Another benchmark study of the performance of different functionals – this time looking at the conformations of small alkanes.1 Martin first establishes high level benchmarks: the difference between the trans and gauche conformers of butane: CCSD(T)/cc-pVQZ, 0.606 kcal mol-1 and W1h-val, 0.611 kcal mol-1; and the energy differences of the conformers of pentane, especially the TT and TG gap: 0.586 kcal mol-1 at CCSD(T)/cc-pVTZ and 0.614 kcal mol-1 at W1h-val.
They then examine the relative conformational energies of butane, pentane, hexane and a number of branched alkanes with a slew of functionals, covering the second through fifth rung of Perdew’s Jacob’s ladder. The paper has a whole lot of data – and the supporting
materials include Jmol-enhanced visualization of the structures! – but the bottom line is the following. The traditionally used functionals (B3LYP, PBE, etc) overestimate conformer energies while the MO6 family underestimates the interaction energies that occur in GG-type conformers. A dispersion correction tends to overcorrect and leads to wrong energy ordering of conformers. But the new double-hybrid functionals (B2GP-PLYP and B2K-PLYP) with the dispersion correction provide quite nice agreement with the CCSD(T) benchmarks.
Also worrisome is that all the functionals have issues in geometry prediction, particularly in the backbone dihedral angles. So, for example, B3LYP misses the τ1 dihedral angle in the GG conformer by 5° and even MO6-2x misses the τ2 angle in the TG conformer by 2.4°.
References
(1) Gruzman, D.; Karton, A.; Martin, J. M. L., "Performance of Ab Initio and Density Functional Methods for Conformational Equilibria of CnH2n+2 Alkane Isomers (n = 4-8),"
The Journal of Physical Chemistry A 2009, 113, 11974–11983 , DOI: http://dx.doi.org/10.1021/jp903640h
Henry Rzepa responded on 07 Nov 2009 at 3:09 am #
We have been using the B2GP-PLYP 5th rung method quite a bit recently. All of this new family of double-hybrid functionals are first implemented and tested, as I understand, in the Orca program by Frank Neese, which is available free of charge at this site. It runs in parallel very well, and its use of the RI-MP2 approximation means its disk storage requirements are quite minimal. It implements analytical first derivatives for B2GP-PLYP (which by the way also includes the empirical dispersion energy corrections) and has internal support for several well known basis sets, including the (aug)-cc-pVnZ series and the especially efficient TZVPP+TZVPP/C basis. There are however some limitations;
No analytical energy 2nd derivatives, which however can be evaluated numerically.
This means that the hunt for transition states is quite slow, particularly for larger molecules.
I think it does not yet implement symmetry. So no gain for such molecules.
It is not yet interfaced into the electron density topological analysis programs, which tend to accept eg WFN or FCHK files such as output by Gaussian (although I should note that Gaussian09 changes the FCHK format, and hence cannot be read into some of these programs).
Gaussian09 implements some of these methods, but as usual with Gaussian one can never be sure that this implementation is identical to the Martin/Grimme ones. If anyone has used Gaussian09 for B2GP-PLYP then I would be interested in the comparison (of course, we must comply with Gaussian’s apparent legal requirement that one must not post benchmarks for their program in public!).
We have integrated Orca into our digital repository, and typical inputs and outputs can be found at the DOI: 10042/to-2878.
Computational Organic Chemistry » Benchmarking conformations: melatonin responded on 11 Apr 2013 at 9:00 am #
[…] predict accurate conformation energies is quite important. Martin has done this for alkanes1 (see this post), and now he has looked at a molecule that contains weak intermolecular hydrogen bonds. He examined […]