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Condens. Matter 2022, 7, 8 3 of 9 optimizing the structures at the PBE0/cc-pVDZ level. Also, Li0 intercalation was modeled because the electron of Li0 is highly delocalized in solid systems, and modeling of Li intercalation into periodic crystals requires system neutrality. The anodic potential was also calculated at the PBE/cc-pVDZ, B3LYP/cc-pVDZ, and ωB97XD/cc-pVDZ levels for comparison purposes. Throughout the calculations, the stability of the structures was confirmed by the absence of any imaginary frequencies. Our choice of the model was further cross-validated against 3D periodic boundary calculations on the unit cell of FOD [1]. For this purpose, we used the ReSpect (Relativistic Spectroscopy) package [28] developed for studies of molecular properties such as the nuclear magnetic and electron paramagnetic resonance parameters [29–31], as well as response to time-dependent electric fields [32–34]. This code recently enabled incorporating periodic boundary conditions together with Gaussian-type basis sets [35] that we used to calculate the electronic band structure and density of states of FOD (Figure 2) at the PBE/ucc-pVDZ level (“u” indicates that the cc-pVDZ basis set was fully uncontracted). We employed a Γ-centered 5 × 11 × 7 mesh of momentum-space points for the ground-state optimization procedure and a 15 × 33 × 21 mesh for the calculation of the density of states. 1.5 1.0 0.5 0.0 0.5 1.0 1.5 0.00 0.01 0.02 0.03 0.04 0.05 0.06 density of states [eV 1] Figure 2. Electronic density of states (DOS) of ferrous oxalate dihydrate (FOD) based on using 3D periodic boundary conditions at the PBE/ucc-pVDZ level. The DOS was calculated using a dense mesh of 15 × 33 × 21 momentum-space points and an artificial Gaussian broadening of σ = 0.01 eV. The dashed line indicates the Fermi level. The value of the bandgap calculated using the DOS is 0.7 eV. 3. Results and Discussion 3.1. Spin State and Electronic Band Structure For the model-based calculations, the ground spin-state was unknown. Considering the presence of three Fe2+ ions in the models, various possibilities from singlet to 13tet were evaluated for the FOD model. The results of most computational levels in supplementary Figure S1 and Table S1 suggest that FOD is high spin (13tet) and its ground state has 1.0 to 24.4 kJ mol−1 (=0.01 to 0.25 eV) energy difference with the first excited state (the 11tet state). At the PBE/cc-pVDZ and SVWN5/cc-pVDZ levels, the 11tet state is more stable than the 13tet state with 18.1 kJ mol−1 (=0.19 eV) and 43.6 kJ mol−1 (=0.45 eV) electronic energy difference, respectively. Regardless of the computational level, the 11tet state presents a curved structure, in contrast to the straight-chain nature of FOD in its crystals [3,15]. Furthermore, our results show a continuous decrease in FOD stability by shifting from the higher spin states to the lower ones. Particularly, the singlet state calculations at most computational levels failed to converge, indicating that the singlet state should be an band energy [eV]PDF Image | Anodic Activity of Hydrated and Anhydrous Iron (II) Oxalate in Li-Ion Batteries
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