Approaches to understanding different relative energies between semiempirical and DFT methods

Question

I am studying Pd(II) metal-organic systems and have used GFN2-xTB (with implicit solvation) for high-throughput optimisation of candidate structures. I use the relative energies (from xtb) of different structural isomers as a screening metric based on empirical results. For the sake of validation, I aim to recreate those relative isomer energy calculations using DFT (optimisation, also with implicit solvation), which has previously been shown to agree with the xtb relative energies, for the top candidates.

I am aware that GFN2-xTB is parameterised with a focus on geometries, frequencies and NCIs - not energies, so validation (by DFT) of its use in my workflow is important.

I have a single case so far (although there may be more) where the relative isomer energies from DFT (PBE0/def2-svp/D3BJ) and xTB are opposing and in this case, I expect the difference to be due to a specific chemical functionality.

My question here is about the approaches one might use to understand this type of result. I do not have a lot of expertise in exploring the specific components of DFT/semiempirical calculations. So far, I have tried to understand this effect with a small model system of the different isomers that isolates the effect of the troublesome functionality. However, I am curious about the best way to analyse the results. I.e. is comparing the energy difference of all of the components (electronic energy, Gsolv, dispersion correction) appropriate?

If anyone could point me in the direction of a good resource on this type of issue, that would be appreciated. I am currently in the process of going back to some basic DFT reading.

Answer 1

When modeling metal-organic systems, it is not uncommon for DFT to be wrong by far more than 5 kJ/mol. They are notoriously tricky to model. On the DFT side of things, I can say you're using a pretty small basis set of def2-SVP. That's going to be one factor limiting the quality of your DFT results. Also, Pd is pretty heavy, and relativistic corrections might be important. None of this is to mention the inherent limitations of PBE0.

On the semi-empirical side, GFN2-xTB is not meant for reliable energies of systems, and I'd expect it to do particularly poorly for transition metal complexes. It is going to be very difficult to understand why the two give very different results, seeing how highly empirical GFN2-xTB is by design. Without a thorough benchmarking comparing the energies of many different systems at the PBE0-D3(BJ)/def2-SVP level of theory and GFN2-xTB level of theory, it's going to be hard to make any claims. It should also be mentioned that there are a few differences here regardless. For instance, GFN2-xTB uses the D4 dispersion correction scheme, whereas you are using D3(BJ) at the DFT level. Furthermore, you are using an implicit solvation model with GFN2-xTB but not with DFT.

Since GFN2-xTB is supposed to be alright for vibrational frequencies, you can compare the vibrational contribution to the enthalpy or Gibbs free energy between PBE0-D3(BJ)/def2-SVP and GFN2-xTB to start. That will give you an idea if it's related to poor geometries and/or frequencies. Beyond that, you can compare the electronic energies. The only way to identify any systematic effect here is to compare the energies for many different systems to see if you can identify trends, and there simply may not be any. Overall, I personally would be very hesitant to compare the relative energies of any inorganic or metal-organic systems using any empirical method, including GFN2-xTB.