Stepwise hydrogenation of N₂ - A large-scale investigation of the performance and basis set convergence of DFT and conventional ab initio methods

The basis set convergence of non-local density functional theory (NL-DFT) using the functionals BLYP, BP86, B3P86, B3PW91 and B3LYP has been investigated. To this end we calculated the heats of hydrogenation of N₂, N₂H₂ and N₂H₄ at the NL-DFT levels using the Pople basis sets from 6-31G(d) up to 6-311+G(3df,3pd), Dunnings correlation consistent basis sets cc-pVDZ, cc-pVTZ, cc-pVQZ and their augmented versions, as well. We also report additional calculations at the BLYP level using Slater-type basis functions up to TZ2P quality. The results are compared with conventional ab initio calculations at the MP2 and CCSD(T) levels with the Pople and Dunning basis sets as well as with available experimental data. The calculated heat of formation of diazene has been compared with several previously published high-level calculations. The combination of B3LYP with the Pople basis set having at least 6-311+G(d,p) quality gives the best DFT results for the three hydrogenation reactions. The B3LYP/6-311+G(d,p) values are better than the MP2 data with the large Pople basis sets. While B3LYP and the other DFT methods converge smoothly when the Pople basis sets become larger, the behavior of B3LYP with respect to the correlation consistent basis sets is puzzling. The calculated heats of formation at B3LYP level with cc-pVDZ, cc-pVTZ and cc-pVQZ basis oscillate, and the oscillation is enhanced with their augmented versions. MP2 and CCSD(T) converge smoothly within the Dunning's cc-pVxZ series of basis sets and their augmented versions. CCSD(T) gives the overall best results for the calculated heats of hydrogenation, but the values that are obtained with the largest basis set still do not have chemical accuracy (≤1 kcal mol^-1). Chemical accuracy is achieved with the extrapolation schemes G2 and CBS-Q.