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Energetics and cathode voltages of LiMPO4 olivines (M = Fe, Mn) from extended Hubbard functionals
Full text linkTransition-metal compounds pose serious challenges to first-principles calculations based on density functional theory (DFT), due to the inability of most approximate exchange-correlation functionals to capture the localization of valence electrons on their d states, essential for a predictive modeling of their properties. In this work we focus on two representatives of a well known family of cathode materials for Li-ion batteries, namely the orthorhombic LiMPO4 olivines (M = Fe, Mn). We show that extended Hubbard functionals with on-site (U) and intersite (V) interactions (so called DFT+U+V) can predict the electronic structure of the mixed-valence phases, the formation energy of the materials with intermediate Li contents, and the overall average voltage of the battery with remarkable accuracy. We find, in particular, that the inclusion of intersite interactions in the corrective Hamiltonian improves considerably the prediction of thermodynamic quantities when electronic localization occurs in the presence of significant interatomic hybridization (as is the case for the Mn compound), and that the self-consistent evaluation of the effective interaction parameters as material and ground-state-dependent quantities allows the prediction of energy differences between different phases and concentrations.THEO
Self-consistent Hubbard parameters from density-functional perturbation theory in the ultrasoft and projector-augmented wave formulations
No full textThe self-consistent evaluation of Hubbard parameters using linear-response theory is crucial for quantitatively predictive calculations based on Hubbard-corrected density-functional theory. Here, we extend a recently introduced approach based on density-functional perturbation theory (DFPT) for the calculation of the onsite Hubbard U to also compute the intersite Hubbard V. DFPT allows us to reduce significantly computational costs, improve numerical accuracy, and fully automate the calculation of the Hubbard parameters by recasting the linear response of a localized perturbation into an array of monochromatic perturbations that can be calculated in the primitive cell. In addition, here we generalize the entire formalism from norm-conserving to ultrasoft and projector-augmented wave formulations, and to metallic ground states. After benchmarking DFPT against the conventional real-space Hubbard linear response in a supercell, we demonstrate the effectiveness of the present extended Hubbard formulation in determining the equilibrium crystal structure of LixMnPO4 (x = 0, 1) and the subtle energetics of Li intercalation.THEO
Magnetic Energy Landscape of a Dymolybdenum Tetraacetate on a Bulk Insulator Surface
No full textThe magnetic states and the magnetic anisotropy barrier of a transition metal molecular complex, dimolybdenum tetraacetate, are investigated via density functional theory (DFT). Calculations are performed in the gas phase and on a calcite (10.4) bulk insulating surface, using the Generalized-Gradient Approximation (GGA)-PBE and the Hubbard-corrected DFT + U and DFT + U + V functionals. The molecular complex (denoted MoMo) contains two central metallic molybdenum atoms, embedded in a square cage of acetate groups. Recently, MoMo was observed to form locally regular networks of immobile molecules on calcite (10.4), at room conditions. As this is the first example of a metal-coordinated molecule strongly anchored to an insulator surface at room temperature, we explore here its magnetic properties with the aim to understand whether the system could be assigned features of a single molecule magnet (SMM) and could represent the basis to realize stable magnetic networks on insulators. After an introductory review on SMMs, we show that, while the uncorrected GGA-PBE functional stabilizes MoMo in a nonmagnetic state, the DFT + U and DFT + U + V approaches stabilize an antiferromagnetic ground state and several meta-stable ferromagnetic and ferrimagnetic states. Importantly, the energy landscape of magnetic states remains almost unaltered on the insulating surface. Finally, via a noncollinear magnetic formalism and a newly introduced algorithm, we calculate the magnetic anisotropy barrier, whose value indicates the stability of the molecule's magnetic moment
Self-consistent DFT+U+V study of oxygen vacancies in SrTiO₃
Full text linkContradictory theoretical results for oxygen vacancies in SrTiO3 (STO) were often related to the peculiar properties of STO, which is a d(0) transition metal oxide with mixed ionic-covalent bonding. Here, we apply, for the first time, density functional theory (DFT) within the extended Hubbard DFT + U + V approach, including onsite as well as intersite electronic interactions, to study oxygen-deficient STO with Hubbard U and V parameters computed self-consistently via density-functional perturbation theory. Our results demonstrate that the extended Hubbard functional is a promising approach to study defects in materials with electronic properties similar to STO. Indeed, DFT + U + V provides a better description of stoichiometric STO compared to standard DFT or DFT + U, the band gap and crystal field splitting being in good agreement with experiments. In turn, also the description of the electronic properties of oxygen vacancies in STO is improved, with formation energies in excellent agreement with experiments as well as results obtained with the most frequently used hybrid functionals, however, at a fraction of the computational cost. While our results do not fully resolve the contradictory findings reported in literature, our systematic approach leads to a deeper understanding of their origin, which stems from different cell sizes, STO phases, the exchange-correlation functional, and the treatment of structural relaxations and spin-polarization.THEO
Magnetic properties of Cr8 and V8 molecular rings from ab initio calculations
No full textMolecular nanomagnets are systems with a vast phenomenology and are very promising for a variety of technological applications, most notably spintronics and quantum information. Their low-energy spectrum and magnetic properties can be modeled using effective spin Hamiltonians, once the exchange coupling parameters between the localized magnetic moments are determined. In this work we employ density functional theory (DFT) to compute the exchange parameters between the atomic spins for two representative ring-shaped molecules containing eight transition-metal magnetic ions: Cr8 and V8. Considering a set of properly chosen spin configurations and mapping their DFT energies on the corresponding expressions from a Heisenberg Hamiltonian, we compute the exchange couplings between magnetic ions which are first, second, and further neighbors on the rings. In spite of their chemical and structural similarities the two systems exhibit very different ground states: antiferromagnetic for Cr8, ferromagnetic for V8, which also features non-negligible couplings between second nearest neighbors. A rationalization of these results is proposed based on the filling of the magnetic centers' d states
Pulay forces in density-functional theory with extended Hubbard functionals: From nonorthogonalized to orthogonalized manifolds
No full textWe present a derivation of the exact expression for Pulay forces in density-functional theory calculations augmented with extended Hubbard functionals and arising from the use of orthogonalized atomic orbitals as projectors for the Hubbard manifold. The derivative of the inverse square root of the orbital overlap matrix is obtained as a closed-form solution of the associated Lyapunov (Sylvester) equation. The expression for the resulting contribution to the forces is presented in the framework of ultrasoft pseudopotentials and the projector-augmented-wave method and using a plane-wave basis set. We have benchmarked the present implementation with respect to finite differences of total energies for the case of NiO, finding excellent agreement. Owing to the accuracy of Hubbard-corrected density-functional theory calculations—provided the Hubbard parameters are computed for the manifold under consideration—the present work paves the way for systematic studies of solid-state and molecular transition-metal and rare-earth compounds
HP -- A code for the calculation of Hubbard parameters using density-functional perturbation theory
Full text linkWe introduce HP, an implementation of density-functional perturbation theory,
designed to compute Hubbard parameters (on-site and inter-site ) in the
framework of DFT+ and DFT++. The code does not require the use of
computationally expensive supercells of the traditional linear-response
approach; instead, unit cells are used with monochromatic perturbations that
significantly reduce the computational cost of determining Hubbard parameters.
HP is an open-source software distributed under the terms of the GPL as a
component of Quantum ESPRESSO. As with other components, HP is optimized to run
on a variety of different platforms, from laptops to massively parallel
architectures, using native mathematical libraries (LAPACK and FFTW) and a
hierarchy of custom parallelization layers built on top of MPI. The
effectiveness of the code is showcased by computing Hubbard parameters
self-consistently for the phospho-olivine LiMnFePO
() and by highlighting the accuracy of predictions of the geometry
and Li intercalation voltages
Accurate electronic properties and intercalation voltages of olivine-type Li-ion cathode materials from extended Hubbard functionals
Full text linkThe design of novel cathode materials for Li-ion batteries would greatly
benefit from accurate first-principles predictions of structural, electronic,
and magnetic properties as well as intercalation voltages in compounds
containing transition-metal elements. For such systems, density-functional
theory (DFT) with standard (semi-)local exchange-correlation functionals is of
limited use as it often fails due to strong self-interaction errors that are
especially relevant in the partially filled shells. Here, we perform a
detailed comparative study of the phospho-olivine cathode materials
LiMnPO, LiFePO, and the mixed transition metal
LiMnFePO () using four
electronic-structure methods: DFT, DFT+, DFT++, and HSE06. We show
that DFT++, with onsite and intersite Hubbard parameters
determined from first principles and self-consistently with respect to the
structural parameters by means of density-functional perturbation theory
(linear response), provides the most accurate description of the electronic
structure of these challenging compounds. In particular, we demonstrate that
DFT++ displays very clearly "digital" changes in oxidation states of the
transition-metal ions in all compounds, including the mixed-valence phases
occurring at intermediate Li concentrations, leading to voltages in remarkable
agreement with experiments. We show that the inclusion of intersite Hubbard
interactions is essential for the accurate prediction of thermodynamic
quantities, balancing the drive for localization induced by the onsite with
intersite orbital hybridizations
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