Automerization of Cyclobutadiene: Multiconfiguration Pair-Density Functional Theory Gives High Accuracy Where Unrestricted Kohn–Sham Density Functional Theory Does Not

The automerization of cyclobutadiene is a classical, well-studied example of a reaction passing through an inherently multiconfigurational transition state; the transition-state geometry is a square biradical that is the prototypical antiaromatic ring system. Here we study and compare two different approaches to treating the barrier height for this reaction by two kinds of density functional methods: unrestricted Kohn-Sham (UKS) calculations and multiconfiguration pair-density functional theory (MC-PDFT). We test 22 functionals for the former and six for the latter. By using multiple software packages, these tests allow us to compare several relatively recent functionals that are rarely compared, such as ωB97M-V, revM11, r²SCAN, M06-SX, CF22D, and DM21. We find the best performance for UKS with ωΒ97Μ-V, M06-2X, and DM21, having errors in the range 2.2-2.7 kcal/mol. Some functionals (MN15-L, revM06-L, PBE0, TPSSh, and r²SCAN) give unphysical transition states, and the mean unsigned error of the 22 UKS barrier heights is 6.4 kcal/mol. With an active space of 8 electrons in 8 orbitals, all six MC-PDFT functionals have unsigned errors in the range 0.2-1.9 kcal/mol, with the lowest error (0.2 kcal/mol) being obtained with MC23. The CASPT2 error is 1.2 kcal/mol with the (8,8) active space and 0.7 kcal/ml with the (6,6) active space. We conclude that MC-PDFT can provide a practical and accurate way to treat inherently multiconfigurational transition states.