What are the best possible methods and available software to compute the spin-state energetics of transition metal complexes?


For computing the spin-state in a metal complex there are many methods available. I'll focus in DFT as one of the most used methodologies.

In a single atom cluster (sometimes described as mononuclear complexes), DFT offers good results compared with wave-function multideterminantal methods.

On the other hand, if the complex is formed by two or more metallic centers, DFT has real troubles while finding the energy of antiferromagnetically coupled states. One of the most used approximations about this is the 'broken-symmetry' approach which permits to calculate the single determinant energy of a certain state. Nice reviews on this about metallic complexes are by Ruiz et. al..[1, 2] With this approach it is possible to somehow approximate the value of the magnetic exchange coupling that finally determines the relative energies of the different spin states, but one should be really careful concerning which particular expression is using for it.


  1. Ruiz, E.; Cano, J.; Alvarez, S.; Alemany, P. Broken symmetry approach to calculation of exchange coupling constants for homobinuclear and heterobinuclear transition metal complexes. J. Comput. Chem. 1999, 20 (13), 1391–1400. DOI: 10.1002/(SICI)1096-987X(199910)20:13%3C1391::AID-JCC6%3E3.0.CO;2-J.
  2. Ruiz, E.; Rodríguez-Fortea, A.; Cano, J.; Alvarez, S.; Alemany, P. About the calculation of exchange coupling constants in polynuclear transition metal complexes. J. Comput. Chem. 2003, 24 (8), 982–989. DOI: 10.1002/jcc.10257.

There's probably no answer to this question.

Best possible method? In general, just build up reasonable structures (don't tunnel vision into one), find their local minima on the given spin-states and just compare their energetics.

The best level of theory is also not really defined. One might say DFT, but I personally do not really trust DFT in general for problems like these. CCSD(T) could be performed, depending on your computational resources (remember, you need to optimize too, which you can probably do on MP2 level in this case and hope for the best), but don't be fooled into thinking CCSD(T) is the golden standard method. It is only the golden standard for large enough basis sets, which could also be an issue with transition metal complexes. Also for heavier elements, you might need to add spin-orbit corrections. Even worse: if the spin states (or just normal electronic states) are not separate enough, you really need a multireference method. Then we should be talking about MRCI, which is extremely complicated, and again, no general answer on how to do it.

As to what code to use, you have a plethora to choose from. Apart from the big names like Gaussian or Q-Chem, you might look into FHI-AIMS for the numerical basis set efficiency - however, this code really only is for DFT, which I would not suggest here. ORCA seems to do excellent on problems on this, and it also has a DMRG method built in, so I strongly suggest ORCA here. Molpro can also be considered for the extremely reliable spin-orbit coupling methods available. But for a general CCSD(T) calculation, I'd stick with the good old Gaussian, as that is, in my experience, the most reliable.

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    $\begingroup$ Sorry, but apart from the first sentence, I don't think your answer is good advice. Sure, DFT has problems and isn't very reliable, but it will at least be fast. MP2 for transition metals is the wrong choice. You first have to exclude any possibility for multi-reference, and then it still is a bit of a gamble. As far as good CCSDx implementations go; it would be a huge surprise if Gaussian would scratch the top 10. $\endgroup$ – Martin - マーチン May 15 '20 at 10:16
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    $\begingroup$ @Martin-マーチン Be careful you might get banned from Gaussian ;) $\endgroup$ – Cody Aldaz May 15 '20 at 19:04
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    $\begingroup$ @Martin-マーチン Interesting input. I do not believe that trusting a method that isn't very reliable but at least fast is a good suggestion. I fail to see the advantage of getting wrong answers quickly. As for coupled cluster and Gaussian, I was just talking from personal good experience with it. I sure do not have experience with ten good implementations; mind sharing your top ones? $\endgroup$ – Ezze May 15 '20 at 20:22
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    $\begingroup$ I've never said to trust DFT, but it will give you something to work with fast. Obviously you will have to do calibration and review, but dismissing it from the start is unjust. MP2 is more demanding, possibly slower and will most likely give you even worse results. As for codes, I also don't have experience with 10 different, but Orca does very well, as does Turbomole, Gamess, Molpro; Gaussian simply hasn't implemented any of the newer models that can significantly reduce computational effort. $\endgroup$ – Martin - マーチン May 15 '20 at 22:13
  • $\begingroup$ CCSD(T) also isn't gold standard for anything except single-reference systems. If you have spin states of transition metal complexes, you probably have significant static correlation, and CCSD(T) will probably yield nonsense. $\endgroup$ – Susi Lehtola Dec 3 '20 at 20:56

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