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A polaron is a quasiparticle used in condensed matter physics to understand the interactions between electrons and atoms in a solid material. The polaron concept was proposed by Lev Landau in 1933 and Solomon Pekar in 1946 to describe an electron moving in a dielectric crystal where the atoms displace from their equilibrium positions to effectively screen the charge of an electron, known as a phonon cloud. This lowers the electron mobility and increases the electron's effective mass. The general concept of a polaron has been extended to describe other interactions between the electrons and ions in metals that result in a bound state, or a lowering of energy compared to the non-interacting system. Major theoretical work has focused on solving Fröhlich and Holstein Hamiltonians. This is still an active field of research to find exact numerical solutions to the case of one or two electrons in a large crystal lattice, and to study the case of many interacting electrons. Experimentally,

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Implications of the DFT plus U method on polaron properties in energy materials

Amina Matt

To model polaronic behavior in strongly correlated transition-metal oxideswith ab initio methods, one typically requires a level of theory beyond that of local density or general gradient density functional theory (DFT) approximations to account for the strongly correlated d-shell interactions of transition-metal oxides. In the present work, we utilize density functional theory with additional on-site Hubbard corrections (DFT+ U) to calculate polaronic properties in two lithium ion battery cathode materials, Li x FePO4 and Li x Mn2O4, and two photocatalytic materials, TiO2 and Fe2O3. We investigate the effects of the + U on-site projection on polaronic properties. Through systematic comparison with hybrid functional calculations, it is shown that + U projection in these model materials can impact upon the band gap, polaronic hopping barrier, and polaronic eigenstate offset from the band edges in a nontrivial manner. These properties are shown to have varying degrees of coupling and dependence on the + U projection in each example material studied, which has important implications for arriving at systematic material predictions of polaronic properties in transition-metal oxides.

Amer Physical Soc2017

Polarons free from many-body self-interaction in density functional theory

Stefano Falletta, Alfredo Pasquarello

We develop a unified theoretical framework encompassing one-body and many-body forms of self-interaction. We find an analytic expression for both the one-body and the many-body self-interaction energies, and quantitatively connect the two expressions through the dielectric constant. The two forms of self-interaction are found to coincide in the absence of electron screening. This analysis confers superiority to the notion of many-body self-interaction over the notion of one-body self-interaction. Next, we develop a semilocal density functional scheme that addresses the many-body self-interaction of polarons, thereby overcoming the limitations of standard density functional theory. Polaron localization is achieved through the addition of a weak local potential in the Kohn-Sham Hamiltonian that enforces the piece-wise linearity of the total energy upon partial electron occupation. Our method equivalently applies to electron and hole polarons and does not require any constraint on the wave functions during the self-consistent optimization. The implementation of this scheme does not produce any computational overhead compared to standard semilocal calculations and achieves fast convergence. This approach results in polaron properties, including the atomic geometry, the electron density, and the formation energy, which are close to those achieved with a hybrid functional that similarly satisfies the piece-wise linearity condition. This suggests that addressing the many-body self-interaction results in a polaron description that is robust with respect to the functional adopted. We illustrate our approach through applications to the electron polaron in BiVO4 , the hole polaron in MgO, and the hole trapped at the Al impurity in α-SiO2.

2022

Oxygen Evolution at the BiVO4-Water Interface: Mechanism of the Water Dehydrogenation Reaction

Sai Lyu, Alfredo Pasquarello, Julia Anna Wiktor

We study the water dehydrogenation reaction at the BiVO4(010)-water interface by combining nudged-elastic-band calculations and electronic structure calculations at the hybrid functional level. We investigate the pathway and the kinetic barrier for the adiabatic reaction going from the hole polaron localized in BiVO4 to the dehydrogenation of the adsorbed water molecule at the interface. The reaction is found to involve the H2O center dot+ radical cation as an intermediate, to have a kinetic barrier of 0.7 eV, and to be initiated by the electron transfer. The calculated kinetic barrier is in good agreement with experiment and is consistent with the slow hole transfer kinetics observed at the surface of BiVO4. To characterize the structural changes occurring during this process, we analyze the O-H distances for three relevant water molecules. We also examine the Wannier functions around the O atom of the adsorbate involved in the reaction to reveal the changes in the electronic structure during the hole hopping. The projected density of states of the lowest unoccupied molecular orbitals allows us to identify the atomic orbitals that are primarily involved in the reaction. We expect that the proposed reaction mechanism generally holds when the surface coverage is dominated by molecularly adsorbed water.

AMER CHEMICAL SOC2022

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