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Condens. Matter 2022, 7, 8 2 of 9 functional theory (DFT)-based calculations using the local density approximation (LDA) and a Hubbard U correction. Also, Zhang et al. [11] have proposed a mechanism for Li+ diffusion into periodic α and β-AFO crystals using the PBE-DFT method. However, no theoretical work has fully addressed the changes in the electrochemical properties of FOD upon dehydration and Li intercalation. Our modeling shows that the structural water molecules of FOD hydrate the interca- lating Li species, which enhances Li adsorption and increases the open-circuit voltage. In contrast, the fully dehydrated material yields a lower voltage that is favorable for anodic materials. Our analysis further indicates that Li0 or Li+ intercalation in FOD yields similar results. 2. Computational Method Note that FOD, AFO, and PHFO can be in the α−monoclinic, β−orthorhombic, or mixed states [6,11], and that their molecular and crystal structures are pressure depen- dent [15]. Bearing this in mind, we used a single chain of the three coordination polymers and ran the calculations on a subunit of their chain structure in order to focus on their intrinsic electrochemical properties rather than their structural features. The subunit con- tained three Fe2+ ions, two C2O42− bidentate anions bridging the metal ions and two or zero axial water molecules for each metal center. To balance the charge of the structures in accord with the coordination mode of the removed oxalate anions, each tail oxalate anion was represented by one OH− anion and one neutral OH group, which resulted in a neutral model. The orientation of the water molecules was adjusted along the lines of the study of Fan et al. [3]. The model structures are shown in Figure 1. The efficacy of the adopted mod- els was further verified by comparison to experimental data and periodic calculations as discussed below and in the “Results and discussion” section. All model-based calculations were performed using the Gaussian 16 A.03 package [16]. Figure 1. The starting models used to represent ferrous oxalate dihydrate (FOD), partially hydrated ferrous oxalate (PHFO), and anhydrous ferrous oxalate (AFO). Blue, red, grey, and white spheres represent the Fe, oxygen, carbon, and hydrogen atoms, respectively. As the properties of FOD are better understood compared with PHFO and AFO, we fo- cused first on FOD. In order to determine the ground state of FOD, we carried out geometry and energy optimizations for various spin-dependent states using a variety of DFT-based approaches, including B3LYP [17], M06-L [18], PBE [19], PBE0 [19], and ωB97XD [20], all using the cc-pVDZ basis set. The PBE method is of particular interest because it has been the function of choice in most existing studies on metal oxalates [11,21–24]. SVMN5 local-spin-density approximation [25] was also used in view of the success of such methods in investigating FOD [3]. Van der Waals interactions were included in all calculations using Grimme’s D3 (GD3) semi-empirical dispersion correction [26] with the exception of computations based on the ωB97XD functional, which intrinsically supports long-range exchange-correlation corrections [20,27]. After identification of the ground state (Table S1 and Figure S1 of the Supporting Information), the computational level was calibrated by comparing the geometries and vibrational frequencies of the model FOD structure with the corresponding experimentally available results [1,15]. As seen from Table S2 and Section S1 (Supporting Information), PBE0/cc-pVDZ shows the smallest error in the modeled structures. Electrochemical po- tentials for FOD, AFO, and PHFO as anode materials were then calculated by inserting a Li+ ion near the central Fe2+ atom (i.e., anodic reaction: Fe2+ + Li+ Fe3+ + Li0) andPDF Image | Anodic Activity of Hydrated and Anhydrous Iron (II) Oxalate in Li-Ion Batteries
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