quantum chemistry - Restricted open-shell versus unrestricted methods for open shell systems

Open-Shell systems (radicals and so on) can be modeled by single-determinant quantum chemical methods using unrestricted (u) or restricted open-shell (ro) methods (I am aware that single-determinant approaches are not always reasonable for open-shell systems, but let's ignore that for a second and suppose we have to use a single-determinant method).

Unrestricted calculations may suffer from spin-contamination. Restricted open-shell calculations remedy this, they are unaffected by spin-contamination. However, restricted open-shell methods are much more computationally expansive. Also, Koopmans' theorem cannot be rigorously applied in the case of ro calculations.

My question is:

Apart from the before mentioned issues, are there any disadvantages of restricted-open-shell computations in comparison to unrestricted calculations? Are there any situations where an unrestricted calculation would be more appropriate than a restricted-open-shell calculation?

[Methods of interest are - for example - MP2, DFT and HF.]

There is already a somewhat related discussion: U- or RO-method for Singlet-Triplet Gap?. However, my question is much broader, it includes for instance: Are there cases when it is absolutely not ok to use ro methods, and you have to use unrestricted methods?

Answer

To be more precise, it's not so much that restricted open-shell calculations are unaffected by spin-contamination as that you are forcing them to give back the multiplicity you want.

Broadly speaking, closed-shell methods, restricted open-shell methods and constrained unrestricted open-shell methods all give correct spin multiplicities, but that's because all of them assume from the beginning which is the correct multiplicity and force it into the calculation - there is always a restriction in place. For closed-shell methods, it is that the orbitals occupied by both spin populations are the same; for restricted open-shell methods, the same applies to all but the excess spin electrons from the larger spin population. But more recent developments point to restricting multiplicity after the fact - by adjusting orbital population to minimise spin contamination. There are a couple of methods to do that, but they start from an unrestricted calculation (much faster, as you mention), and then force the population in a way that minimises spin contamination - either by forcing orthogonality constraints between the $\alpha$ and $\beta$ determinants, or by parametrising spin contamination in a way that allows it to be fitted to the expected total multiplicity by constraining occupation. This retains the computational advantage and simpler mathematical implementation of unrestricted methods but makes sure that the multiplicity of the model system reflects the multiplicity of the modelled system with generally very small additional computational effort.

I'd suggest that this is going to be an active area of research that will see increased use in the next few years.