Question: I would like to construct a model analytical potential function for collision between CH3Cl and Ar. This would be the sum of CH3Cl intramolecular + CH3Cl---Ar intermolecular potential. First I would like to generate the ab Initio data points to be fitted using double many-body expansion or similar functions. I know how to set up PES scans (bond, angle, dihedral etc) using gaussian, Orca and Psi4 but I don't know how I would approach this problem. I would greatly appreciate if anyone would give a detailed procedure on how I can go about solving this and similar problems. Thanks.

Answer: 
We attempted to solve a similar problem when studying the (also highly symmetrical) $\ce{CH4}$ and $\ce{CF4}$ homo- and hetero-dimers. I found it easiest to use internal coordinates and fixed molecular geometries to generate the hypersurface, but we also had large computational resources at our disposal and we might have benefitted from using even more, especially to generate more points at larger intermolecular distance.[Chattoraj, Risthaus, Rubner, Heuer, Grimme, *J. Chem. Phys.*, **142**, 164508 (2015)](http://dx.doi.org/10.1063/1.4919079)

In your particular case, you should be able to use

* the $\ce{Ar}$-$\ce{C}$ distance
* the $\ce{Ar}$-$\ce{C}$-$\ce{Cl}$ (0 to 180°)
* a $\ce{Ar}$-$\ce{C}$-$\ce{Cl}$-$\ce{H}$ angle, wherein you use the $\ce{H}$ closest to the $\ce{Ar}$ (-60 to 60°)

The tricky part remains: picking the right values with which to cover the intervals, which is a bit of trial and error. Some researchers have used "self-healing" approaches, which mean that the configurations with the worst differences between reference and your model are used to refine the model.

If you plan to not use a fixed molecular geometry, my approach is of course not valid.
For 1D analytic potentials, I highly recommend to use [my potential energy form](https://aip.scitation.org/doi/abs/10.1063/1.3264688) or a slight simplification of it, which I can help you with. This is known as the [Morse/Long-Range (MLR) potential](https://en.wikipedia.org/wiki/Morse/Long-range_potential) and is now the "industry standard" in high-accuracy spectroscopy and some other areas.

For analytic ***multi-dimensional*** potential energy surfaces, there's a few options.

**Richard Dawes** and co-workers have done a lot of work in the area:

* [The construction of *ab initio*-based potential energy surfaces](https://onlinelibrary.wiley.com/doi/abs/10.1002/9781119518068.ch5) (book chapter)
* [AUTOSURF: A code for automated construction of potential energy surfaces](https://core.ac.uk/download/pdf/161954606.pdf) (software)

**Hui Li** has generalized the MLR potential (mentioned at the beginning of this answer, for 1D potentials) to multi-dimensional ***intermolecular*** potentials for Van der Waals complexes and reactions:

* [Overview](https://www.tandfonline.com/doi/abs/10.1080/00268976.2018.1429687)
* [3D potential for $\ce{CO2 - He}$](https://pubs.rsc.org/--/content/articlelanding/2008/cp/b800718g/unauth#!divAbstract)
* [5D potential for $\ce{H+3 + CO→H2 + HCO+}$ and $\ce{H+3 + CO→H2 + HOC+}$](https://aip.scitation.org/doi/abs/10.1063/1.3041494)
* [6D potential for $\ce{OCS - H2}$](https://aip.scitation.org/doi/abs/10.1063/1.4996086)

Also I have generalized the MLR potential to multi-dimensional ***intramolecular*** potentials [here](https://ui.adsabs.harvard.edu/abs/2018isms.confEWB04D/abstract), and have some notes on it [here](https://github.com/ndattani/polyMLR). You may also like to look at the publications lists of Joel Bowman, Hua Guo, Per Jensen, David Schwenke, Antonio Varandas (a co-author of the book [Molecular Potential Energy Functions](https://rads.stackoverflow.com/amzn/click/com/0471905402), and many others (there's just so many ways to do it!).