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

Department of Materials Science and Engineering , Massachusetts Institute of Technology, Cambridge, Massachusetts, United States
Physical Review Letters (Impact Factor: 7.51). 10/2006; 97(10):103001. DOI: 10.1103/PhysRevLett.97.103001
Source: PubMed


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 Fe2 and Fe2- to the addition elimination of molecular hydrogen on FeO+. The Hubbard U is determined with a novel self-consistent procedure based on a linear-response approach.

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    • "It is contingent from these VASP calculations that the results obtained using PBE are in better agreement with experiments compared to PBE0. There have been also efforts to study the effects of including Hubbard U with PBE calculations [29] [30]. We have also considered Fe-rich isomers of Fe-Pt clusters (namely Fe 3 Pt and Fe 4 Pt) for understanding the ground state structures as obtained with PBE as well as with PBE0 functional for different fixed spin multiplicities. "
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    ABSTRACT: Atomic structure, alloying behavior, and magnetism in small Fe-Pt clusters We report results of the atomic structure, alloying behaviour, and magnetism in FemPtn (m + n = 2-10) clusters using projector augmented wave (PAW) pseudopotential method and spin-polarized generalized gradient approximation (GGA) for the exchange-correlation energy. These results are compared with those obtained by using HCTH exchange-correlation functional and LANL2DZ basis set in Gaussian program and the overall trends are found to be similar. As in bulk Fe-Pt alloys, clusters with almost equal composition of Fe and Pt have the largest binding energy and the largest heat of nanoalloy formation for a given number of atoms in the cluster. There are some deviations due to the different symmetries in clusters and in cases where the total number of atoms is odd. The lowest energy isomers tend to maximize bonds between unlike atoms with Fe (Pt) atoms occupying high (low) coordination sites in the core (surface) of the cluster. The binding energy, heat of formation, and the second order difference of the total energy show Fe2Pt2, Fe4Pt4, and Fe4Pt6 clusters to be the most stable ones among the different clusters we have studied. The magnetic moments on Fe atoms are high in Pt-rich clusters as well as in small Fe-rich clusters and decrease as the aggregation of Fe atoms and the cluster size increases. The maximum value of the magnetic moments on Fe atoms is ~ 3.8μB whereas for Pt atoms it is 1μB. These are quiet high compared with the values for pure Fe as well as bulk FePt and Fe3Pt phases while bulk Pt is non-magnetic. There is significant charge transfer from those Fe atoms that interact directly with Pt atoms. We discuss the hybridization between the electronic states of Pt and Fe atoms as well as the variation in the magnetic moments on Fe and Pt atoms. Our results provide insight in to the understanding of the nanoalloy behaviour of Fe-Pt and we hope that this would help to design Fe based nanoalloys and their assemblies with high magnetic moments for strong magnets without rare earths as well as Pt alloy catalysts.
    Full-text · Article · Aug 2015 · Physical Review B
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    • "Such a discrepancy may be resolved when the Hubbard U is determined in a more rigorous self-consistent approach. In this approach, the Hubbard U is determined from the linear response of a series of DFT + U ground states (with a series of trial U values) to the local perturbation until a consistent result is achieved (Kulik et al., 2006). Fig. 9 shows the relative enthalpies of LS, IS, and low-QS HS with respect to high-QS HS (Mg 0.875 Fe 0.125 )SiO 3 in GGA(+U) and LDA (+U) calculation. "
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    ABSTRACT: With the guidance of first-principles phonon calculations, we have searched and found several metastable equilibrium sites for substitutional ferrous iron in MgSiO3 perovskite. In the relevant energy range, there are two distinct sites for high-spin, one for low-spin, and one for intermediate-spin iron. Because of variable d-orbital occupancy across these sites, the two competing high-spin sites have different iron quadrupole splittings (QS). At low pressure, the high-spin iron with QS of 2.3–2.5 mm/s is more stable, while the high-spin iron with QS of 3.3–3.6 mm/s is more favorable at higher pressure. The crossover occurs between 4 and 24 GPa, depending on the choice of exchange-correlation functional and the inclusion of on-site Coulomb interaction (Hubbard U). Our calculation supports the notion that the transition observed in recent Mössbauer spectra corresponds to an atomic-site change rather than a spin-state crossover. Our result also helps to explain the lack of anomaly in the compression curve of iron-bearing silicate perovskite in the presence of a large change of quadrupole splitting, and provides important guidance for future studies of thermodynamic properties of this phase.
    Full-text · Article · May 2010 · Earth and Planetary Science Letters
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    • "In this approach, the consistency between the response and the DFT+U ground states should be achieved. The Hubbard U determined this way is called self-consistent U (Kulik et al. 2006). This method, however, was not used in calculations reviewed here. "
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    ABSTRACT: Results of several first-principles calculations on the spin-state crossover of iron in lower-mantle minerals have been reviewed. The LDA+U method gives desirable atomic and electronic structure in ferropericlase, (Mg,Fe)O. Both low-spin and high-spin ferropericlase are insulating. Jahn-Teller distortion is observed around iron in the high-spin state. A vibrational virtual crystal model (VVCM) permitted calculations of thermodynamic properties of this system at lower mantle conditions. Predictions are overall in good agreement with several experimental data sets. They display anomalies in the bulk modulus and allowed predictions of anomalies in thermodynamic properties and of the elastic signature of this phase in the mantle. An intriguing possibility of a viscosity anomaly caused by this crossover in the mantle has been raised. Improvements in these calculations to go beyond the ideal HS-LS solid solution are still desirable, as well as self-consistent calculations of the Hubbard U. These upgrades should improve agreement between predictions and measurements of crossover pressure ranges. (Mg,Fe)SiO3 perovskite is a more difficult system to investigate, therefore more controversial. Currently, there is lack of consensus regarding the existence of IS iron in perovskite. AU calculations, irrespective of exchange-correlation functional used, agree on one issue: the IS state is not energetically competitive and no HS-to-IS crossover is expected to occur at lowermantle pressures. The calculated HS-LS crossover pressure in ferrous iron strongly depends on the exchange-correlation functional (LDA, GGA, or DFT+U), and on the iron distribution in the supercell. This makes it more difficult to compare results with or interpret experimental data. A non-ideal HS-LS solid solution treatment appears to be essential for this system. On the positive side, the HS-LS crossover does not appear to affect the compressibility of this system to experimentally detectable levels. In the lower mantle, the change in compressibility of this system should be even less detectable. A thorough study of ferric iron using a more appropriate exchange-correlation functional or the DFT+U method is still needed for more extensive comparison between experimental data and theoretical results. (Mg,Fe)SiO3 post-perovskite is the least understood phase. Existing experimental data appear contradictory, and computational work is limited. The spin-state crossover in (Mg,Fe) SiO3-post-perovskite is still a wide open question.
    Full-text · Article · Apr 2010 · Reviews in Mineralogy and Geochemistry
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