scale the potential in compute ti

Hi everyone,

I would like to calculate the free energy of L-J fluid using compute ti. If I scale the potential as U(lambda)=lambda*U_LJ, then in lammps, the value will be calculated as U(lambda) / lambda * lambda’=U(lambda) / lambda. I am some confused why U(lambda) / lambda is related with lambda? because I think U(lambda) should be proportional to lambda.

Thank you!
Alvin

Hi everyone,

I would like to calculate the free energy of L-J fluid using compute ti.

​what *kind* of free energy? there are many kinds.​

If I scale the potential as U(lambda)=lambda*U_LJ, then in lammps, the
value will be calculated as U(lambda) / lambda * lambda'=U(lambda) /
lambda. I am some confused why U(lambda) / lambda is related with lambda?
because I think U(lambda) should be proportional to lambda.

​have you ever heard of a thing called the chain rule?​ remember that
compute ti provides the derivative.

axel.

Hi Axel,

Thank you for your reply! I want to calculate the Helmholtz free energy in NVT ensemble. Yes, I understand the chain rule. if U(lambda)=lambdaU_LJ, then d U(lambda) / d lambda = d (lambdaU_LJ) / d lambda = U(lambda) / lambda * lambda’ = U(lambda) / lambda. Can U(lambda) / lambda be written as U_LJ, if so, why the derivative dU(lambda) / d lambda is related with lambda?

Thank you!
Alvin

Hi Axel,

Thank you for your reply! I want to calculate the Helmholtz free energy in
NVT ensemble.

​this is not the answer that i am looking for. you want to know the free
energy of what process?
since absolute energies are meaningless here, you can only compute free
​energy *differences*, but for that you need multiple states to start from
and end up at.

Yes, I understand the chain rule. if U(lambda)=lambda*U_LJ, then d
U(lambda) / d lambda = d (lambda*U_LJ) / d lambda = U(lambda) / lambda *
lambda' = U(lambda) / lambda. Can U(lambda) / lambda be written as U_LJ, if
so, why the derivative dU(lambda) / d lambda is related with lambda?

​i cannot follow the logic of your argument. you seem to be missing the
point that you are trying to compute a *free* energy from a *potential*
energy and that you are taking an ensemble average.

perhaps, if you look at the expression here, it will become more obvious to
you: http://en.wikipedia.org/wiki/Thermodynamic_integration

axel

Yeah! I know where I am wrong! Thank you!

Alvin