# Potential energy surface when spin changes

I'm trying to compute potential energy surface of S4 molecule (in MOLPRO 2015) along S2-S2 bond (it has a trapezoidal shape) from equilibrium to the dissociation threshold, all the other coordinates are fixed. S4 is a singlet (0 unpaired electrons) in the ground state but a quintuplet once it's dissociated (2 independent S2 molecules in the ground state, each has 2 unpaired electrons). I tried to do CCSD(t) calculations with spin 0 and 2. With spin=0 I get the right energy at the equilibrium but too high energy at the dissociation limit and it's vice versa for spin=2. I need a single surface to solve the Schrodinger equation in so I was thinking about just taking minimum between the two surfaces but I'm not sure if it's a correct way to do it.

This problem doesn't seem to be that rare so I think there should be a well known way to tackle it. I think MRCI can use a mix of the two states, adjusting coefficients in the process to make the transition smooth, but I'm not sure how to properly do it.

Dissoziation is a typical multi-reference problem, where single-reference methods like Coupled-Cluster usually fail. Therefore CASSCF+MRCI would be the better approach here anyway.

If you have a crossing Singlet and Quintuplet state, then you should calculate both. Different spin states do not mix, therefore there is no avoided crossing to be expected. The dissociation of the molecule will remain on its respective PES. To go from the at dissociation limit excited Singlet state to the Quintuplet you need some coupling. Something that switches the spin of the electrons. (I don't know what an actual process would be in this case, maybe some stimulated emission.) So you should NOT just take the minimum of those two curves!

You should include both spin states (at least, maybe you need more) in the CASSCF state average, to get balanced orbitals. Make sure CASSCF results in smooth PESs for both states before attempting MRCI. For MRCI you probably need to do independent calculations for both states, as Molpro does not allow different symmetries at the same time here. (But thats fine, as they should not mix anyway.)

Alternatively, you could try other multi-references approaches like MRCC or CASPT2, but I don't have any experience with those.

• So if I do two independent MRCIs, I'll get two surfaces, is that right? How do I combine them into a single surface then?
– QNA
Aug 1, 2017 at 13:37
• Yes you get two. But you can NOT combine them! You can only consider transitions between them, which requires some kind of coupling, for example an electromagnetic field, like a laser. This depends on what you need the two PESs for. Without a coupling, the molecule will remain in the state it started from! Aug 1, 2017 at 14:02

So, as I realized later, two triplets can still give you a singlet in total when the spins have opposite directions, so my total spin remains 0 throughout the whole dissociation process. I didn't manage to fix spins orientation with CCSD(T) and I'm not sure if it's possible but MRCI worked just fine out of the box automatically orienting spins to make a singlet and it gave me good dissociation energies. But I had to use state average eventually (as was pointed out by @Feodoran) because points in the middle did not want to converge.