Various methods going beyond density functional theory (DFT), such as DFT+U, hybrid functionals, meta-GGAs, GW, and DFT-embedded dynamical mean field theory (eDMFT), have been developed to describe the electronic structure of correlated materials, but it is unclear how accurate these methods can be expected to be when applied to a given strongly correlated solid. It is thus of pressing interest to compare their accuracy as they apply to different categories of materials. Here we introduce a novel paradigm in which a chosen set of beyond-DFT methods is systematically and uniformly tested on a chosen class of materials. For a first application, we choose the target materials to be the binary transition metal oxides FeO, CoO, MnO, and NiO in their antiferromagnetic phase and present a head-to-head comparison of spectral properties as computed using the various methods. We also compare with available experimental angle-resolved photoemission spectroscopy (ARPES), inverse-photoemission spectroscopy, and with optical absorption. For the class of compounds studied here, we find that both B3LYP and eDMFT reproduce the experiments quite well, with eDMFT doing best, in particular when comparing with the ARPES data.
Assessment of electronic structure methods for the determination of the ground spin states of Fe( ii ), Fe( iii ) and Fe( iv ) complexes
Our ability to understand and simulate the reactions catalyzed by iron depends strongly on our ability to predict the relative energetics of spin states. In this work, we studied the electronic structures of Fe 2+ ion, gaseous FeO and 14 iron complexes using Kohn–Sham density functional theory with particular focus on determining the ground spin state of these species as well as the magnitudes of relevant spin-state energy splittings. The 14 iron complexes investigated in this work have hexacoordinate geometries of which seven are Fe( ii ), five are Fe( iii ) and two are Fe( iv ) complexes. These are calculated using 20 exchange–correlation functionals. In particular, we use a local spin density approximation (LSDA) – GVWN5, four generalized gradient approximations (GGAs) – BLYP, PBE, OPBE and OLYP, two non-separable gradient approximations (NGAs) – GAM and N12, two meta-GGAs – M06-L and M11-L, a meta-NGA – MN15-L, five hybrid GGAs – B3LYP, B3LYP*, PBE0, B97-3 and SOGGA11-X, four hybrid meta-GGAs – M06, PW6B95, MPW1B95 and M08-SO and a hybrid meta-NGA – MN15. The density functional results are compared to reference data, which include experimental results as well as the results of diffusion Monte Carlo (DMC) calculations and ligand field theory estimates from the literature. For the Fe 2+ ion, all functionals except M11-L correctly predict the ground spin state to be quintet. However, quantitatively, most of the functionals are not close to the experimentally determined spin-state splitting energies. For FeO all functionals predict quintet to be the ground spin state. For the 14 iron complexes, the hybrid functionals B3LYP, MPW1B95 and MN15 correctly predict the ground spin state of 13 out of 14 complexes and PW6B95 gets all the 14 complexes right. The local functionals, OPBE, OLYP and M06-L, predict the correct ground spin state for 12 out of 14 complexes. Two of the tested functionals are not recommended to be used for this type of study, in particular M08-SO and M11-L, because M08-SO systematically overstabilizes the high spin state, and M11-L systematically overstabilizes the low spin state.
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- Award ID(s):
- 1665391
- NSF-PAR ID:
- 10058350
- Date Published:
- Journal Name:
- Physical Chemistry Chemical Physics
- Volume:
- 19
- Issue:
- 20
- ISSN:
- 1463-9076
- Page Range / eLocation ID:
- 13049 to 13069
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Vibrational frequencies for a selected set of transition metal carbonyl complexes are computed with various forms of density functional theory (B3LYP, BP86, M06, and M06-L), employing several different basis sets. The computed frequencies for the carbonyl stretches are compared to the experimental values obtained from gas phase infrared spectra of isolated neutrals and ions. Recommended carbonyl-stretch scaling factors which are developed vary significantly for different functionals, but there is little variation with basis set. Scaled frequencies compared to experimental spectra for cobalt and tantalum carbonyl cations reveal additional variations in multiplet patterns and relative band intensities for different functionals.more » « less
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Platinum is used extensively as a catalyst for a wide variety of chemical reactions, though its scarcity and price present limitations to expansions of its use. To understand the origin of platinum's versatility—with the goals of both improving the efficiency of existing catalysts and mimicking its reactivity with more abundant metals—the mechanisms of platinum-catalyzed chemical reactions must be understood via structural and spectroscopic characterization of these catalysts under operando conditions. Such data, typically consisting of complex mixtures of species, often prove challenging to interpret, inviting the aid of chemical theory. DFT calculations in particular have proven successful at predicting structural and spectroscopic parameters of transition metal species, though a thorough investigation of how these methods perform for platinum-based complexes has yet to be undertaken. Herein, we evaluated the performance of geometry optimization for five commonly used functionals (BP86, PBE, B3LYP, PBE0, and TPSSh) in combination with various ligand basis sets, relativistic approximations, and solvation and dispersion models. We applied these DFT methods to a training set of 14 platinum-containing complexes with varying sizes, oxidation states, and number and type of ligands and determined that the best-performing method was the PBE0 functional together with the def2-TZVP basis set for the ligand atoms, the ZORA relativistic approximation, and solvation and dispersion corrections. The ability of this DFT methodology to accurately predict metrical parameters was confirmed using two case studies, most notably by comparing the DFT optimized geometry of a previously uncharacterized complex to newly collected EXAFS data, which showed excellent agreement.more » « less
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null (Ed.)Iron-based extended metal atom chains (EMACs) are potentially high-spin molecules with axial magnetic anisotropy and thus candidate single-molecule magnets (SMMs). We herein compare the tetrairon( ii ), halide-capped complexes [Fe 4 (tpda) 3 Cl 2 ] ( 1Cl ) and [Fe 4 (tpda) 3 Br 2 ] ( 1Br ), obtained by reacting iron( ii ) dihalides with [Fe 2 (Mes) 4 ] and N 2 , N 6 -di(pyridin-2-yl)pyridine-2,6-diamine (H 2 tpda) in toluene, under strictly anhydrous and anaerobic conditions (HMes = mesitylene). Detailed structural, electrochemical and Mössbauer data are presented along with direct-current (DC) and alternating-current (AC) magnetic characterizations. DC measurements revealed similar static magnetic properties for the two derivatives, with χ M T at room temperature above that for independent spin carriers, but much lower at low temperature. The electronic structure of the iron( ii ) ions in each derivative was explored by ab initio (CASSCF-NEVPT2-SO) calculations, which showed that the main magnetic axis of all metals is directed close to the axis of the chain. The outer metals, Fe1 and Fe4, have an easy-axis magnetic anisotropy ( D = −11 to −19 cm −1 , | E / D | = 0.05–0.18), while the internal metals, Fe2 and Fe3, possess weaker hard-axis anisotropy ( D = 8–10 cm −1 , | E / D | = 0.06–0.21). These single-ion parameters were held constant in the fitting of DC magnetic data, which revealed ferromagnetic Fe1–Fe2 and Fe3–Fe4 interactions and antiferromagnetic Fe2–Fe3 coupling. The competition between super-exchange interactions and the large, noncollinear anisotropies at metal sites results in a weakly magnetic non-Kramers doublet ground state. This explains the SMM behavior displayed by both derivatives in the AC susceptibility data, with slow magnetic relaxation in 1Br being observable even in zero static field.more » « less
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Complexes containing a transition metal atom with a 3d4–3d7 electron configuration typically have two low-lying, high-spin (HS) and low-spin (LS) states. The adiabatic energy difference between these states, known as the spin-crossover energy, is small enough to pose a challenge even for electronic structure methods that are well known for their accuracy and reliability. In this work, we analyze the quality of electronic structure approximations for spin-crossover energies of iron complexes with four different ligands by comparing energies from self-consistent and post-self-consistent calculations for methods based on the random phase approximation and the Fermi–Löwdin self-interaction correction. Considering that Hartree–Fock densities were found by Song et al., J. Chem. Theory Comput. 14, 2304 (2018), to eliminate the density error to a large extent, and that the Hartree–Fock method and the Perdew–Zunger-type self-interaction correction share some physics, we compare the densities obtained with these methods to learn their resemblance. We find that evaluating non-empirical exchange-correlation energy functionals on the corresponding self-interaction-corrected densities can mitigate the strong density errors and improves the accuracy of the adiabatic energy differences between HS and LS states.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/C7CP01263B
