How Accurate Are the Minnesota Density Functionals for Noncovalent Interactions, Isomerization Energies, Thermochemistry, and Barrier Heights Involving Molecules Composed of Main-Group Elements?

The 14 Minnesota density functionals published between the years 2005 and early 2016 are benchmarked on a comprehensive database of 4986 data points (84 data sets) involving molecules composed of main-group elements. The database includes noncovalent interactions, isomerization energies, thermochemistry, and barrier heights, as well as equilibrium bond lengths and equilibrium binding energies of noncovalent dimers. Additionally, the sensitivity of the Minnesota density functionals to the choice of basis set and integration grid is explored for both noncovalent interactions and thermochemistry. Overall, the main strength of the hybrid Minnesota density functionals is that the best ones provide very good performance for thermochemistry (e.g., M06-2X), barrier heights (e.g., M08-HX, M08-SO, MN15), and systems heavily characterized by self-interaction error (e.g., M06-2X, M08-HX, M08-SO, MN15), while the main weakness is that none of them are state-of-the-art for the full spectrum of noncovalent interactions and isomerization energies (although M06-2X is recommended from the 10 hybrid Minnesota functionals). Similarly, the main strength of the local Minnesota density functionals is that the best ones provide very good performance for thermochemistry (e.g., MN15-L), barrier heights (e.g., MN12-L), and systems heavily characterized by self-interaction error (e.g., MN12-L and MN15-L), while the main weakness is that none of them are state-of-the-art for the full spectrum of noncovalent interactions and isomerization energies (although M06-L is clearly the best from the four local Minnesota functionals). As an overall guide, M06-2X and MN15 are perhaps the most broadly useful hybrid Minnesota functionals, while M06-L and MN15-L are perhaps the most broadly useful local Minnesota functionals, although each has different strengths and weaknesses.