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