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Condens. Matter 2022, 7, 8 4 of 9 excited state as the convergence of highly excited states is challenging when DFT methods are applied. The 13tet and singlet states differ by over 5 eV in energy. Beyond the model-based calculations, the electronic structure of FOD was obtained by running full periodic calculations on its unit cell at the PBE/ucc-pVDZ level, which yielded total energy of −195,183.57 eV per unit cell. The model-based calculations at the PBE/cc-pVDZ and PBE/ucc-pVDZ levels, respectively, gave the total electronic energies of −144,367.79 eV and −144,372.09 eV, including the zero-point energy (ZPE) correction. Figure 2 shows the density of states obtained from the periodic calculation with a bandgap of 0.7 eV. The vertical gap at the Γ point is 0.94 eV indicating that FOD is an indirect semiconductor. Notably, the periodic calculations of Fan et al. using Ceperley-Alder local- density approximation with plane-wave basis set and a Hubbard-U correction [3] found a direct bandgap of 1.13 eV in FOD, while our model-based PBE/cc-pVDZ (PBE/ucc-pVDZ) calculations estimate the bandgap to be 1.36 (1.42) eV and the experimentally determined band gaps are 2.10 eV [4] and 2.17 eV [36]. Although DFT-based methods are well known to underestimate the bandgap in semiconductors [37], our model-based PBE/cc-pVDZ and PBE/ucc-pVDZ calculations reproduce the electronic properties of FOD reasonably. Since our model-based PBE/ucc-pVDZ calculations were affected by the poor quadrature accuracy, we expect the PBE/cc-pVDZ results to be more reliable. 3.2. Intercalation Mechanism The anodic response of FOD, PHFO, and AFO depends on the mechanism of Li dif- fusion and intercalation. The mechanism of Li+ diffusion into the channels of AFO is explained by Zhang et al. [11], who reported a value of 3.11×10−10 cm2 s−1 for anodic diffusion of Li+ into α@β-FeC2O4. They argue that Li+ can diffuse through the short diffu- sion channels created between the AFO chains [11], which show low resistance against Li+ diffusion. However, fast transmission of Li+ at higher cycling rates can lead to irreversible structural defects [11]. Moreover, they deduced from their modeling and experimental results that Li+ ions occupy the primary sites of water molecules or they just diffuse bi- laterally along the chains (the hydrogen bonding network between the two chains) and hop between the layers [11]. Such a diffusion mechanism is at play in the Li0 and Li+ intercalated structures shown in Figures 3, S2, and S3. Based on the obtained structures, both Li0 and Li+ prefer binding to the oxalate oxygens of PHFO and AFO, consistent with the bilateral diffusion mode. In the case of FOD, the Li0 and Li+ intercalation mech- anisms involve the replacement of an axial water molecule, subsequent modification of the hydrogen bonding network, and induction of curvature in the straight-chain structure. This intercalation model suggests hydration of Li by the structural FOD water molecules. Reversible and irreversible structural changes induced by Li intercalation have also been reported for other Fe-containing electrodes [38,39]. To ascertain that the changes in the hydrogen bonding and chain curvature of FOD are not an artifact of the chosen modeling parameters, the starting FOD structure (Figure 1) was optimized in the presence of Li+ at both PBE/cc-pVDZ and PBE0/cc-pVDZ levels by considering two possibilities: (a) FOD structure being fully flexible, and (b) the edge Fe2+ ions and their attached water and hydroxyl groups being fixed in their positions. The results (Figure S4) confirm that water displacement/Li+ hydrolysis is the key to intercalation of Li+ into FOD, and hydrogen-bonding-network modification and curvature induction are inevitable. Furthermore, the results demonstrate that the conservation of the crystal structure of FOD, PHFO, and AFO (straight ferrous oxalate chains) depends on the presence of axial water molecules or intercalated Li.PDF Image | Anodic Activity of Hydrated and Anhydrous Iron (II) Oxalate in Li-Ion Batteries
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