To date, there are curves calculated from first principles, moreover, quite accurately, for a large number of diatomic molecules.
For example, you can use such curves for a number of diatomics of general interest from our work
https://iopscience.iop.org/article/10.1088/0953-4075/49/12/125102/meta
All required data are tabulated in Supplementary to this article (please, request, if unavalialbe from IOP).
If you need something else special, we can try to calculalate, although here you will have to think especially.
I know that curves can be calculated but I meant to check which simple functional forms would be the best.
I have recently made ab initio research (Article First principles study of the high temperature partition fun...
) and I'm willing to start cooperation also on ab initio PECs to continue such studies. If you send me your e-mail I will give you the details of what I have in mind.
As far as I know, simple functionals (DFT) can not be succesful for the PEC calculatiions, especially at large internuclear separation.
Ab initio methodology in your recent CPL work is just relevant (CASSCF+MRCI) .
If it's convenient for you, here's my email: [email protected]
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