# What is the procedure for constructing an ab initio potential energy surface for CH3Cl + Ar?

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.

• +1 and welcome to the site!!! Thank you for contributing your question here and we hope to see much more of you!!! Related question and answer: mattermodeling.stackexchange.com/q/2415/5 – Nike Dattani Dec 24 '20 at 17:54
• @NikeDattani Thanks for your warm welcome. I have seen the question you are pointing to but though similar to my question, the information sought it different. – fred85 Dec 24 '20 at 18:57

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)

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.

• Thank you for your answer. This is the approach I would use for intermolecular potential. I intent to fix CH3Cl on its centre of mass (COM) and scan Ar-COM distance and assign angles to scan with reference to this COM. How to transform the internal coordinates into this new COM coordinate is still not clear to me though this approach is very common in the Literature. Your approach of using C atom as a reference seems a bit straight forward. I will read your paper and see if I can adopt it here. I still have to determine the CH3Cl intramolecular potential though. – fred85 Dec 24 '20 at 18:51
• @fred85 It would be highly preferable for your question to only be about the fitting, and not about the determination of the potential. Your question said you already know how to determine the potential, but if you did have questions about that, I think it ought to be a separate question here. – Nike Dattani Dec 24 '20 at 22:38
• @NikeDattani maybe I didn't come clear in this question. I know how to do a potential energy scans for bonds, angles, and dihedrals. Is this the only information one would need for global PES fit? For example, if I want to fit the ab initio data to your MLR potential do I have to scan and fit each mode (stretch, bend, etc) separately and sum up these individual components to get the intramolecular potential? – fred85 Dec 25 '20 at 17:53
• @fred85 Okay, let's chat here: chat.stackexchange.com/rooms/117652/spectroscopy-potentiology. Comments on answers aren't supposed to become very lengthy discussions, but we can talk as much as we want in the chat room :) – Nike Dattani Dec 28 '20 at 4:06

For 1D analytic potentials, I highly recommend to use my potential energy form or a slight simplification of it, which I can help you with. This is known as the Morse/Long-Range (MLR) 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:

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:

Also I have generalized the MLR potential to multi-dimensional intramolecular potentials here, and have some notes on it here. 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, and many others (there's just so many ways to do it!).

• Probably I should have been more specific in my question. I want to fit the intramolecular to your MLR potential and the intermolecular to Antonio Varandas (or exp-6) potential. Thanks for your pointers, I will have a look at them and especially your notes on how to fit the intramolecular potentials. As for the intermolecular the only challenge I had was on how to define the COM and the trick given by Y. Zhai will be very useful. – fred85 Dec 25 '20 at 17:49

On the fitting, I would recommend Dr. Nike Dattani's answer. You can also try some other methods such as those using neural networks.

I read your discussion and find that may be you have also some issues with the scanning using ab initio methods.

The intermolecular interaction is often read $$\Delta V_{\rm int}=\Delta V_{\rm int}(R, \theta, \phi),$$ where $$R$$, $$\theta$$, and $$\phi$$ define the position of Ar as if the COM of CH3Cl locates at the origin of the polar coordinate system. To scan this, the most common way to do the job is to write the Z-matrix, which defines the relative position of the atoms by given the distance between two, angle between three, and dihedral between four atoms. In our group, this job is often done by hand, because there are no to much atoms here. If you need, you can check the manual of your preferred software, like in Molpro, it is here.

If you can define the geometry of one geometry, you can scan the global PES by changing the parameters in the Z-matrix.

I believe the trick here is to use dummy centre to represent the COM. It means the centre is just an indicator for a reference position instead of a real atom. In the link to the Molpro manual, it is the Q or X atom.

Also notice that if you are scanning the intermolecular PES, you need to minimize the Basis set suerposition error (BSSE) by using counterpoise correction, where you need calculate the energy using the same basis (remember to include the basis for the dummy molecule) three times for every geometry and get the interaction potential as $$\Delta V_{\rm int}=E({\rm CH_3Cl+Ar})-E({\rm CH_3Cl})-E({\rm Ar}),$$ where the $$E$$'s are the energy get from the ab initio package you use.

Note that you will find the terminology are greatly different among packages. In my limited experience, CFOUR will call the first dummy centre (the Q or X ones) as 'dummy atom' while call the latter one 'ghost atoms'. The difference between the two lies in whether the basis functions of the atom are kept in the ab initio computation.

• Thank you. The use of dummy atom to represent the COM is a very useful trick. I knew I needed R, $\theta$ and $\phi$ but didn't know how to define them. Thanks. – fred85 Dec 25 '20 at 16:49