Solving 1D Poisson equation

Code: download the script here

-equation.pdf : the equation I used with the normalization parameters

-script.sh : just an awk command to remind how to use the script. If you run it, the example should work and you will produce the file  smooth_charges.dat.

-param_smooth.dat : the first line contains the cell parameters. The second line contains the position on the z-axis where to "fold" the cell since it is symmetric

-ACF.dat and dati-bader.dat you obtained with your Bader calculations.

-smooth_charges.awk : the awk script which does all the analysis.

1) Right now, there are only the atoms H, Na, O Cl, Pt which are defined.

2) The script produces 1 file with 24 sets of data with 9 columns each.

The general header of the file allows to understand what is the point of each column (z-axis, atom contribution and linear combination of the atomic charges)

There is a header for each set in order to explain what it is. There are the units for all the sets so you cannot do any error. 

When we wrote the article, we took the sets :

*number 4 "#Density charges (e.Ang-3) : electrons + core"

You calculate the difference between the electric charge and the nuclear charge. Then you add some Gaussians and you normalize by the volume.

*number 20 "#Electrostatic potential (e.Ang-1) : electrons + core (Water ref1, Pt ref2)"

You integrate first with water as reference in order to have an electric charge at 0 in bulk water. Then you integrate a second time taking Pt as reference in order to have an electrostatic potential at 0 in Pt bulk.