Predicting bond dissociation energy and bond length for bimetallic diatomic molecules: a challenge for electronic structure theory

Accurately predicting bond length and bond dissociation energy for bimetallic diatomic molecules that involve metal-metal multiple bonds is a great challenge for electronic structure theory, in part because many of these molecules have inherently multi-configuration wave functions, a characteristic that is variously labeled as strong correlation or multireference character. Although various popular density functionals are widely used in studying metal-metal bonding in catalysis, their accuracy can be questioned, and it is important to see both how well and how poorly a functional can perform. Here we test 50 Kohn-Sham exchange-correlation density functionals for selected 3d and 4d hetero- and homonuclear bimetallic diatomic molecules against experimental bond lengths and bond energies. We found that for the majority of the density functionals, the mean unsigned error in predicting the bond length is larger than 0.08 Å, and for the bond energy, half of the functionals give a mean unsigned error larger than 20 kcal mol^-1. This indicates that such highly multireference bimetallic systems are challenging for KS-DFT. However, some exchange-correlation functionals perform significantly better than average for both bond energies and bond lengths, in particular, BLYP, M06-L, N12-SX, OreLYP, RPBE, and revPBE, and are recommended for both kinds of calculations. Other functionals that perform relatively well for bond lengths include MGGA_MS0, MOHLYP, OLYP, PBE, and SOGGA11, and other functionals that perform relatively well for bond energies include GAM, M05, M06, MN15, and τ-HCTHhyb. Although some of these functionals (M05, M06, MN15, N12-SX, and τ-HCTHhyb) contain a nonzero percentage of Hartree-Fock exchange, a broader conclusion is that Hartree-Fock exchange brings in a static correlation error and usually tends to make the results, especially the bond lengths, less accurate. We find some significant differences between all-electron calculations and calculations with effective core potentials. For analysis, the article also presents CASSCF calculations of the percentage contributions of the dominant configurations, and the paper compares orbitals and configurations obtained in DFT calculations to those in CASSCF calculations. The equilibrium bond distance of Rh₂ is not available from experiments, and we predict it to be 2.22 Å. The bond energy of VCr is not available from experiments, and we predict it to be 52.9 kcal mol^-1.