This study explores the degree to which GGA, meta-GGA, hybrid GGA, and hybrid meta-GGA functionals of density functional theory (DFT), when used with the 6-31+G(d) basis set, are able to reproduce the MP2/6-31+G(d) structures and energetics of the species involved in the reactions of halomethyllithium carbenoids with ethylene. While many popular DFT functionals have been parametrized and/or benchmarked using various databases, the scarcity of experimental structural and energetic information for organolithium compounds has resulted in their exclusion from these training and test sets. In this work, we first establish a set of practical benchmark reaction energetics against which the performance of DFT methods for larger molecules can be compared. Next, we examine the performance of 13 DFT functionals spanning the second, third, and fourth rungs of the "Jacob's ladder" using 84 molecules and 78 reactions. The main conclusions are (a) the meta-hybrid GGA M06-2X is the best functional among the set for organolithium chemistry, (b) the hybrid GGA PBE1PBE consistently yields equilibrium and transition-state geometries that are very close to the MP2 predictions, and (c) MP2//M06-L or MP2//PBE1PBE model chemistries are excellent low-cost alternatives to the costly MP2. However, this work also showed that the very popular B3LYP functional is a rather poor choice for these systems.

The B3LYP, M06, M06L, M062X, MPW1K, and PBE1PBE DFT methods were evaluated for modeling nickel-catalyzed coupling reactions. The reaction consists of a nucleophilic attack by a carbanion equivalent on the nickel complex, S(N)2 attack by the anionic nickel complex on an alkyl halide, and reductive elimination of the coupled alkane product, regenerating the nickel catalyst. On the basis of CCSD(T)//DFT single-point energies, the B3LYP, M06, and PBE1PBE functionals were judged to generate the best ground state geometries. M06 energies are generally comparable or superior to B3LYP and PBE1PBE energies for transition state calculations. The MP2 and CCSD methods were also evaluated for single-point energies at the M06 geometries. The rate-determining step of this reaction was found to be nucleophilic attack of a L(2)NiR anion on the alkyl halide.