Sunday, November 11, 2012

Benchmarking Semiempirical Methods for Thermochemistry, Kinetics, and Noncovalent Interactions: OMx Methods Are Almost As Accurate and Robust As DFT-GGA Methods for Organic Molecules

Martin Korth and Walter Thiel Journal of Chemical Theory and Computation 2011, 7, 2929-2936 (Paywall)
Highlighted by Jan Jensen

This paper presents a thorough benchmark of six semiempirical method: AM1, PM6, SCC-DFTB, OM1, OM2, and OM3, as well as their corresponding dispersion-corrected versions.  The OMx methods, developed by Thiel, include orthogonalization corrections and are available in the MNDO99 code.

The methods are benchmarked using a 370-entry subset of the GMTKN24 database (containing only H, C, N, and O) constructed by Goerigk and Grimme for the evaluation of the "true" performance of quantum mechanical methods.  This database is comprised of 24 chemically different subsets of experimental or CCSD(T)/CBS (or similar) data, such as barrier heights, conformational energies, ionization potentials, etc.

Overall OM3 performs best with a mean absolute deviation (MAD) of 7.9 kcal/mol, which is not too different from MAD obtained with DFT: PBE/TZVP (6.6 kcal/mol) and B3LYP/TZVP (4.8) kcal/mol.  Surprisingly, PM6 performs significantly worse than AM1: 18.2 vs 14.5 kcal/mol.

The error is largest for the MB08-165 subset consisting of decomposition energies of randomly generated artificial molecules, specifically designed to test robustness and general applicability. This proves a real challenge for PM6 with a MAD of 128.4 kcal/mol.  If this subset, as well triplets and quartets, are removed, PM6 now outperforms AM1 (though not by much: 10.2 vs 12.2 kcal/mol) and OM3 is now within 1.5 kcal/mol of the DFT results!

A previous highlight indicated that PM6 out-performs AM1 and PM3 when it comes to barrier heights.  I was therefore surprised to see that, in this study, the PM6-MADs for the two barrier-height subsets (BH76 and BHPERI) were higher or comparable to AM1.  OM3 (or OM2) performs best again and in the case of BH76 out-performs PBE!  It is worth noting that the benchmarking consists of single-point energies using the structures in the database.  It is possible that computing the barriers using stationary points obtained using the respective methods will change the picture.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 Unported License.  


  1. I think one reason the OM1-3 methods aren't as widely adopted is because they're simply not implemented in many programs. AM1 has huge reach because MOPAC is public domain, and the method is implemented in almost everything these days. Similarly, I know many academic users trying PM6 (and almost certainly PM7) simply because Jimmy Stewart makes OpenMOPAC free for academic use.

    Out of curiosity, what programs have OMx implementations?

    1. Yes, I agree with you. Jimmy is also very helpful when it comes to implementing PM6 in other program (it'll be in GAMESS soon). As far as I know, the OMx methods are only available in MNDO99, which costs €600 for academics (executable only). Personally, I think it's a shame when you consider all the hard work that went into constructing these methods.

  2. When we studied the performance of several semi-empirical methods for phosphoryl transfer reactions ( ), we found that the geometries given by PM6 were markedly different than those of DFT. This didn't happen with other semi-empiricals, and it could be the cause of the bad behaviour of PM6 with single point calculations in this paper by Thiel and co-workers.

    1. The study focussed on H, C, N, O compounds so P is not the problem here.

      I skimmed your paper. It seems that PM6 failed mainly for the TS geometry for one reaction, correct? I couldn't really figure out how it failed (i.e. what was wrong with the TS structure), but I should read your paper more carefully when I have a minute.