Introduction

Metal organic frameworks (MOFs) are new functional materials that combine a wide variety of properties and applications. They contain inorganic and organic networks that can be easily functionalised to get tuneable properties. Commonly used in sensing, catalysis, ion exchange, separations or gas storage [1–7], they have recently been thought as possible candidates for applications in lithium energy storage (Li-ion batteries) [8–9]. The interest of using such open-space frameworks for Li-Ion battery applications relies on an expected increase of the kinetics of lithium diffusion, which is one of the major limitation of dense electrodes. Among them, the iron-based Fe{OH(BDC)} (BDC - O2C-C6H4-CO2 - benzodicarboxylate) compound was recently tested as a cathode material in a Li-ion battery cell [9]. Its electrochemical activity with respect to elemental lithium has shown interesting performances, such as good cycling life and rate capability. Unfortunately, the material suffers from a rather poor capacity of about 70 mAh/g, associated with the insertion of at most 0.5 Li per iron atom. This is half the capacity of the commonly used LiCoO2 [10] or olivine LiFePO4 cathode materials [11]. These first attempts are nevertheless encouraging because the number of inserted lithium could be, in principle, increased up to one Li per transition metal (TM), i.e. one electron per TM, thus doubling the capacity of the material. In the present case of Fe{OH(BDC)}, it would correspond to the reduction of all iron ions from the +III to the +II oxidation state, instead of one every iron. To this goal, one has first to figure out the origin of this limited lithium insertion in elucidating the electronic structure of the system.

First-principles density functional calculations have proven to be powerful in predicting the thermodynamic, structural and electronic properties of a wide series of solids, especially in the field of lithium energy storage [12–15]. It is also well admitted that variants of the standard density functional theory (DFT) such as the self-interaction DFT+U [16, 17] methods are required to properly account for the electron correlation in dense transition metal oxides [18–20] or rare earth-based systems [21]. In this method, non-integer or double occupations of the 3d electronic levels are penalised by the introduction of two additional interaction terms, namely, the one-site Coulomb interaction term U and the exchange interaction term J, by means of an effective parameter U eff = U − J. This approach was then used to investigate the electronic structure of the Li x Fe{OH(BDC)} (x = 0 to 1). The structural, magnetic and redox properties were then studied as a function of U eff, varying from the DFT limit (U = 0) to the strongly correlated limit (U eff = 9 eV).

Computational details

Calculations were performed using the plane wave DFT code from the Vienna ab initio simulation package (VASP) [22, 23] within the DFT+U formalism [16, 17] using the Liechtenstein method [24] with J = 1 eV. For the sake of comparison, all observables were computed from the DFT limit (U = 0) to the strongly correlated limit (U eff = 9.0 eV) within both the local density approximation (LDA) [25] and the generalised gradient approximation of Perdew–Burke–Erzenhorf (GGA-PBE) [26, 27] for the exchange and correlation potentials. The electron wave functions were described in the projected augmented wave formalism (PAW) [28] and a real-space projection was further used for the total wave function analyses. The plane wave energy cut-off was set up to 1000 eV, and a value of 600 eV was chosen as the default parameter. The Brillouin zone integration was done in a k-point grid as uniformly distributed as possible, using a 5 × 3 × 5 Monkhorst–Pack mesh (38 irreducible k-points) for structural relaxations and a 7 × 5 × 7 (123 irreducible k-points) for density of states and band structure analyses. The ionic convergence was done with respect to both the atomic forces (less than 3.10−3) and the energies (less than 10−5).

Results

The Fe{OH(BDC)} system crystallises in the C 2/c space group (a = 6.882 Å, b = 21.249 Å, c = 6.763 Å, β = 114.62°) whose primitive unit cell is indexed in the P −1 space group (a = 6.882 Å, b = 11.150 Å, c = 6.763 Å, β = 107.7°, γ = 113.4°). As shown Fig. 1, the structure is described by chains of corner-shared FeO6 distorted octahedra running along the a-axis, and connected to each other through benzo-dicarboxylate (BDC) organic linkers in the b-direction. Such BDC packing yields a π-like stacking along the c-axis. Two iron atoms occur in each chain. They are bonded to six oxygen atoms belonging to two bridging hydroxo (OH) groups for the apical ligands and two bidentate carboxylate groups for the equatorial ligands. This leads to distorted FeO6 octahedra, described by two short Fe-OH apical bonds (2x Fe-Oa = 1.964 Å), and four longer Fe-OC equatorial bonds (2 × Fe-Oe = 2.012 Å and 2 × Fe-Oe = 2.112 Å).

Fig. 1
figure 1

Crystal structure of Fe{OH(BDC)} (P −1 space group) projected in the (a, b) and (b, c) planes, the chains of FeO6 octahedra running along the a-axis. Iron, oxygen and carbon atoms are illustrated by green, red and grey circles, respectively. The most probable Li sites are given by crosses

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Table 1 reports the experimental and computed lattice parameters, bond distances and equilibrium volumes for the Fe{OH(BDC)} system, obtained from full structural relaxations for various U eff from the DFT limit (U = 0) to the strongly correlated limit (U eff = 9 eV).

Table 1 Lattice parameters, unit cell volume Ω, Fe-O bond distances and iron local magnetic moments (μFe) for the neutral Fe{OH(BDC)} compound computed within the GGA-PBE functional for various U eff values from the DFT limit (U = 0) to the strongly correlated one (U eff = 9 eV)
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As often reported in dense transition metal oxides [18–20], the bond lengths and, therefore, the lattice parameters are slightly overestimated compared to experiments, whilst no significant variations result from the increase of U eff. It is surprising to note that the c-lattice parameter is also well reproduced by the calculations although weak Van der Waals interactions occur in that direction. A very small dependence of the total energy is, however, obtained with respect to the increase of the c-lattice parameter, consistent with a very low c-compressibility. The LDA leads to equivalent results for the c-lattice parameter. Nevertheless, as shown in Fig. 2, both the Fe-O bonds and the lattice parameters are underestimated, in full agreement with the well-known feature of LDA to overestimate binding energies. Focusing now on the inorganic chains, a less-distorted octahedral geometry is observed for the FeO6 entities compared to experiments. They show four nearly equivalent Fe-O bonds in their equatorial plane and two smaller apical Fe-O bonds, in agreement with a greater π-donor character for the hydroxyl ligands compared to the carboxylate ones. As a consequence of the more localised picture provided by the DFT+U formalism, the iron local magnetic moment slightly increases as a function of U eff. It corresponds to the S = 5/2 high-spin configuration, in agreement with the FeIII oxidation state detected by Mössbauer spectroscopy measurements [9]. Note that within the LDA, the magnetic moments fall down to S = 1/2 for U eff < 3.0 eV.

Fig. 2
figure 2

Variations in % of a lattice parameters and b the Fe-O apical and equatorial bond distances computed with respect to experiments within the LDA+U and GGA+U approximations, as a function of U eff

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To seek for any long-range magnetic order, the energies of both the anti-ferromagnetic and the ferromagnetic structures were computed as a function of U eff. As shown Table 1, the anti-ferromagnetic structure is favoured up to U eff = 7 eV lying a few k B T lower than the ferromagnetic one. According to the literature, U eff values lower than 5 eV should be used to properly account for iron oxides ground state properties [20]. The stabilisation of the ferromagnetic structure at larger U eff (9 eV) should thus result from a too large localisation of the metallic 3d orbitals. This suggests weak anti-ferromagnetic interactions along the chains with a probable anti-ferromagnetic ordering at very low temperature. An insulating ground state is, therefore, expected for such an anti-ferromagnetic chain of high-spin FeIII ions. This is supported by the density of states (DOS) of Fig. 3 in which the iron spin-up and spin-down contributions are given together with the ligand-type contribution. On this DOS, each band consists of opposite spins on the two iron atoms occurring along the chain, namely, Fe(1) and Fe(2). For these two atoms, a gap occurs between the spin-up/spin-down electronic states consistent with the high-spin configuration of the FeIII. As a result of the 3d electron localisation that increases as a function of U eff, the energy band gap also increases from U eff = 0 to 9 eV (note shown here), leading to a typical Mott–Hubbard insulating behaviour for low U eff values and to a charge transfer insulating behaviour for larger U eff values. As DFT is known to underestimate the optical gaps, the right U eff value one should use in the calculations to properly describe the electronic ground state of Fe{OH(BDC)} cannot be fairly determined here by simply comparing the experimental gaps to the computed ones. However, the redox properties of Fe{OH(BDC)} should not be drastically affected by the magnitude of these electronic gaps, as the nature of the first empty electronic bands does not change in the whole range of U eff.

Fig. 3
figure 3

Partial DOS projected on the Fe(1) and Fe(2) 3d orbitals for the neutral Fe{OH(BDC)} compound computed within the GGA+U approximation for U eff = 4 eV, using the Liechtenstein method (J = 1 eV). The positive and negative DOS correspond to the spin-up and spin-down DOS, respectively. The Fermi level is given by the vertical dotted line, as the zero reference energy

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The electrochemical behaviour of Fe{OH(BDC)} was then investigated using the U eff = 4 eV recommended in the literature for iron oxides [20]. As a large number of lithium sites can be considered in the initial structure, we first started with the addition of extra electrons in the electronic structure of Fe{OH(BDC)}. As shown by the DOS of Fig. 3, one additional electron should fill half the first empty band of Fe{OH(BDC)}. Because this band results from FeIII(5/2)−FeIII(−5/2) anti-ferromagnetic interactions, no electronic de-localisation is expected along the chain for the additional electron. This is consistent with the spin-gap opening observed in the DOS of the reduced Fe{OH(BDC)}−1/2 compound of Fig. 4 and with the localisation of the extra electron on every iron (see Fig. 5). A mixed-valence FeIII/FeII state is, therefore, stabilised as Li is inserted into the starting material. Similar results are obtained when we added one Li+ in the reduced Fe{OH(BDC)}−1/2 compound. The mixed-valence state is associated with significant structural changes for the local FeII environment compared to the initial FeIII one. The different sites considered in our calculations for Li insertion are illustrated by crosses on Fig. 1. When Li is inserted in site I, a significant Fe-OH bond elongation is observed in the relaxed crystal structure of \({\text{Li}}^{{\text{I}}} _{{{\text{0}}{\text{.5}}}} {\text{Fe}}{\left\{ {{\text{OH}}{\left( {{\text{BDC}}} \right)}} \right\}}\) leading to alternating short and long Fe-OH bridges along the chain and to the formation of (OH)−-Li+. This local distortion results in a slight decrease of the a-lattice parameter and a larger increase of the c-lattice parameter (a = 6.80 Å and c = 7.30 Å), thus opening the channels of the MOF architecture. When Li is inserted in site II, a significant contraction of the channels is associated with the stabilisation of the FeIII/FeII mixed-valence state. In particular, a significant decrease of the c-lattice parameter (c = 6.40 Å) is observed for the \({\text{Li}}^{{{\text{II}}}} _{{{\text{0}}{\text{.5}}}} {\text{Fe}}{\left\{ {{\text{OH}}{\left( {{\text{BDC}}} \right)}} \right\}}\) due to the interaction of Li+ with the COO− group, and to the formation of the (O = C-O)−-Li+. Such a distortion partially destroys the π-conjugation of the BDC linker, which is compensated by an efficient π-stacking interaction along the c-axis. Very close voltages are computed for the two insertion sites (V I = 2.50 V and V II = 2.52 V compared to V = 2.7 V experimentally), in agreement with the similar DOS obtained for the LiI 0.5Fe{OH(BDC)} and \({\text{Li}}^{{{\text{II}}}} _{{{\text{0}}{\text{.5}}}} {\text{Fe}}{\left\{ {{\text{OH}}{\left( {{\text{BDC}}} \right)}} \right\}}\) structures. Nevertheless, it seems unlikely that these two sites can be electrochemically achieved in the meantime, in particular, for they induce opposite structural breathing of the open channels. We are now undertaking the structural relaxations of various LiiFe{OH(BDC)} (i = I/II, I/I, II/I) to check whether is it theoretically possible to insert more lithium in the structure. From an electronic point of view, we do not see any obvious reason to avoid further insertion as the spin-gap observed in the Li0.5Fe{OH(BDC)} structures is lower than that of the starting material. Nevertheless, under electrochemical conditions, some of the organic molecules present in the solvent can fill (at least partially) the open channels of the MOF. If these molecules were able to solvate and transport Li+ into the structure, the kinetics of Li insertion should be favoured. However, a large c-lattice parameter should result from the insertion of these molecules, thus lowering the thermodynamical stability of site II. At this stage, it is thus tempting to correlate this kinetics/thermodynamics competition to the small capacity of the Fe{OH(BDC)} compound.

Fig. 4
figure 4

Partial DOS projected on the Fe(1) and Fe(2) 3d orbitals for the reduced Fe{OH(BDC)}−1/2 compound computed within the GGA+U approximation for U eff = 4 eV, using the Liechtenstein method (J = 1 eV). The positive and negative DOS correspond to the spin-up and spin-down DOS, respectively. The Fermi level is given by the vertical dotted line, as the zero reference energy

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Fig. 5
figure 5

Atomic net population analysis for the reduced Fe{OH(BDC)}−1/2 compound computed within the GGA+U approximation for U eff = 4 eV, using the Liechtenstein method (J = 1 eV)

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Conclusion

In the present study, we have shown that Fe{OH(BDC)} is a charge transfer or a Mott–Hubbard anti-ferromagnetic insulator, described by chains of iron ions in the (S = 5/2) high-spin state, in agreement with Mössbauer spectroscopy. Very close structural parameters are obtained whatever the U eff parameter used in the GGA+U calculations from the DFT limit (U = 0 eV) to the strongly correlated limit (U eff = 9 eV) showing that the crystal structure is not governed by the electron correlation. The proper FeIII S = 5/2 spin configuration is obtained from U eff = 3 eV in the LDA+U calculations and for any U eff values in the GGA+U calculations, in agreement with the more de-localised picture provided by the local density approximation. Each of the crystallographic sites considered in the calculations as possible Li insertion sites for the reduced Li0.5Fe{OH(BDC)} compound leads to the stabilisation of a localised FeIII/FeII mixed-valence state along the inorganic chains. A spin-Peierls-like phase transition is likely to be the origin of this mixed-valence state, resulting in a spin-gap opening in the electronic band structure due to local structural distortions around the FeIIO6 monomers. Whether Li+ gets close to the hydroxyl bridge of the inorganic chains or to the carboxylate group of the organic linkers, very different structural changes are observed in the reduced Li0.5Fe{OH(BDC)} relaxed structures. They correspond to opposite breathings of the MOF open channels, suggesting that all Li sites could not be reached under normal electrochemical conditions. An interesting outlook of this work would be to check the influence of the solvent used in the electrochemical cells on the Li content inserted into the MOF structures. Other alternatives to bypass the limited capacity of Fe{OH(BDC)} could also be found in replacing iron by lower 3d-filled transition metal or in decreasing the π-donor character of the in-chain bridging ligands. This should open new routes for the design of hybrid compounds with tuneable redox properties.