# [gmx-users] Re: Re: Re: Re: Which/What is the adequate overlap

Mike Nemec mike.nemec at stud.uni-due.de
Wed Jul 10 13:13:46 CEST 2013

```Hi Thomas,

> Hi Mike,
>
> Your confusion might stem from a very simple issue.
> To see the overlap of the forward and backward distributions,
> you have to plot
>
>  N(+Delta H(lambda=x) | lambda=y) and
>  N(-Delta H(lambda=y) | lambda=x).
>
Do I understand it right, that for instance (consider lambda step = 0.5)
ONLY
N(+Delta H(lambda=0) | lambda=0.5) AND N(-Delta H(lambda=0.5) |
lambda=0)
has to overlap, and then
N(+Delta H(lambda=0.5) | lambda=1) AND N(-Delta H(lambda=1) |
lambda=0.5)
has to overlap, to get an accurate estimation of the free energy
difference, and not (essentially) other distributions? An example would
really help me out of my confusion :(

> That is, you have to plot the histogram for the negative of the energy
> difference samples in the backward direction.
>
And is it right, that N(-Delta H(lambda=y) | lambda=x) equals N(+Delta
H(lambda=y) | lambda=x) if I
simply mirror the distribution at the y-axis?

> See also the original paper of Charles Bennett for an explanation of
> the overlap and how it is measured.
>
I read the original paper a couple of times, and I understand, that the
squared value of the standard deviation (eq 11) measures the overlap.
And according to Fig.5, I understand, that the (complementary) fermi
functions have to show an overlap and that in principle the method
calculates the perturbation between A -> B via a shifted state by a
constant C in between. But I cannot bring it to the context of the g_bar
output
N( Delta H(lambda=x) | lambda=y).

How are the fermi functions and the constant C related to N( Delta
H(lambda=x) | lambda=y) in detail?
Or did I miss the definition in Bennett's paper, where is said, which
distributions in detail have to overlap and how they are defined?

> Best,
> Thomas.
>
> ---------------------------------------------------------------------------------
>
> R. Thomas Ullmann, PhD
> Theoretical & Computational Biophysics
> Max Planck Institute for Biophysical Chemistry
> Am Fassberg 11
> Göttingen, Germany
> thomas.ullmann at mpibpc.mpg.de
> www.bisb.uni-bayreuth.de/People/ullmannt
> ---------------------------------------------------------------------------------
>
>
>
Thank you for any help,

Mike

```