Slope of the potential when both molecules "touch"?

Question

My aim is to model the potential energy surface for two colliding H2 molecules. More specifically, I needed the order of magnitude of the slope of the potential at the moment when two colliding H2 molecules "touch". How do I obtain this?

Answer 1

If you have two atoms colliding, we rarely talk about them "touching" because the potential energy between them will tend to infinity as the internuclear distance tends to zero. For example, you can see what the potential looks like as $r \rightarrow 0$ in the figure of my answer to: Converting adsorption binding energy to absolute temperature. This is often called the "united-atom limit" (there's many papers with that term in the title!) and the slope is just obtained from the Coulomb $1/r$.

But what you're asking, is essentially about four hydrogen atoms, two of them forming one $\ce{H2}$ molecule, and the other two of them forming a second $\ce{H2}$ molecule. Are they colliding in a "T" shape (one $\ce{H2}$ is perpendicular to the other $\ce{H2}$), or in an "I" shape (collinear, with the left $\ce{H}$ atom of one molecule hitting the right $\ce{H}$ atom of the other one), or with a shape like "=" in whcih both molecules are parallel?

You can calculate the potential energy surface with an ab initio quantum chemistry software, depending on your desired initial and final geometry.

I have made hundreds of input files and output files for such calculations, available for free here.

One example of a homonuclear 4-atom system (very similar to having four $\ce{H}$ atoms, but the atoms are $\ce{C}$ instead) is here.

The input file is as follows (in this case the software used was MRCC, and I've made slight changes to make it simpler for you):

#TITLE
basis=def2-TZVPP
calc=CC(4)
mem=12GB

unit=angs
geom=xyz
4

C  1.2247  0.0000 0.0000
C -1.2247  0.0000 0.0000
C  0.0000 -0.7286 0.0000
C  0.0000  0.7286 0.0000

You can simply change the lines starting with C to start with H, and pick a geometry (x,y,z coordinates for each H) that you desire. The program will give you an ab initio energy. Then you repeat the process for different geometries as two of the (bounded) $\ce{H}$ atoms collide with the other two, in whatever configuration you desire ("T" shape, "I" shape, "=" shape, etc.).

Since $\ce{H}$ is the first element of the periodic able, studies of it are considered quite "fundamental", so you may even be able to find the potential energy surface online!