Exploring the impact of semicore level electronic relaxation on polaron dynamics: An adiabatic ab initio study of ${\mathrm{FePO}}_{4}$

Exploring the impact of semicore level electronic relaxation on polaron dynamics: An adiabatic ab initio study of ${FePO}_{4}$

Zi Wang and Kirk H. Bevan

Phys. Rev. B 93, 024303 – Published 19 January 2016

Abstract

In the present work, we study the effects of the electronic relaxation of semicore levels on polaron activation energies and dynamics. Within the framework of adiabatic ab initio theory, we utilize both static transition state theory and molecular dynamics methods for an in-depth study of polaronic hopping in delithiated ${LiFePO}_{4} ({FePO}_{4})$ . Our results show that electronic relaxation of semicore states is significant in ${FePO}_{4}$ , resulting in a lower activation barrier and kinetics that is one to two orders faster compared to the result of calculations that do not incorporate semicore states. In general, the results suggest that the relaxation of states far below the Fermi energy could dramatically impact the ab initio polaronic barrier estimates for many transition metal oxides and phosphates.

Received 9 October 2015

DOI:https://doi.org/10.1103/PhysRevB.93.024303

Physics Subject Headings (PhySH)

Hopping transport Polarons

Density functional theory First-principles calculations Molecular dynamics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zi Wang and Kirk H. Bevan

Materials Engineering, McGill University, Montréal, Québec, H3A 0C5, Canada

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Vol. 93, Iss. 2 — 1 January 2016

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Figure 1
Two-site electron polaron picture. Nuclear and electronic reorganization must occur to enable a polaron to reach the activation energy $E_{a}$ , which represents the total energy $(E)$ change that must be contributed by the system to move from a polaron localized on one atom (larger red circles) to another atom (smaller blue circles). At the intermediate transition state, the electron is shared by both sites (equally sized purple circles). During this transition, valence (vb), semicore (sc, in green), and deep-core (dc) levels $(ɛ)$ may electronically reorganize/relax and contribute to $E$ . Electronic coupling between polaronic sites is represented by $J$ .
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Figure 2
The atomic structure of ${FePO}_{4}$ . A polaron located on one site (labeled ${Fe}_{1}$ ), with an isosurface of the real space charge density shown in grey. Its nearest neighbor is labeled ${Fe}_{2}$ , and its neighbor in the out of plane direction is labeled ${Fe}_{3}$ . Consequently, we study both the common in-plane nearest-neighbor pathway (NN) as well as the closest interlayer pathway (IL). (Image generated with the vesta software package [29].)
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Figure 3
Projected density of states (PDOS) for the two Fe atoms taking part in the electron transfer process for three relevant configurations represented by the schematic images of ${FeO}_{6}$ coordinations as introduced in Fig. 1. The PDOS for majority and minority spin are plotted on the positive and negative vertical axis, respectively. The semicore $3 s$ (green peaks, left) and $3 p$ (blue peaks, center) states lie deep below the Fermi energy, while the $3 d$ (red curves, right) valence states contribute to the chemistry of the system. (a) PDOS of the intrinsic ground-state configuration (“GS”) without additional electrons introduced. [(a), inset)] Real-space distribution of the Fe $3 s$ semicore states. (b) PDOS of the polaronic ground state (“POL”), i.e., the electron is fully localized on one Fe site. (c) PDOS of the transition state (“TST”), where both Fe sites have similar coordination and share the additional electron.
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Figure 4
Activation energies (a) and (b) calculated with the CI-NEB method [33] using both 8-valence $3 d^{6} 4 s^{2}$ ( ${Fe}_{fc}$ blue upright triangles) and 16-valence $3 s^{2} 3 p^{6} 3 d^{6} 4 s^{2}$ ( ${Fe}_{sc}$ red squares) Fe potentials, together with the level splitting at the transition state arising from the site coupling in (c) and (d), respectively. (a) and (c) nearest-neighbor (NN) barrier. (b) and (d) interlayer (IL) barrier.
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Figure 5
Correlation analysis on a sample MD run. We calculate the average Fe- $O_{6}$ bond lengths of all 16 Fe sites scaled to unity, and multiply these values with their respective projected $3 d$ electron occupations (also scaled to unity). The resulting charge-lattice correlation statistic should give a reasonable indication of the current polaron location.
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Figure 6
Polaron AIMD hopping statistics. (a) Nearest-neighbor hopping. (b) Nearest interlayer hopping. Red line: linear fit of semicore calculations at $T = 143$ , 166, 200, 250, and 300 K. Blue line: linear fit of frozen core calculations at $T = 300$ , 350, 400, 450, and 500 K. Inset: exponential Poisson distribution of hopping times shown for one temperature point. The mean of this distribution was taken to be the mean hopping rate at that particular temperature. Similar statistics were done for each temperature point on these Arrhenius plots.
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Physical Review B

covering condensed matter and materials physics

Exploring the impact of semicore level electronic relaxation on polaron dynamics: An adiabatic ab initio study of ${FePO}_{4}$

Zi Wang and Kirk H. Bevan

Phys. Rev. B 93, 024303 – Published 19 January 2016

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Physical Review B

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Exploring the impact of semicore level electronic relaxation on polaron dynamics: An adiabatic ab initio study of FePO4

Zi Wang and Kirk H. Bevan

Phys. Rev. B 93, 024303 – Published 19 January 2016

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Exploring the impact of semicore level electronic relaxation on polaron dynamics: An adiabatic ab initio study of ${FePO}_{4}$