum { exp (-W(i) /kT )} , i = 1 ....N
*

*> 2. p(i)= exp (-W(i) /kT ) / S
*

*> 3. <W(i)> = W(i)*p(i) / S
*

*>
*

*> Could you tell me that my method is right ?
*

James,

I am not sure I fully understand your question, because you do not

mention what the subindex i is in your formulas.

Now, the formula from wikipedia is basically right, except for a couple

of comments.

First, it must be clear that F is really \Delta F. This is designed for

free energy differences and NOT absolute free energies. Second, the

exponential average of work values is over a set of runs, ALL starting

from an equilibrated ensemble at a certain value of the coordinates (s)

to be changed. The average then involves MANY runs.

The second line F = < W > + ...... is a cumulant expansion of

exponential average. I do not recommend using using this unless you

really know what you are doing.

Your formulas on how to implement this are not quite right.

If you are thinking about the index i meaning time steps on one

simulation, then it is not right.

The subindex i should refer to the same distance and DIFFERENT simulations.

Once that is done:

1. S = ( sum { exp (-W(i) /kT )}/N) , i = 1 ....N

2. \Delta F = - kT ln(S)

I hope this makes things a bit clearer.

Adrian

Date: Wed, 02 May 2007 09:26:30 +0200

James W wrote:

James,

I am not sure I fully understand your question, because you do not

mention what the subindex i is in your formulas.

Now, the formula from wikipedia is basically right, except for a couple

of comments.

First, it must be clear that F is really \Delta F. This is designed for

free energy differences and NOT absolute free energies. Second, the

exponential average of work values is over a set of runs, ALL starting

from an equilibrated ensemble at a certain value of the coordinates (s)

to be changed. The average then involves MANY runs.

The second line F = < W > + ...... is a cumulant expansion of

exponential average. I do not recommend using using this unless you

really know what you are doing.

Your formulas on how to implement this are not quite right.

If you are thinking about the index i meaning time steps on one

simulation, then it is not right.

The subindex i should refer to the same distance and DIFFERENT simulations.

Once that is done:

1. S = ( sum { exp (-W(i) /kT )}/N) , i = 1 ....N

2. \Delta F = - kT ln(S)

I hope this makes things a bit clearer.

Adrian

-- 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 adrian.qtp.ufl.edu ============================================================================ To announce that there must be no criticism of the president, or that we are to stand by the president right or wrong, is not only unpatriotic and servile, but is morally treasonable to the American public." -- Theodore Roosevelt ----------------------------------------------------------------------- The AMBER Mail Reflector To post, send mail to amber.scripps.edu To unsubscribe, send "unsubscribe amber" to majordomo.scripps.eduReceived on Sun May 06 2007 - 06:07:03 PDT

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