# [gmx-users] How do I calculate the difference between two energy values?

Peter Stern peter.stern at weizmann.ac.il
Thu Aug 27 11:55:04 CEST 2015

```Indeed:
Sqrt(0.23**2+1.31**2)=1.33

-----Original Message-----
From: gromacs.org_gmx-users-bounces at maillist.sys.kth.se [mailto:gromacs.org_gmx-users-bounces at maillist.sys.kth.se] On Behalf Of Johnny Lu
Sent: Thursday, August 27, 2015 3:31 AM
To: gmx-users at gromacs.org
Subject: Re: [gmx-users] How do I calculate the difference between two energy values?

Let x(t) be coulomb decoupling at time t.
Let y(t) be VdW decoupling at time t.

I guess the most safe way to get the answer is:
calculate z(t) = x(t) + y(t)
then, calculate standard deviation of z(t).

If x(t) and y(t) are independent and both x(t) and y(t) are normally distributed, then I guess using the error propagation rule is fine.
(https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables)

On Tue, Aug 25, 2015 at 2:15 PM, Peter Stern <peter.stern at weizmann.ac.il>
wrote:

> I believe that this is a statistics question and not a gromacs
> question :-).
>
> 51.4 +/- 1.33 kJ/mol
>
>
> > On 25 באוג׳ 2015, at 14:44, minky son <minky0710 at gmail.com> wrote:
> >
> > Dear GROMACS users,
> >
> > I have been studying free energy calculation in Justin tutorial.
> >
> > I performed VDW decoupling and coulomb decoupling simulations separately.
> >
> > I obtained the free energy values for each simulation using gmx bar.
> >
> > coulomb decoupling simulation = 60.88 +/- 0.23 kJ/mol VDW decoupling
> > simulation= -9.48 +/- 1.31 kJ/mol
> >
> > So, I want to calculate the sum of the two energy values,
> >
> > specially the second term (51.4  +/- ???).
> >
> >
> >
> > Regards,
> > --
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