B3LYP-D3 vs. B97-D3 (effect of hybrid and semi-local GGAs)
B97-D3 serves to increase the binding strength of the system and of
adsorbates more than B3LYP-D3 because GGA bonded interactions tend to be
stronger than their hybrid counterparts that include exact
exchange.52 This paper shows a decrease in adsorption
energy from B3LYP-D3 to B97-D3 of ~0.2 eV. Bond lengths
with B97-D3 are slightly smaller for N2, NH,
NH2, and NH3, and larger for N.
Gas-phase vibrational frequencies with B97-D3 are closer to experimental
benchmarks as well as theoretical benchmarks of non-empirical GGAs.
B3LYP-D3 overestimates the frequency of most modes, sometimes by as much
as 100-200 cm-1, as in the case of the
N2 stretch. Adsorbed to the catalyst, B97-D3 is the only
method that correctly predicts the lowest energy bonding pattern and
orientation of N2.43,53 Despite both
functionals including dispersion corrections, both continue to underbind
dispersion-bound N2.
A notable difference in the ground state multiplicity and spin density
profile of the catalyst surface exists between B97-D3 and the hybrid
methods (figures in Supplementary Data). Despite this fact, after
adsorption of an intermediate to the catalyst surface, the resulting
spin density profiles follow an almost identical trend as the hybrid
methods. This may imply B97-D3 has more difficulty predicting the
correct ground state structure before adsorption since the surface is a
charge-transfer complex with unpaired electrons, two characteristics
often modeled better by methods with exact exchange (although dispersion
helps).52 Since the density profiles are a match after
adsorption, all three methods result in the same site preferences across
all adsorbates (with the exception of N2 and NH(100)
using B3LYP-D3). This fact, combined with more accurate thermodynamic
data and reduced computation time, make B97-D3 a viable option for
continued study of this system and related metal cluster systems. B97-D3
includes minimal empiricism, sitting in the top 10 least-parameterized
semi-empirical methods, according to one study of seventy
functionals.52