[gmx-users] Computing free energy differences from the dH/dl values directly

Miguel Caro miguel.caro at aalto.fi
Thu Jul 20 12:47:23 CEST 2017


I want to do thermodynamic integration directly from the ∂H/∂λ\partial H
/ \partial \lambda values in the md.xvg files, rather than using gmx
bar, because I want to do several manipulations (eventually). On the
tutorial on solvated methane how to use gmx bar is explained, however
this is a black box tool so I would like to understand a bit better what
it's doing and how it handles the raw derivatives.

I have a system (one methanol solvated in water) where I decouple
Coulomb interactions before decoupling vdW interactions. The md.xvg
files give me ∂H/∂λvdW\partial H / \partial \lambda_{vdW} and
∂H/∂λcou\partial H / \partial \lambda_{cou}, and so I am
computing ⟨∂H/∂λ⟩=⟨∂H/∂λvdW⟩∂λvdW/∂λ+⟨∂H/∂λc⟩∂λc/∂λ\langle \partial H /
\partial \lambda \rangle = \langle \partial H / \partial \lambda_{vdW}
\rangle \partial \lambda_{vdW} / \partial \lambda + \langle \partial H /
\partial \lambda_{c} \rangle \partial \lambda_{c} / \partial \lambda "by
hand".  I am then using a spline to generate smoother curves in λ\lambda
from the discrete array (21 data points, one for each λ\lambda value) of
the expectation values. I then integrate this smooth curve, although I
guess I could also use a quadrature rule applied to the original data
before smoothing. The final free energy difference I obtain like this is
about 5% larger than the value given by gmx bar.

I would like to know if what I am doing makes sense and if the
difference with gmx bar is to be expected (for instance because of how
the integral is performed or some other fundamental difference).

Many thanks,



*Dr. Miguel Caro*
/Postdoctoral researcher/
Department of Electrical Engineering and Automation,
and COMP Centre of Excellence in Computational Nanoscience
Aalto University, Finland
Personal email: *mcaroba at gmail.com*
Work: *miguel.caro at aalto.fi*
Website: http://mcaroba.dyndns.org

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