Quantum Theory of Atoms in Molecules (QTAIM)

The topology of the electron density is analysed by mathematical methods
The first derivative of the electron density is the gradient vector field
Zero of the gradient vector field determines critical points in the electron density
To characterize these critical points the curvature is used.

AIMALL
http://aim.tkgristmill.com/download/download.html
(Linux, MacOS, Windows)
or on aurora /lunarc/nobackup/projects/snic2019-35-66/Justin/programs/AIMAll/aimstudio.ish
aimall on Aurora

Non-covalent interactions (NCI)

• Documentation for the program can be found here:
  https://www.lct.jussieu.fr/pagesperso/ contrera/nciplot.html
  If you want to use the software more extensively, there are several exercises available on the homepage.
  

• The NCIPlot program can read xyz files, wfn or wfx files.
  

• The xyz file contains the number of atoms in the system you want to study and the coordinates of the atoms. If you read in an xyz file, the program automatically uses promolecular densities for the calculation.
  
  3
  water
  O     1.396405    -0.121399    -0.040373
  H     1.465873     0.195903     0.874079
  H     1.472634     0.685789    -0.573657
  
  

• Wfn or Wfx files contain information about the wavefunction and can be used to read information from a previous quantum chemical calculation.
  The wfn format is older and it is limited to 999 atoms. Also if you are working with effective core potentials, the wfx format is better.

NCIplot
https://www.lct.jussieu.fr/pagesperso/contrera/nciplot.html
on aurora:
export NCIPLOT_HOME=/lunarc/nobackup/projects/snic2019-35-66/Justin/programs/nciplot-master/src_ nciplot_4.0/
nciplot

1. Create an input file, e.g. water.inp
   1
   water.xyz
2. export NCIPLOT_HOME=/lunarc/nobackup/projects/snic2019-35-66/Justin/programs/nciplot-master/src_ nciplot_4.0/
3. nciplot water.inp >water.out
4. Start vmd
   vmd
   File - Load visualization state
   open the file water.vmd.
   Graphics – Representations
   Make sure that you are looking at the Isosuface representation and change the Isovalue.
   
5. Look at the 2D plots with gnuplot
   gnuplot
   # Gnuplot script for mapping NCI color code over NCI diagrams
   set terminal pngcairo enhanced
   set encoding iso_8859_1
   set output 'water.png'
   set key
   set ylabel 's(a.u.)' font "Helvetica, 30"
   set xlabel 'sign({/Symbol l}_2){/Symbol r}(a.u.)' font "Helvetica, 30"
   set pm3d map
   # Define a color gradient palette used by pm3d
   set palette defined (-0.04 "blue",0.00 "green", 0.04 "red")
   set format y "% .2f"
   set format x "% .2f"
   set format cb "% -.2f"
   set border lw 4
   set xtic  -0.06,0.01,0.06 nomirror rotate font "Helvetica"
   set ytic   0.0,0.25,1.0 nomirror font "Helvetica"
   # set the color bar tics
   set cbtic  -0.06,0.01,0.06 nomirror font "Helvetica"
   set xrange [-0.06:0.06] 
   set yrange [0.0:1.0]
   # set the range of values which are colored using the current palette
   set cbrange [-0.06:0.06]
   plot 'water.dat' u 1:2:1 w p lw 6 palette t ''
   

1. Create an input file, e.g. water.inp
   1
   water.wfn
2. Use the same steps above to run nci and look at the results.

Looking at NCI-ingegral values

1. Sample input file:
   2
   waterB.xyz
   waterA_100.xyz
   INTERMOLECULAR
   ONAME water_100
   
2. The INTERMOLECULAR keyword means that only inter- molecular interactions are considered in the calculation of the integral values.
   ONAME sets the name of the output file.
3. Each xyz file contains one water molecule. The position of the one in waterB.xyz is always fixed, whereas the one in waterA *.xyz is moved further apart, according to the scaling of the distance.
4. Look at the integral values ”Integration over the volumes of rhoˆn” for n=2.5. The easiest way to do this is if you use grep:
   grep -A5 ”Integration over the volumes of rhoˆn” *out | grep ”n=2.5”
   
5. Do not assume  that there is a direct relationship between the value of the integral and the interaction energy. There seems to be a relationship, but it is not an easy (linear) one and more research still needs to be done.
   If you are interested in the interpretation of the value of the NCI-integral, have a look at the following two papers:
   https://doi-org.bases-doc.univ-lorraine.fr/10.1021/acs.jctc.0c00063
   https://doi-org.bases-doc.univ-lorraine.fr/10.1021/acs.jcim.9b00950 (for MD simula- tions)

• The IGMPlot program can process xyz files (then it uses the promolecular approximation) and wfn files (to use the wavefunction from a quantum chemical calculation).
  

• Documentation for the IGMPlot program can be found here:
  http://igmplot.univ-reims.fr/ DOC/doc.pdf
  The software itself comes with a number of tests, which can be a very useful starting point, many of them are also the examples shown in the documentation.

• Example input file:
  2
  
• water1.xyz
  
  water2.xyz
  RADIUS 1.5 0.5 0.5 5.0
  

• Without the radius keyword, the program is still working, but the automatically chosen cube size is too small to visualise all isosurfaces.

• IGM detects intermolecular interactions only if two separate xyz files are given as input. Each of the two xyz files contains one water molecule each.

• Run the program by
  igmplot water.inp > water.out

• Like NCI, with IGM you can visualise 3D and 2D plots.
  

• Load the igm.vmd file as visualisation state in vmd.
  Enable the visualisation of the intramolecular interactions with double clicking on the red D in the main window. 

• For the 2D plots, use the gnuplot script igm water.gp. This will provide you with two png files, one for the inter- and one for the intramolecular interactions.
  
  # Gnuplot script for IGM
  set terminal pngcairo enhanced
  set encoding iso_8859_1
  set output 'intra.png'
  set key
  set ylabel '{/Symbol d}g(a.u.)' font "Helvetica, 20"
  set xlabel 'sign({/Symbol l}_2){/Symbol r}(a.u.)' font "Helvetica, 20"
  set border lw 2
  set yrange [0.0:0.5]
  plot 'out-igm.dat' u 1:3 w p lc rgb "blue" title "dg intra"
  set terminal pngcairo enhanced
  set encoding iso_8859_1
  set output 'inter.png'
  set key
  set ylabel '{/Symbol d}g(a.u.)' font "Helvetica, 20"
  set xlabel 'sign({/Symbol l}_2){/Symbol r}(a.u.)' font "Helvetica, 20"
  set border lw 2
  set yrange [0.0:0.1]
  plot 'out-igm.dat' u 1:4 w p lc rgb "blue" title "dg inter"
  

Electron Localization Function (ELF)