Hi, folks. A very conceptual question here…

How is the SCF reference for EOM-CC calculations selected?

I know that this question sounds like a trivial one (“Pick the lowest, dummy!”), but we currently have a system where it’s not obvious.

For example, let’s say that we have states of two different electronic symmetries. And we can land on either state at the SCF level. Because they’re different symmetries, a stability analysis identifies them both as stable. The lower-energy SCF solution yields a *higher-energy* EOM result, and vice versa.

Should we select the lower-energy SCF state because it’s the “more correct” reference state? Or should we target the lowest-possible-energy EOM state, even if it originates from an excited SCF determinant?

Thanks!

Ryan

If you use the higher-energy state, do you perhaps run into a problem of T1 trying to rotate your reference into the lower-energy state? Or does the different symmetry prevent that?

Hi, John. Thanks for checking in on this item. For the structures that we are considering, the symmetry prevents the collapse to the lower SCF state. But it’s somewhat finicky to control. I only happened to stumble on this issue when starting from an asymmetric structure. It still optimized to a symmetric structure but at a notably lower EOM energy…and higher SCF energy. It’s possible that those EOM solutions could even cross somewhere–effectively a fictitious state crossing–but I haven’t explored the surface enough to see if that outcome occurs in this system.

I guess this system just raised some more fundamental questions for me regarding EOM. If the full manifold of EOM electronic states can be generated when starting from different SCF solutions, which one is correct?

@annakrylov : Any thoughts here?

We’re digging this system back out for our collaborator, and I think we’ll just move forward with the lowest SCF state for now (when possible). But the reference dependence is a quirky side of EOM that I’ll confess that I don’t fully grasp. Thanks!

Ryan, sorry I missed this. The short answer is you choose the reference that is most suitable for generating your target states, that is, from which the target states can be produced by single EOM operators (1p1h in EE or 1p in EA or 2p in DEA). It can be an excited SCF solution and in many cases we do exactly that. For example, it is preferred to use ROHF or another spin-pure reference rather than lowest-energy spin or symmetry broken UHF solution. Conceptually, CC does not require lowest-energy SCF solution. To give more concrete recommendation, I will need to look at the system – can you please post the structure and brief explanations?

Thanks, Anna. I appreciate the info!

The systems that we’re studying involve metal-carbene cations, including RhCH2+ and CoCH2+. They are both even-electron systems, but the singlet and triplet states are close in energy. Our collaborator originally used DFT calculations for this purpose, and we found through our own tests that the singlet/triplet assignment of the ground state was wildly functional-dependent. Enter EOM…

In the Rh case, we just used the lowest triplet SCF state for EOM-SF, and the states seemed to work out just fine (although I need to revisit my assignment of them, based on the other thread :)). They nicely explained some of the vibrational spectra that were observed, for example.

For Co, though, we ran into the reference dependence mentioned above. Basically, the lowest SCF state leads to higher EOM energy, and vice versa.

I’ve attached two jobs for comparison. The first (job1) is just an optimization of the C2v structure and targeting the A1 transition. (We ran analogous optimizations for A2/B1/B2.) The second job (job2) was an attempt to test a Cs structure; it optimized to a C2v geometry but with a notably lower energy than any of the C2v-initialized cases.

job1.out

job2.out

Ryan, I ran a couple of quick calculations: 2 with finite geometries from job 1 ad job 2 and one with initial geometry from job1. The spin-contamination of the references is quite bad - <S^2> more than 3! It means that either wrong triplet is found by SCF or that triplets are problematic because of the degeneracy of the d-orbitals. I noticed that at C2v structures, the triplet SOMOs are of A1 symmetry, not sure whether it is expected or not (for isolated carbene, the triplet SOMOs are a1b2). I see that SF states are also contaminated, which is always the case when reference is bad, but it seems that they predict that the lowest state is triplet for all 3 jobs. I would try to look first into the triplet states and their orbitals, to get an idea of what is going on.

To get a better idea about triplets, I looked at the quintet (and done single SF calculation from it). SCF found B2 reference SOMOs (3 0 0 1) and the lowest SF state from this reference is A1 triplet (B2 transition). The next triplet is about ~1 eV above, which is not too bad but not too good either. From the orbital energies, you can see that 4 alpha orbitals are nearly degenerate and then the next 2 are also close. So I ran heptet and I see that now that all nearly degenerate orbitals are singly occupied, which is good. S^2 of the reference improves too. The SF finds one well-behaved quintet state, with low spin-contamination and well separated from others. So I think you probably can work with quintet reference, but then you will need to build Heisenberg Hamiltonian from it to get other states, as we did here: https://iopenshell.usc.edu/pubs/pdf/jcc-44-367.pdf

I also ran DEA calculation using +3 quintet reference – another way to capture these triplets. Unfortunately, we do not have S^2 implemented for DE yet, so am not sure how to interpret these states.

It gave me one low state (seems like the same A1 triplet), followed by another state 1 eV up, and one more also very close. So it all confirms that triplets in this system are not simple and can cause trouble.

With the d5 configuration, it could be quite tricky to get all states correctly.

I cannot figure out how to attach outputs to this, I can send them to you by email.

Thanks, Anna. I’ll be digging into the cobalt case this weekend.

Your message spurred me to revisit RhCH2+, which I thought that we had already handled sufficiently. Now I’m questioning our existing results for this case. What I thought was a pair of low-lying states of different symmetry (whose vib spectra nicely matched experiment) were actually the “same” state, obtained from EOM off of different SCF states. In short, they were, unintentionally, an A1 transition off of an A1 reference and an A2 transition off of an A2 reference.

But that case reignited my questions about the EOM reference. I’m currently running a test for RhCH2+, for example, that begins the geometry optimization as an (a1a2 → A2) SCF triplet but crosses to an (a1a1–> A1) SCF solution during the geometry optimization. Since the symmetry of the *transition* is specified in the input file–rather than the target-state symmetry–we really have few tools to target the right state from the outset. We can kill the job, snag the coordinates, and reset the symmetry of the transition (and hope that it doesn’t swap back)…but that approach seems awfully non-generalizable. Is there a practical hurdle to assigning the symmetries of both the reference state and the transition (inside the code) and then allowing the user to choose target-state symmetries instead?