Density Functional Theory in Transition-Metal Chemistry: A Self-Consistent Hubbard $U$ Approach

Transition-metal centers are the active sites for a broad variety of biological and inorganic chemical reactions. Notwithstanding this central importance, density-functional theory calculations based on generalized-gradient approximations often fail to describe energetics, multiplet structures, reaction barriers, and geometries around the active sites. We suggest here an alternative approach, derived from the Hubbard $U$ correction to solid-state problems, that provides an excellent agreement with correlated-electron quantum chemistry calculations in test cases that range from the ground state of ${\mathrm{Fe}}_2$ and ${\mathrm{Fe}}_2^{-}$ to the addition elimination of molecular hydrogen on ${\mathrm{FeO}}^{+}$. The Hubbard $U$ is determined with a novel self-consistent procedure based on a linear-response approach.

Figure 1

Linear response $U_{\mathrm{out}}$ calculated from the $\mathrm{GGA}+U_{\mathrm{in}}$ ground state of ${}^7\Delta _u$ ${\mathrm{Fe}}_2$, together with the extrapolated $U_{\mathrm{scf}}$. $U_0$ is $U_{\mathrm{out}}$ calculated for $U_{\mathrm{in}}=0$.

Figure 2

Potential energy surface and geometries for the ${\mathrm{FeO}}^{+}+{\mathrm{H}}_2$ reaction using GGA (blue) as compared against a CCSD(T) reference (black). Solid indicates sextet while dashed indicates quartet.

Figure 3

Potential energy surface and geometries for the ${\mathrm{FeO}}^{+}+{\mathrm{H}}_2$ reaction using $\mathrm{GGA}+U$ (5 eV) (blue) as compared against a CCSD(T) reference (black). Solid lines indicate sextet while dashed lines indicate quartet, as in Fig. 2.