Hydrogen bonding represents a particular challenge to computational quantum chemistry. The figures below show the energy of two different "proton sponge" molecules as a function of the position of a proton as it moves between the donor and acceptor. They are taken from a nice paper I blogged about before.
The different curves correspond to different "levels" of theory and methods.
MP2 stands for second-order perturbation theory (Moller-Plesset) beyond Hartree-Fock.
The other four methods involve density functional theory [DFT] with different functionals.
The different methods give significantly different values for the energy barrier [or whether it exists all] and the positions of the minima.
Which method is "correct", i.e. the most reliable? How does one decide?
What can one benchmark against?
Higher level quantum chemistry [e.g. multi-reference methods] are not possible on large molecules.
Do these differences matter?
After all, isn't 1 kcal/mol [40 meV] just room temperature and so defines "chemical accuracy"?
Does 1/30 of an Angstrom really matter?
There are important situations where the differences in results between methods, especially the size of the barrier, will have a large effect on the results of simulations. For example, path integral molecular dynamics simulations of proton transfer in biomolecules, and of quantum nuclear effects in water. Now there are many simulations using DFT based methods. Some just pick a functional and go from there.
I would like to suggest that one way to benchmark different methods is to compare the above one dimensional potential with the simple parametrisation used in my recent preprint on quantum nuclear effects in hydrogen bonded complexes, and shown in the Figure below. This potential seems to have properties that are consistent with a wide range of experiments [bond lengths, vibrational frequencies, isotope effects] for a diverse set of chemical complexes.
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