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Publication# Topology, Oxidation States, and Charge Transport in Ionic Conductors

Résumé

Recent theoretical advances, based on a combination of concepts from Thouless' topological theory of adiabatic charge transport and a newly introduced gauge-invariance principle for transport coefficients, have permitted to connect (and reconcile) Faraday's picture of ionic transport-whereby each atom carries a well-defined integer charge-with a rigorous quantum description of the electronic charge-density distribution, which hardly suggests its partition into well defined atomic contributions. In this paper, these progresses are reviewed; in particular, it is shown how, by relaxing some general topological conditions, charge may be transported in ionic conductors without any net ionic displacements. After reporting numerical experiments which corroborate these findings, a new connection between the topological picture and the well-known Marcus-Hush theory of electron transfer is introduced in terms of the topology of adiabatic paths drawn by atomic trajectories. As a significant byproduct, the results reviewed here permit to classify different regimes of ionic transport according to the topological properties of the electronic structure of the conducting material. Finally, a few recent applications to energy materials and planetary sciences are reported.

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Publications associées (5)

Concepts associés (18)

Electronic structure

In physics, electronic structure is the state of motion of electrons in an electrostatic field created by stationary nuclei. The term encompasses both the wave functions of the electrons and the ene

Charge électrique

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Planétologie

La planétologie est la science qui étudie les planètes et les autres objets célestes condensés à l'exception des étoiles, comme les planètes naines, les astéroïdes, les comètes et les satellites, voi

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Density functional approximations fail to provide a consistent description of weak molecular interactions arising from small electron density overlaps. A simple remedy to correct for the missing interactions is to add a posteriori an attractive energy term summed over all atom pairs in the system. The density-dependent energy correction, presented herein, is applicable to all elements of the periodic table and is easily combined with any electronic structure method, which lacks the accurate treatment of weak interactions. Dispersion coefficients are computed according to Becke and Johnson’s exchange-hole dipole moment (XDM) formalism, thereby depending on the chemical environment of an atom (density, oxidation state). The long- range ∼R-6 potential is supplemented with higher-order correction terms (∼R-8 and ∼R-10) through the universal damping function of Tang and Toennies. A genuine damping factor depending on (iterative) Hirshfeld (overlap) populations, atomic ionization energies, and two adjustable parameters specifically fitted to a given DFT functional is also introduced. The proposed correction, dDXDM, dramatically improves the performance of popular density functionals. The analysis of 30 (dispersion corrected) density functionals on 145 systems reveals that dDXDM largely reduces the errors of the parent functionals for both inter- and intramolecular interactions. With mean absolute deviations (MADs) of 0.74-0.84 kcal mol-1, PBE-dDXDM, PBE0-dDXDM, and B3LYP-dDXDM outperform the computationally more demanding and most recent functionals such as M06-2X and B2PLYP-D (MAD of 1.93 and 1.06 kcal mol-1, respectively).

2010This thesis is concerned with the theoretical study of the adsorption of molecules and thin films to single-crystal metal surfaces. First-principles electronic calculations are performed in the framework of density functional theory in the local density approximation (LDA-DFT), by using a plane-wave formalism, norm-conserving pseudopotentials and the supercell method. For the calculation of the electronic ground state and the subsequent structural optimizations we use the Car-Parrinello technique, modified for the optimal treatment of metallic systems. This method has been improved in this work with the introduction of a Lagrangian formalism and a mathematically conserved constant of motion in the presence of variable fractional occupancies. Complex mechanisms involving substantial reconstructions of the substrate are elucidated by the study of the C60/Al(111) system. We find that the interaction of C60 molecules with the Al(111) surface is predominantly covalent, and that the adsorbates bind optimally to the surface if an Al vacancy is created directly underneath. The removed Al atoms form a (6 x 6) array of ad-dimers in the interstices of the C60 overlayer, to which they strongly bind. Large-scale structural relaxations performed directly on a surface unit cell containing three C60 molecules lead to a reconstructed structure with two vacancies and an Al ad-dimer which is significantly more stable than the unreconstructed one. This spontaneous local process, rather than the compression state of the C60 overlayer, explains why one C60 molecule out of three protrudes from the surface upon reconstruction. The delicate interplay of many competing factors occurring at the interface between different media is investigated through the study of ultrathin MgO films deposited on the Ag(100) surface. We consider pseudomorphic MgO films of thickness ranging from one to three atomic layers, and we study the evolution of the surface electronic properties as a function of coverage. We find that already three MgO monolayers are sufficient to fully develop the electronic structure of the single-crystal MgO surface, in agreement with experimental findings. We discuss the reliability of the LDA-DFT results for the band structure by using simple 1D models for the dielectric properties of the system.

We conduct a detailed investigation of defects in two representative amorphous oxides: amorphous Al2O3 (am-Al2O3) and TiO2 (am-TiO2), by combining ab initio molecular dynamics (MD) simulations and hybrid functional calculations. Our results indicate that oxygen vacancies and interstitials occur neither in am-Al2O3 nor in am-TiO2 due to structural rearrangements which assimilate the defect structure, and that the injection of extra holes can lead to the formation of O-O peroxy linkages. In am-Al2O3, hydrogen is found to be amphoteric. Based on localized Wannier functions, we identify the nominal charge state and the composition of the defect core units related to C and N impurities in am-Al2O3, which are found to depend on the total charge set in the simulation cell. Through the adopted electron counting rule, we assess that carbon and nitrogen impurities are only found in neutral and in singly positive charge states, respectively, indicating that none of them gives charge transition levels in am-Al2O3. In addition, those defect core units are shown to incorporate a varying number of oxygen atoms, by which their formation energy is dependent on the oxygen chemical potential. In addition, we propose an exchange mechanism for hole transport in am-TiO2 that relies on the simultaneous breaking and forming of O-O peroxy linkages that share one O atom. Through the use of nudged-elastic-band calculations, a hopping path as long as 1.2 nm with barriers of 0.3-0.5 eV is demonstrated, suggesting that hole diffusion through O-O peroxy linkages is viable in am-TiO2.
In this work, we also determine the band alignment between various semiconductors and liquid water by combining MD simulations of atomistic interface models, electronic-structure calculations at the hybrid-functional and GW levels, and a computational standard hydrogen electrode (SHE). Our study comprises GaAs, GaP, GaN, CdS, ZnO, SnO2, rutile and anatase TiO2. For each semiconductor, we generate atomistic interface models with liquid water at the pH corresponding to the point of zero charge. The MD simulations are started from initial configurations, in which the water molecules are either molecularly (m) or dissociatively (d) adsorbed on the semiconductor surface. The calculated band offsets are found to be strongly influenced by the adsorption mode at the semiconductor-water interface, leading to differences larger than 1 eV between m and d models of the same semiconductor. We then assess the accuracy of various ab initio electronic-structure schemes in determining the band alignment. In the last part, we try to evaluate photocatalysts for water-splitting by considering the surface coverage and the energy alignment. We determine surface concentrations of water molecules, protons, and hydroxyl ions adsorbed at the semiconductor-water interfaces mentioned above as a function of pH. This is achieved through the calculation of the acidity constants at the surface sites, which are derived from ab initio MD simulations and a grand-canonical formulation of adsorbates. It is finally shown how the potential of a semiconductor material as photocatalysts for water splitting can be inferred by combining the nature of the surface coverage and the alignment of the band edges to the relevant redox levels.