Density Functional Theory in Transition-Metal Chemistry: Relative Energies of Low-Lying States of Iron Compounds and the Effect of Spatial Symmetry Breaking Anastassia Sorkin, Mark A. Iron, and Donald G. Truhlar* Department of Chemistry and Supercomputing Institute, UniVersity of Minnesota, Minneapolis, Minnesota 55455-0431 Received September 25, 2007 Abstract: The ground and lower excited states of Fe 2 , Fe 2 - , and FeO + were studied using a number of density functional theory (DFT) methods. Specific attention was paid to the relative state energies, the internuclear distances (r e ), and the harmonic vibrational frequencies (ω e ). A number of factors influencing the calculated values of these properties were examined. These include basis sets, the nature of the density functional chosen, the percentage of Hartree- Fock exchange in the density functional, and constraints on orbital symmetry. A number of different types of generalized gradient approximation (GGA) density functionals (straight GGA, hybrid GGA, meta-GGA, and hybrid meta-GGA) were examined, and it was found that the best results were obtained with hybrid GGA or hybrid meta-GGA functionals that contain nonzero fractions of HF exchange; specifically, the best overall results were obtained with B3LYP, M05, and M06, closely followed by B1LYP. One significant observation was the effect of enforcing symmetry on the orbitals. When a degenerate orbital (π or δ) is partially occupied in the 4 Φ excited state of FeO + , reducing the enforced symmetry (from C 6v to C 4v to C 2v ) results in a lower energy since these degenerate orbitals are split in the lower symmetries. The results obtained were compared to higher level ab initio results from the literature and to recent PBE+U plane wave results by Kulik et al. (Phys. Rev. Lett. 2006, 97, 103001). It was found that some of the improvements that were afforded by the semiempirical +U correction can also be accomplished by improving the form of the DFT functional and, in one case, by not enforcing high symmetry on the orbitals. 1. Introduction Transition-metal centers have great versatility in their bond- ing. Consequently, accurate theoretical treatment of transi- tion-metal chemistry demands a flexible theoretical frame- work that treats all energetically accessible spin states, spin couplings, and valence states in an even-handed fashion, which in wave function theory requires a multiconfigurational treatment. This poses a difficult problem for the Kohn-Sham density functional theory (DFT) because all information on the multiconfigurational character of the wave function is contained in the exchange-correlation energy E XC , which is computed from an electron density that is in turn obtained from a single Hartree product of orbitals. 1,2 Even when a single antisymmetrized product (Slater determinant) of orbitals does not describe the true electronic wave function well, the Kohn-Sham ground-state energy is correct if one solves the Kohn-Sham equations for the orbitals that give the lowest-energy solution, 1 even though the Kohn-Sham orbitals and eigenvalues, except for the highest orbital eigenvalue, 3 do not have any strict physical significance, 4-6 and the Kohn-Sham Slater determinant that generates the accurate electron density may have different spin properties than the true wave function. 7-9 Nevertheless, great progress has been made in understanding transition-metal chemistry in terms of the Kohn-Sham theory. 10-13 * Corresponding author e-mail: truhlar@umn.edu. 307 J. Chem. Theory Comput. 2008, 4, 307-315 10.1021/ct700250a CCC: $40.75 © 2008 American Chemical Society Published on Web 01/01/2008