Density Functional Theory in Transition-Metal Chemistry:  Relative Energies of Low-Lying States of Iron Compounds and the Effect of Spatial Symmetry Breaking

Abstract

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 HartreeFock 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.

Towards quantifying the role of exact exchange in predictions of transition metal complex properties

“…31,78,79 Including higher order dependence on the density as in a meta-GGA improves identification of some high-spin states: Fe(II) (NH 3 ) 6 and Fe(III) (NCH) 6 are predicted to be high spin with a meta-GGA, while they were predicted to be low-spin with a GGA. However, meta-GGA results are inconsistent: Fe(III) (NH3) 6 31,80 but the meta-GGA predicts both to be low-spin.…”

Benchmarking the performance of time-dependent density functional methods

“…Several benchmark studies [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] have explored the performance of using ground-state density functionals within the adiabatic approximation for the calculation of vertically excited states using TDDFT. The scope of the previous benchmark studies has been primarily limited to singlet valence excited states [36][37][38][39] with very few benchmarks considering triplet valence [40][41][42] or singlet and triplet Rydberg excited states.…”

“…In addition, very few benchmark studies have investigated the performance of meta-generalized gradient approximation (mGGA) density functionals for the calculation of vertical excitation energies with TDDFT. [44][45][46][47][48] It is therefore of interest to perform benchmarks that assess the performance of density functionals, including recently developed mGGA functionals, for the vertical excitation energy calculation of singlet, triplet, valence, and Rydberg excited states using TDDFT.…”

Mechanistic insights into the reductive dehydroxylation pathway for the biosynthesis of isoprenoids promoted by the IspH enzyme

“…To shed light on this issue we investigated the larger model M3, with 456 atoms, using DFT+U and plane wave calculations, as implemented in VASP, which performs quite well for magnetic molecules. 52 Indeed, earlier studies showed that VASP calculations reproduced G09 results within a 0.5 kcal mol –1 limit of accuracy. 53 Using model M3 we re-optimized the structures along the favored reaction pathway corresponding to the reduced [Fe 4 S 4 ] + state in the presence of a protonated Glu126.…”