DFT+U in Dudarev's formulation with corrected interactions between the electrons with opposite spins: The form of Hamiltonian, calculation of forces, and bandgap adjustments

Orbital-Resolved DFT+U for Molecules and Solids

We present an orbital-resolved extension of the Hubbard U correction to density-functional theory (DFT). Compared to the conventional shell-averaged approach, the prediction of energetic, electronic and structural properties is strongly improved, particularly for compounds characterized by both localized and hybridized states in the Hubbard manifold. The numerical values of all Hubbard parameters are readily obtained from linear-response calculations. The relevance of this more refined approach is showcased by its application to bulk solids pyrite (FeS2) and pyrolusite (β-MnO2), as well as to six Fe(II) molecular complexes. Our findings indicate that a careful definition of Hubbard manifolds is indispensable for extending the applicability of DFT+U beyond its current boundaries. The present orbital-resolved scheme aims to provide a computationally undemanding yet accurate tool for electronic structure calculations of charge-transfer insulators, transition-metal (TM) complexes and other compounds displaying significant orbital hybridization.

Review on Magnetism in Catalysis: From Theory to PEMFC Applications of 3d Metal Pt-Based Alloys

The relationship between magnetism and catalysis has been an important topic since the mid-20th century. At present time, the scientific community is well aware that a full comprehension of this relationship is required to face modern challenges, such as the need for clean energy technology. The successful use of (para-)magnetic materials has already been corroborated in catalytic processes, such as hydrogenation, Fenton reaction and ammonia synthesis. These catalysts typically contain transition metals from the first to the third row and are affected by the presence of an external magnetic field. Nowadays, it appears that the most promising approach to reach the goal of a more sustainable future is via ferromagnetic conducting catalysts containing open-shell metals (i.e., Fe, Co and Ni) with extra stabilization coming from the presence of an external magnetic field. However, understanding how intrinsic and extrinsic magnetic features are related to catalysis is still a complex task, especially when catalytic performances are improved by these magnetic phenomena. In the present review, we introduce the relationship between magnetism and catalysis and outline its importance in the production of clean energy, by describing the representative case of 3d metal Pt-based alloys, which are extensively investigated and exploited in PEM fuel cells.

Dipole Switching by Intramolecular Electron Transfer in Single-Molecule Magnetic Complex [Mn12O12(O2CR)16(H2O)4]

We study intramolecular electron transfer in the single-molecule magnetic complex [Mn₁₂O₁₂(O₂CR)₁₆ (H₂O)₄] for R = -H, -CH₃, -CHCl₂, -C₆H₅, and -C₆H₄F ligands as a mechanism for switching of the molecular dipole moment. Energetics is obtained using the density functional theory (DFT) with onsite Coulomb energy correction (DFT + U). Lattice distortions are found to be critical for localizing an extra electron on one of the easy sites on the outer ring in which localized states can be stabilized. We find that the lowest-energy path for charge transfer is for the electron to go through the center via superexchange-mediated tunneling. The energy barrier for such a path ranges from 0.4 to 54 meV depending on the ligands and the isomeric form of the complex. The electric field strength needed to move the charge from one end to the other, thus reversing the dipole moment, is 0.01-0.04 V/Å.

Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems

Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a confluence and coaction of expertise in computer science and physical sciences. This Review is written for new and experienced researchers working at the intersection of both fields. We first provide concise tutorials of computational chemistry and machine learning methods, showing how insights involving both can be achieved. We follow with a critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful (and useful) predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design.

A local-orbital density functional formalism for a many-body atomic Hamiltonian: Hubbard-Hund's coupling and DFT + U functional

In the conventional DFT + U approach, the mean field solution of the Hubbard Hamiltonian associated with thedorf(iσ) electrons of a transition metal atom is used to define the DFT + U potential acting on theiσ-electrons. In this work, we go beyond that mean field solution by analyzing the correlation energy and potential for a multi-level atom described by a Kanamori Hamiltonian connected to different channels representing the environment. As a first step, we analyze the many-body solution of our model, using a local-orbital density functional formalism that takes as independent variables the orbital occupancies,n_iσ, of the atomic orbitals; accordingly, we present the corresponding density functional solution describing the correlation energy and potential as a function ofn_iσ. Then, we use this analysis to introduce a DFT + U potential extending previous proposals to materials with arbitrarily high correlation. In particular, we find that this potential mainly screens the conventional mean field potential contribution, and also yields new terms associated with the number of atomic electrons. Our results show that the atomic correlation effects enhance the role played by the intra-atomic exchange interaction and favor the formation of magnetic solutions.

Evaluation of optical band gaps and dopant state energies in transition metal oxides using oxidation-state constrained density functional theory

We report the use of oxidation-state constrained density functional theory (OS-CDFT) to calculate the optical band gaps of transition metal oxides and dopant state energies of different doped anatase. OS-CDFT was used to control electron transfer from the valence band maximum of the transition metal system to the conduction band minimum or to the dopant state in order to calculate the band gap or the dopant state energies respectively. The calculation of the dopant state energies also allows identification of the transition responsible for the reduced band gap of the doped system in ambiguous cases. We applied this approach to the band gap calculation in TiO₂anatase and rutile, vanadium pentoxide (V₂O₅), chromium(III) oxide (Cr₂O₃), manganese(IV) oxide (MnO₂), ferric oxide (Fe₂O₃), ferrous oxide (FeO) and cobalt(II) oxide (CoO). The dopant state energies calculations were carried out in the V-, Cr-, Mn-, and Fe-doped anatase.

Evaluation of redox potentials of cathode materials of alkali-ion batteries using extended DFT+U+U↑↓ method: The role of interactions between the electrons with opposite spins

Limitations of the DFT+U approach (e.g., in Dudarev's formulation) applied for accurate evaluation of redox potentials of cathode materials of alkali-ion batteries with U parameters calculated via the linear response (LR) method are discussed. In contrast to our previous studies, where redox potentials of several cathode materials have been calculated in a good agreement with experiment (e.g., NaMnO₂, LiFePO₄, and LiTiS₂), herein, we analyze other cathode materials, such as LiNiO₂ and Ni- and V-containing phosphates for which this method provides much underestimated redox voltages. We ascribe this limited predictive power of the DFT+U method, parameterized via LR, to the absence of corrections of Coulomb interactions between the electrons with opposite spins. Using the recently proposed extended DFT+U+U_↑↓ functional, which includes the aforementioned corrections, we show how redox potentials of Ni- and V-based compounds could be calculated in a much better agreement with experiment, also proposing a procedure of parameterization of such calculations. Thus, our extended method allows us to calculate redox potentials of several important materials more accurately while retaining good agreement with experiment for structures where the standard DFT+U method also accurately predicts electrochemical properties.

The Hubbard-U correction and optical properties of d0 metal oxide photocatalysts

We report a systematic investigation of individual and multisite Hubbard-U corrections for the electronic, structural, and optical properties of the metal titanate oxide d⁰ photocatalysts SrTiO₃ and rutile/anatase TiO₂. Accurate bandgaps for these materials can be reproduced with local density approximation and generalized gradient approximation exchange-correlation density functionals via a continuous series of empirically derived U^d and U^p combinations, which are relatively insensitive to the choice of functional. On the other hand, lattice parameters are much more sensitive to the choice of U^d and U^p, but in a systematic way that enables the U^d and U^p corrections to be used to qualitatively gauge the extent of self-interaction error in the electron density. Modest U^d corrections (e.g., 4 eV-5 eV) yield the most reliable dielectric response functions for SrTiO₃ and are comparable to the range of U^d values derived via linear response approaches. For r-TiO₂ and a-TiO₂, however, the U^d,p corrections that yield accurate bandgaps fail to accurately describe both the parallel and perpendicular components of the dielectric response function. Analysis of individual U^d and U^p corrections on the optical properties of SrTiO₃ suggests that the most consequential of the two individual corrections is U^d, as it predominately determines the accuracy of the dominant excitation from O-2p to the Ti-3d t_2g/e_g orbitals. U^p, on the other hand, can be used to shift the entire optical response uniformly to higher frequencies. These results will assist high-throughput and machine learning approaches to screening photoactive materials based on d⁰ photocatalysts.

Thermal spin crossover in Fe(ii) and Fe(iii). Accurate spin state energetics at the solid state

Parametrization of PBE+U under the D3 and D3-BJ dispersion corrections to study Fe^II and Fe^III-based Spin Crossover complexes.