# CCL: Amber free energy equation

From: Daquan Gao <d0gao001.gwise.louisville.edu>
Date: Tue, 17 Jun 2003 12:33:39 -0400

Dear CCLers or AMBER users:

Having a question about the equation with free energy perpurbation:

The equation is , among other variations:

Delta G = -kT ln <exp(-(H(lambda + d lambda) - H (lambda))/kT) >

Now in gibbs, I used nstlim = 1, nrun = 100, almdel =0.01, isldyn = -3.

The reason I used nstlim =1 is I wanted to test the equation.

The isldym = -3 means I have a starting state at lambda = 1.0, and a
final state of lambda =0.0 which is when the ligand disappears.

Now my questions:

After the first nrun, there is still only one set of energies, (either
Etot or EPtot or something other terms.). There is already a free energy
for "reverse" given. How was this achieved? There has not been any
energy differences yey.

At nrun = 2, I have lambda = 0.99, the previous state is lambda = 1.00.
Now I have two sets of energies, I would be able to get a delta H =
H(0.99)- H(1.00). This is the ansemble average, since there is only one
such delta H! But the result is not that number. I don't understand the
number given in gibbs in that stage.

What exactly is the equation that is being used in gibbs?

I have looked at the references, all says the above equation. Only
Amber7 mentioned a reference by Brooks in JCP. It looked a little
different, but only added DS and DE terms. Don't you get DG direcly from
the above eqution?