# CCL: Determine statistical distribution of chemical species based on
energi

*From*: Billy McCann <thebillywayne!=!gmail.com>
*Subject*: CCL: Determine statistical distribution of chemical
species based on energi
*Date*: Tue, 9 Jun 2015 12:05:18 -0400

Sent to CCL by: Billy McCann [thebillywayne(a)gmail.com]
>Can you determine theoretical statistical distributions of these states
based on energies calculated by DFT or ab initio calculations?
Yes. It's quite simple, actually. You'll want to calculate the free
energy of the conformers, etc. and then find the Boltzmann
distribution. See the above responses for details into partition
functions and the rest. Typically your software will calculate these
and have them in the output file.
https://en.wikipedia.org/wiki/Boltzmann_distribution
>Which types of energies would you need?
Free energies. Be sure to convert the free energies to the desired
standard state.
>How would you do it?
See equation 10.49 in Cramer's book, Essentials of Computational Chemistry.
I was looking at some point in my research to get more precise
calculations by finding the Gibb's free energy of an equilibrium
population.
I wrote a python script to compute the relative populations.
It can be found here. https://gist.github.com/thebillywayne/47d77ea6b0e03b245144
Take note that if you have degenerate states, you simply feed them
into the script twice.
I also have a script that calculates the inverse, that is, starts with
the abundances and calculates the free energies.
Note that these populations are calculated at 298K. Change the RT
variable if you want a different temperature.
It's always a little nerve racking to share code with a broad
community. But I welcome feedback.
--
Billy Wayne McCann, Ph.D.
http://bwayne.sdf.org
irc://irc.freenode.net:bwayne