  Proton-transfer (PT) between organic complexes is a common and important
biochemical process. Unfortunately, PT energy barriers are difficult to
accurately predict using density functional theory (DFT); in particular, the
generalized gradient approximation (GGA) tends to underestimate PT barriers.
Moreover, PT typically occurs in environments where dispersion forces
contribute to the cohesion of the system; thus, a suitable exchange-correlation
functional should accurately describe both dispersion forces and PT barriers.
This paper provides benchmark results for the PT barriers of several density
functionals including several variants of the van der Waals density functional
(vdWDF). The benchmark set comprises small organic molecules with inter- and
intra-molecular PT. The results show that replacing GGA correlation with a
fully non-local vdW-DF correlation increases the PT barriers, making it closer
to the quantum chemical reference values. In contrast, including nonlocal
correlations with the Vydrov-Voorhis (VV) method or dispersion-corrections at
the DFT-D3 or the Tkatchenko-Scheffler (TS) level has barely any impact on the
PT barriers. Hybrid functionals also increase and improve the energies and the
best performance is provided by a hybrid version of the consistent-exchange van
der Waals density functional vdW-DF-cx. For the formic acid dimer PT system, we
analyzed the GGA exchange and non-local correlation contributions. The analysis
shows that the repulsive part of the non-local correlation kernel plays a key
role in the PT energy barriers predicted with vdW-DF.
