Spin States & Multistage Optimizations
why it matters; our approach; some case studies
Predicting the spin states of molecules (how many unpaired electrons there will be) is a very important task in a lot of different domains:
In organic light-emitting diodes (OLEDs), the energy gap between singlet and triplet states is incredibly important: high triplet energies are desirable for deep blue OLEDs, while low singlet–triplet gaps allow for thermally activated delayed fluorescence (TADF).
Carbenes, commonly used as photoaffinity labels in chemical biology, can exist in both singlet and triplet states: the triplet state reacts as a diradical, while the singlet states performs the (typically desired) C–H activation processes.
In photocatalysis, tuning the triplet energy of photosensitizers dictates which substrates can be activated by a given catalyst, making it crucial to understand the singlet–triplet gap of both substrate and catalyst. (See, for instance, this paper on triplet sensitization of oximes.)
And for any computations on transition metals, knowing the spin state of a given complex is table stakes for any downstream calculations.
There are a lot of point solutions for spin-state prediction floating around in the literature based on quantum chemistry, machine learning, or simple geometric heuristics, often highly optimized to achieve maximum accuracy for a given class of compounds. Today, we’re releasing a workflow on Rowan to quickly predict the relative energies of different spin states for any molecule with good accuracy and great transferability. Here’s what this looks like:
In the above case, benzophenone is predicted to favor the singlet state over the triplet state by 64.3 kcal/mol. Behind the scenes, we run optimizations and correct the final results with single-point energies, using highly optimized “composite” DFT methods wherever possible. “Rapid” mode uses GFN2-xTB for geometry optimization and r2SCAN-3c for single-point energies, while “careful” mode uses B97-3c for geometry optimization and wB97X-3c for single-point energies.
For closed-shell organic molecules like this, we found that “rapid” mode generally finds good agreement with literature values. We looked at six classic triplet sensitizers (benzophenone, xanthone, thioxanthone, dicyanobenzene, dicyanonaphthalene, and dicyanoanthracene) and were able to exactly reproduce the correct ordering of triplet energies (ref), although the energy of the high-spin state was slightly underestimated in every case. The largest of these calculations–thioxanthone–took less than four minutes to run!
We also tried using Rowan to predict the spin states of reactive carbenes useful in chemical biology: using “careful” mode, methylene (link) is correctly predicted to favor the triplet state by about 9 kcal/mol, while dichlorocarbene (link) is correctly predicted to favor the singlet state by about 20 kcal/mol. (“Rapid” calculations seem less reliable for these reactive intermediates.)
For transition metals, DFT is known to struggle at predicting relative spin states with quantitative accuracy: a recent benchmark from Radon and co-workers suggests that range-separated hybrids (like wB97X-3c) perform better than functionals with global exact exchange (like B3LYP or TPSSh). We found generally sane performance for the organometallic complexes we looked at, like MnCp2, although getting the energy gaps quantitatively correct every time will probably require time-consuming coupled-cluster calculations or similar.
As a part of this release, we’re also launching a new multi-stage optimization workflow, which automatically optimizes compounds at multiple levels of theory before running a final single-point calculation. Combining multiple levels of theory is almost always the most efficient way to get high-quality results within a given computational budget, but is often neglected because of the human time parsing and resubmitting all the jobs requires. With Rowan’s new workflow, we handle all that for you: just select your level of theory and click “Submit”.
We’re excited to share these streamlined tools with our users and hear about how they work in the wild: as always, let us know what we can be doing to better support you and your science!