# [gmx-users] (dH/dl) calculation

Thu Nov 9 17:51:38 CET 2006

```Dear David and Mauricio,

I am also confused about the details of dgdl (or dHdl) calculation in
GROMACS. For example, if the lambda is fixed at certain value, how did the
program determine dHdl?
My initial understanding was kind of similiar to that of Mauricio that dHdl
equals the difference in total potential energy between two time frame
(snapshots). However, this seems does not make sense when lambda is fixed.
Could you give more details about the calculation of the derivative dHdl at
each snapshot? Thank you.

Best regards,

Lei Zhou

On 11/6/06, David Mobley <dmobley at gmail.com> wrote:
>
> Mauricio,
>
> I'm somewhat confused by your question and notation. However, I think
> the basic answer is something like this: In molecular dynamics, you
> know the Hamiltonian from which you are sampling; call it H(x,p, l),
> where x denotes all of the positions, p the momentums, and l lambda.
> This, of course, is closely linked to the potential energy. Anyway, at
> any snapshot, you can simply take the derivative dH(x,p,l)/dl, and you
> have dH/dl at that snapshot. This is usually straightforward since you
> know the dependence of all of the terms in your Hamiltonian on lambda,
> so you actually have the functional form for dH/dl as well -- so it
> just involves taking the appropriate combination of positions,
> momentums, etc. This is of course all handled internally by the code.
> <dH/dl>, then, is just the time-average of dH/dl, which can be
> evaluated every step by the code.
>
> I am not sure if that's helpful at all, as I'm not entirely sure what
> problem you're having. After all, whenever you do TI calculations in
> GROMACS, the code gives you back dG/dl (or dH/dl, or dA/dl) for every
> snapshot in an xvg output file. Are you just confused about how the
> code gets this (I think I just answered that above), or are you trying
> to figure out how to use it? If you're confused about how to use it,
> try to ask a question that relates to the specific issue you're
>
> Best wishes,
> David Mobley
> UCSF
>
>
> On 11/5/06, Mauricio Sica <msica at unq.edu.ar> wrote:
> > Dear experts
> >
> > I am doing FEP (thermodynamic integration method) simulations.
> > I have a questions about <dH/dl> calculation in GROMACS.
> > Take in mind equation 3.77 from the GROMACS 3.3 manual.
> > There, dA/dl is calculated as
> >
> > dA/dl = SS{ (dH/dl) exp()dp dq } / SS{ exp()dp dq = <dA/dl>NVT;l }
> >
> > where SS are doble integrals (sorry for the notation).
> >
> > My question is: how is (dH/dl) (in the middel-term of the equation)
> > calculated?
> > My idea is that the difference V(L=1)-V(L=0) is calculated for every
> time
> > step (irrespective of the lambda value of the simulation) and <dG/dl> is
> > the time average of that difference.
> >
> > <dG/dl> = < V(L=1)(i)-V(L=0)(i)/1 >
> >
> > Is this correct?
> >
> >
> > Thanks
> >
> >
> >
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