Impact of Ligand Substitution and Metal Node Exchange in the Electronic Properties of Scandium Terephthalate Frameworks

The search for sustainable alternatives to established materials is a sensitive topic in materials science. Due to their unique structural and physical characteristics, the composition of metal–organic frameworks (MOFs) can be tuned by the exchange of metal nodes and the functionalization of organic ligands, giving rise to a large configurational space. Considering the case of scandium terephthalate MOFs and adopting an automatized computational framework based on density-functional theory, we explore the impact of metal substitution with the earth-abundant isoelectronic elements Al and Y, and ligand functionalization of varying electronegativity. We find that structural properties are strongly impacted by metal ion substitution and only moderately by ligand functionalization. In contrast, the energetic stability, the charge density distribution, and the electronic properties, including the size of the band gap, are primarily affected by the termination of the linker molecules. Functional groups such as OH and NH2 lead to particularly stable structures thanks to the formation of hydrogen bonds and affect the electronic structure of the MOFs by introducing midgap states.


Introduction
Metal-organic frameworks (MOFs) are porous materials formed by metal atoms bound together by organic linkers. 1,2The peculiar structure and chemical tunability of MOFs 3,4 offer great potential in many technological areas including gas storage and conversion, [5][6][7] optoelectronics, [8][9][10] and catalysis. 11,12The size of the pores, as well as their electronic and optical properties, can be modulated by the choice of the metallic nodes and/or the molecular ligands. 13,14The latter, furthermore, can be functionalized with specific groups having electron-withdrawing or -donating ability, thus offering an additional handle to tune the characteristics of the MOFs. 15,16It is evident that so many degrees of freedom give rise to an enormous configurational space that calls for high-throughput (HT) screening approaches to be properly explored.
Experimentally, HT synthesis of MOFs has been established since the end of the past century 17 and has been exploited, among other purposes, 18 to maximize the performance of zeolitic imidazolate frameworks for CO 2 capture, 19 and to optimize the structure of porous chromium terephthalate to host particularly large guest molecules. 204][25] The advantages of this approach are numerous: It does not demand experimental synthesis and characterization; it enables exploring a potentially infinite amount of constituent combinations; it offers an overview of the fundamental properties of the MOFs on a quantum-mechanical level.
The current quest for new materials to adhere to sustainability requirements further stimulates HT computational studies on MOFs with the task of identifying suitable alternatives to specific ligand molecules that are toxic or hazardous. 26Likewise, many metallic species pose challenges regarding availability and extraction costs.Scandium is a prominent example in this regard.While being presently in high demand due to the favorable mechanical properties of Al-Sc alloys 27,28 and for its applicability in medical laser technologies, 29 this element is tremendously hard to harvest.Currently, scandium is mainly recovered as a byproduct from the production of other metals 30 or from bauxite residues. 31Furthermore, its production is concentrated in a few world areas, which do not include those mostly requesting it, such as Europe. 32Scandium-based MOFs have recently emerged as promising materials for carbon oxide sequestration [33][34][35] and fluorescence sensing. 36,37However, the limited availability of Sc calls for alternatives.Aluminum and yttrium, both isoelectronic with scandium and more abundant on the Earth's crust, are seen as suitable substitutes for this element in MOFs.
Also, a recent study 38 has shown that Al replacement of Sc ions in a Sc-based MOF enhances the CO 2 adsorption ability of the material.
Motivated by this experimental evidence and by the interest in discovering sustainable alternatives to established MOFs, we present a computational study based on DFT investigating the structural and electronic properties of scandium terephthalate scaffolds modified by metal-ion substitution and ligand functionalization.By applying an in-house implemented automated workflow for ab initio calculations, 39 we construct 24 structures and analyze their equilibrium geometries and their energetic stability at varying metal nodes and molecular functionalization.We discuss the larger impact of the metallic species on the structural properties in contrast with the moderate effect of the ligand substituents which merely induce some steric hindrance.Interestingly, all explored MOFs are stable and linker functionalization has a large impact in this respect.By means of partial charge analysis, we shed light on the bonding among the involved species revealing also in this case the significant influence of ligand terminations.We finally discuss the electronic properties of the considered systems, which are all large-band-gap semiconductors expected to absorb ultraviolet radiation.
The functional groups influence considerably the size of the fundamental gap.In particular, OH and NH 2 groups give rise to mid-gap states that alter even qualitatively the electronic characteristics of the MOFs.

Methodology
The computational workflow used in this study is implemented in an in-house developed library embedding routines for data mining, HT DFT calculations based on the AiiDA infrastructure, 21,40 and post-processing tools.This package, initially designed for inorganic crystals, 39 has been purposely tailored here to investigate MOFs (see Figure 1).The initial input includes structural information about the scaffold which, in this case, is scandium terephthalate.In the first computational step, the primitive unit cell of the constructed structures, their space group, and k-paths are identified using the python libraries seekpath 41 and spglib. 42The backbones of the organic ligands are stripped off of their native terminations and subsequently equipped with the chosen functional groups.Likewise, the Sc nodes are replaced with Y and Al atoms, giving rise to the final pool of input structures for the automatized DFT calculations.The remaining part of the workflow is equivalent to the one presented in Ref. 39, to which we redirect interested readers for further information.The specific details of the DFT runs are optimized for MOFs.Specifically, the threshold for the minimization of interatomic forces is set to 0.025 eV/Å, a relatively large parameter for stiff and dense inorganic crystals but suitable for flexible and porous frameworks; for the same reason, during optimization, only the angles of the unit cell are constrained instead of the space group; finally, the k-mesh is constructed with equidistant points separated by 0.2 Å −1 , which is adequate to accurately sample the relatively small Brillouin zones of the considered MOFs.
All DFT calculations are performed with the code CP2K 43 which implements the Gaussian and plane-wave method. 44Core electrons are accounted for by the dual-space pseudopotentials of the Goedecker-Teter-Hutter type 45 while valence electrons are represented within the MOLOPT triple-ζ basis set including two polarization functions shipped with the code.To ensure numerically converged results, the plane-wave cut-off and the relative cutoff values are set to 600 Ry and 100 Ry, respectively.The Perdew-Burke-Ernzerhof (PBE) functional 46 is used in all calculations in conjunction with Grimme D3 method 47   In the first stage, the MOF structure is loaded via a CIF file or directly from an online database.The python module seekpath analyzes the high-symmetry points of the first Brillouin zone and detects the space group of the structure outputting the primitive cell and the k-path.In the second step, the primitive cell undergoes the desired structural modifications (metal node exchange and ligand functionalization).In step 3, each structure is optimized until the convergence threshold is reached.Finally, the electronic properties including band structure, PDOS, and partial charges are calculated.
for long-range dispersion interactions.The code critic2 48 is employed to calculate partial charges within the Bader method 49 and the Yu-Trinkle integration scheme. 50

Structural Properties and Stability
Sc, Al, Y The MOF studied in this work is the small-pore scandium terephthalate with chemical formula Sc 2 (BDC) 3 , consisting of Sc metal nodes and of 1,4-benzene-dicarboxylate as molecular linkers, see Figures 2a,b.The pores with a radius of about 3 Å favor gas absorption. 33is MOF undergoes a phase transition at 225 K from the monoclinic (space group C2/c) to the orthorhombic phase (space group F ddd, see Figure 2a) with the latter exhibiting negative thermal expansion. 333][54] In this study, the orthorhombic phase of scandium terephthalate extracted from Ref. 33 is used as a basis to construct the substituted MOFs.Sc is replaced by the isoelectronic elements Al and Y, and the linker molecules are functionalized at the sites marked in green in Figure 2b.In addition to the H termination (Figure 2c), methyl, nitrogen dioxide, atomic Cl and Br, the amino group, the hydroxyl group, and the carboxylic group are considered (see Figures 2d-j, respectively).This way, 24 different structures are obtained as an input for the DFT calculations.Regardless of the specific composition, the topology of the considered MOFs is characterized by two inequivalent linker molecules.The corresponding sites are labeled herein as L1 and L2 and appear in the structure with a ratio 1:2 (see Figure 3).Molecules on the L1 site lie parallel to one of the crystal axes while those in L2 form an angle of approximately 60 • with it, giving rise to the peculiar triangular shape of the pore in this MOF.For the linkers in L1, the functional groups lie on the same plane of the phenyl ring, thereby inducing a torsion in the CO 2 groups binding the ligands to the metal nodes.In contrast, in L2, the functionalized carbon rings as well as the CO 2 groups binding them to the metal atoms are slightly twisted (see Figure 3).These qualitative differences can be quantified by evaluating the distances between the metal ion and the O atom of the CO 2 groups and by the dihedral angle of the latter; these results are reported in the Supporting Information (SI) on Tables S1   and S2.After these considerations, we are equipped for the analysis of the structural characteristics of the relaxed unit cells of the considered MOFs which we assess in terms of their volume.As shown in Figure 4a (the raw data are reported in Table S3), the size of the unit cell varies significantly depending on the metal nodes while ligand functionalizations introduce changes on a smaller scale.This behavior can be explained by the different atomic radii of the considered metal atoms: the largest (smallest) volumes pertain to the structures with Y (Al) atoms, which indeed have the largest (smallest) size among the species adopted for the nodes.Similar trends are found also for the distances between the metal atoms and the oxygen atoms belonging to the CO 2 groups of the linker, see Table S1.

L1 L2 L2
Focusing now on the effects induced in the volume by ligand functionalization, we notice similar but not identical trends for the three considered scaffolds (see Figure 4a).In the Al-based MOFs, the smallest volume is found for the H-passivated linker while all functionalizations lead to an increase in the unit-cell size.This finding can be explained in terms of steric hindrance: with COOH this effect is particularly pronounced and can be intuitively understood considering the large size of this group.In the Sc-and Y-based MOFs, we notice some slightly different trends.Keeping the H-passivated structure as a reference, we notice that only methyl functionalization and the highly electron-withdrawing terminations Cl, Br, and NO 2 lead to a larger unit-cell volume.With OH and NH 2 , instead, the Sc-and Y-based MOFs experience a slight decrease in volume due to the formation of hydrogen bonds between the oxygen atoms of the BDC and the H atom of the functional group.Corresponding interatomic separations range between 1.952-2.019with OH and 1.720-1.778Å with NH 2 , see Table S4.It is worth noting that hydrogen bonds are formed also in the presence of the COOH group but only at the L2 site.In the Al-based MOFs, characterized by the smallest volumes, their effect is dramatic and leads to symmetry breaking.
After the examination of the structural properties, we now move to the analysis of the stability which we assess by examining the formation energy per atom.This quantity is computed as the difference between the total energies of the MOFs and the most stable crystalline phases of its constituting elements taken from Materials Project: 55 In Eq. ( 1), E(M OF ) is the total energy per atom of the relaxed MOF while E(M), E(O), E(C), E(H) and E(A FG i ) are the total energies per atom of the elemental crystalline phases of the metal atoms (M = Sc, Al, Y), of oxygen, carbon, hydrogen, and of each atom A X i of the functional group (X), respectively.Under these conditions, zero-point energies and thermal contributions are not included.
As reported in Figure 4b (see also Table S6), we find similar trends of stability for MOFs with the same metal node.The Al-based frameworks, which are characterized by the smallest volumes (Figure 4a), have the least negative formation energies, namely, they are less stable than their Sc-and Y-based siblings.Conversely, the large-volume Y-containing MOFs feature the most negative formation energies suggesting their larger stability over the other considered scaffolds.Functionalization with Cl and Br atoms as well as with the NH 2 , NO 2 , and CH 3 groups gives rise to less stable structures compared to those containing OH and COOH, which stabilize the MOFs through the formation of hydrogen bonds (see Table S4).Although the NH 2 -group forms hydrogen bonds as well, the corresponding bond lengths are larger and therefore contribute less substantially to stabilizing the MOFs.

Partial Charge Analysis
We now turn to the analysis of the partial charges of the considered MOFs calculated using the Bader scheme. 49We examine the results obtained for the metal atoms (Figure 5a) as well as for all the species included in the backbone of the linkers (Figures 5b-g) and in their functionalization (Figure 5h).In this analysis, we distinguish between the values obtained for the ligands at the inequivalent sites L1 and L2.
The partial charges calculated for the metal atoms are positive in all structures, with the largest values pertaining to Al and the lowest to Sc (see Figure 5a).This trend may be puzzling considering the electronegativity of these elements.However, in the MOF environment, the metal atoms form ionic bonds with the neighboring oxygens, as testified by the results plotted in Figure 5b.It can also be noted in passing that in a highly electronegative environment Sc atoms exhibit even lower partial charges than those shown in Figure 5a, as recently discussed in a first-principles study on ScF 3 . 56Considering the values displayed in Figure 5a,b (see also Tables S7-S9), it is evident that the positive charge on the metal ions is almost entirely compensated by the negative charge of the oxygens bound to them.
Analyzing the trends according to the ligand functionalization, we find that the ionicity of the metal-oxygen bond is more pronounced in the MOFs hosting OH and NH 2 groups.This behavior can be understood by recalling that in the presence of these terminations, hydrogen bonds are formed: both OH and NH 2 make available an additional hydrogen atom in the vicinity of the oxygens thus enhancing the partial charges of the latter.This hypothesis is confirmed by considering the results obtained for the carbon atom C1, which is bound to both O atoms in the BDC linker (Figure 2b), and indeed, is positively charged in all considered MOFs (Figure 5c).The smallest values for the partial charges are obtained in the structures functionalized with OH and NH 2 groups, while the largest ones are collected for the structures with NO 2 ligand termination, again mirroring the trend seen in Figure 5b for the O atoms.
We continue this analysis by inspecting the partial charges on the C atoms of the phenyl ring (Figures 5d-f) as well as of their H and X terminations (Figures 5g-h), with H being the hydrogen passivating the rings of all systems (Figure 2b) and X indicating the varying functional atoms or groups.At a glance, it is evident that the electronic distribution in those species is negligibly influenced by the metal node.C2, C4, and H atoms show very small partial charges, thereby reflecting the covalent character of their bonds.However, especially for C4 and H, the values obtained in the molecules at the L1 and L2 sites differ visibly, while no significant differences are noticed for C2.These findings can be understood considering the location of the corresponding atoms in the linker molecule (see Figure 2b): C4 is passivated by H while C2 is surrounded only by carbon atoms.Both C4 and H are generally characterized by positive charges, which become negative in C4 atoms at the L2 molecular site in the presence of the electron-donating functionalizations such as H, CH 3 , and NH 2 (see Figure 5e and 5h).In contrast, with NO 2 terminations, the partial charges of C4 undergo a visible increase in both L1 and L2 ligands due to the electron-withdrawing nature of this group.It should be noted, though, that the absolute values for the charges on C4 remain below 0.1 electrons (see Figure 5f).Finally, for C3 and X, which are bound to each other (see Figure 2b), we notice mirror trends.The large positive charges (>0.25 e − ) accumulated on C3 with X = OH, NO 2 , NH 2 (Figure 5e) are reflected by the equally large but negative values on the functional groups (Figure 5h).Conversely.with the other ligand terminations (H, CH 3 , Br, and COOH), we obtain very small partial charges for C3.

Electronic Properties
We start the analysis of the electronic properties by looking at the band gaps of all the considered MOFs.By inspecting Figure 6 (see also Table S6), we notice at a glance that variations induced by linker functionalization are on the order of an eV, while the exchange of the metal node leads to fluctuations of hundreds of meV at the most.The MOFs with H-passivated linkers exhibit the largest band gaps, ranging between approximately 3.00 eV It should be stressed that the band-gap values plotted in Figure 6 are obtained with the semi-local functional PBE, which is known to underestimate this property in crystalline materials up to 50% of their actual values. 57On the other hand, qualitatively, the trends provided by PBE are usually reliable and Figure 6 should be interpreted as such.This assessment is supported by the fact that our trends for the band-gaps are consistent with earlier studies performed on the MOF MIL-125 with CH 3 , NO 2 , NH 2 , and OH functionalizations 58,59 using the range-separated hybrid functional HSE. 60In light of the relatively large band-gap values delivered by our PBE calculations, we can speculate that most of the MOFs considered in this work are unlikely good absorbers of visible light: their absorption onset is expected to be in the ultraviolet region.Only the systems including OH, NH 2 , and Br terminations can be possibly excluded from this estimation.To confirm or disprove this speculation, DFT results with more advanced approximations for the exchange-correlation potential or even many-body perturbation theory calculations 61 are demanded for future work.
We continue our analysis of the electronic properties of the considered MOFs by inspecting their band structures and projected density of states (pDOS).We start from the systems with H-terminated ligands in order to rationalize first the core features of the MOFs and the impact of metal-node exchange.As shown in Figure 7, the band gap is direct in all systems and located at the Γ-point.Overall, the displayed bands show little dispersion due to the strong localization of the electronic states on the organic linkers.3][64][65][66][67] In the valence region, bands are almost flat along the Γ-Y-T-Z-Γ path in the Brillouin zone (see Figure S1) while larger dispersion appears elsewhere.We can relate the band dispersion with the orientation of the linker molecules in the unit cell: along the (reciprocal) directions parallel to the carbon conjugation of the linker, the electron mobility is larger, and, hence, the bands are more dispersive.This rationale is supported by the analysis of the pDOS which reveals a correspondence between bands characterized by a large dispersion and states dominated by C p-orbitals, especially in the conduction region (see Figure 7).
The electronic levels closest to the frontier exhibit carbon-oxygen hybridization, indicating the contribution of the CO 2 at the connection between the BDC linkers and the metal nodes, as well as contributions from the d-orbitals of the metal atoms particularly for the structures with Sc and Y (Figure 7b,c).In the case of the Al-based MOF, the orbital contributions of the metal ions are further away from the frontier (Figure 7a), due to the small size Supported by these findings, we continue our analysis by inspecting the impact of the linker functionalization on the electronic structure of the considered MOFs focusing on the pDOS of the Sc-based frameworks, see Figure 8; the corresponding band structures are reported in Figure S2.At a glance, we identify the general trends for the band gaps discussed above with reference to Figure 6.With all terminations except for OH and NH 2 , the reduction of the band gap compared to the H-passivated system is due to a rigid lowering of the lowest conduction states (with CH 3 , Cl, Br, and COOH) combined with an upshift of the higher valence-band manifold (with NO 2 ).In contrast, OH and NH 2 terminations (Figure 8f and h) give rise to a localized state with O-and N-p character pinning the top of the valence band and thus effectively reducing the size of the band gap by about 50% compared to the other groups.In the presence of the CH 3 functionalization, the highest valence state receives contributions from the p-and s-orbitals of the methyl group (Figure 8b) in addition to the p-orbitals of the carbon atoms of the BDC molecule characterizing its H-passivated sibling (Figure 8a).With halogen terminations, the p-orbitals of Cl and Br strongly contribute to the occupied frontier states owed to the large electronegativity of these elements, see Figure 8c,d, leading to the discussed reduction of the gap.We note in passing that in those systems, the valence-band maximum is shifted from the Γ to the high-symmetry point L giving rise to an indirect band gap of 2.13 and 1.69 eV for the Cl-and Br-terminated MOFs, respectively (see Figure S2).Finally, with the NO 2 functionalization (Figure 8g), the O porbitals of the functional group contribute to the highest valence state, introducing a distinct peak at the valence-band maximum similar to the methyl group (see Figure 8b).
The discussion reported above on the Sc-based MOFs can be readily extended to the systems with Al and Y nodes (see Figures S3-S6).As commented above with reference to Figure 7, the influence of the metal atoms on the electronic structure is expectedly small and does not affect the region around the gap.On the other hand, the electronic fingerprints of the ligand functionalizations, including the gap states induced by the OH and NH 2 are preserved regardless of the metal node.

Conclusions
In summary, we presented a computational study based on automatized DFT calculations on the structural and electronic properties of scandium terephthalate MOFs with ligand functionalization and metal-node exchange.In our analysis, we considered eight linker ter- In conclusion, our results demonstrate that substituting the Sc node with isoelectronic and earth-abundant elements such as Y and Al alters the volume of the MOFs but does not significantly affect their electronic properties.In contrast, ligand functionalization has a large impact on the stability, charge distribution, and electronic structure of the systems.
Based on these findings we can conclude that exchanging Sc atoms with Al or Y represents a sustainable alternative to preserve the fundamental characteristics of terephthalate frameworks.Additional tuning to target desired applications can be realized by choosing appropriate ligand functionalizations.

Figure 1 :
Figure1: Sketch of the workflow adopted in this work supported by the AiiDA infrastructure.In the first stage, the MOF structure is loaded via a CIF file or directly from an online database.The python module seekpath analyzes the high-symmetry points of the first Brillouin zone and detects the space group of the structure outputting the primitive cell and the k-path.In the second step, the primitive cell undergoes the desired structural modifications (metal node exchange and ligand functionalization).In step 3, each structure is optimized until the convergence threshold is reached.Finally, the electronic properties including band structure, PDOS, and partial charges are calculated.

Figure 2 :
Figure 2: a) Ball-and-stick representation of the orthorhombic primitive unit cell of the scandium terephthalate Sc 2 (BDC) 3 plotted with VESTA. 51b) Building unit of Sc 2 (BDC) 3 with C atoms depicted in black and indexed according to their (in)equivalent sites, H atoms shown in white, O atoms in red, and the metal center in gray: Al and Y are considered in addition to Sc.The adopted functional groups, marked in green in panels a) and b), include c) H, d) CH 3 , e) NO 2 , f) Cl and g) Br, h) NH 2 , i) OH, and j) COOH.

Figure 4
Figure 4: a) Optimized unit-cell volumes and b) formation energies (E F orm ) of all considered MOFs.

Figure 5 :
Figure 5: Partial charges calculated with the Bader scheme of the a) metal ions (M), b) O atoms, c)-f) C atoms, g) H atoms in the backbone of the ligand, and h) functional group as a whole in all the considered MOFs.Solid and dashed lines in panels b)-h) denote the molecular L1 and L2 sites, respectively, while the metal species in the scaffold are indicated by blue circles (Al), down-pointing orange triangles (Sc), and up-pointing green triangles (Y).

Figure 6 :
Figure 6: Calculated band gaps of all the considered MOFs.

Figure 7 :Figure 8 :
Figure 7: Band structure and projected density of states (pDOS) of the H-terminated MOFs with metal nodes a) Al, b) Sc, and c) Y.The valence band maximum is set to 0 eV.The pDOS includes contributions summed over the atomic orbitals of the metal node (M) and of the O, C, and H atoms. X labels for the H atoms passivating the phenyl ring in the sites assigned to the functional group.
minations, including H, CH 3 , NO 2 , Cl, Br, NH 2 , OH, and COOH, as well as the isoelectronic elements Al and Y to replace Sc.We found that all 24 considered structures are stable, exhibiting negative values of formation energies per atom.The largest stability is obtained with COOH and OH terminations in the Sc-and Y-based MOFs.We identified a direct correlation between the atomic radius of the metal node and the unit-cell volume.The effects of linker termination are more pronounced in the Al-based MOFs, characterized by the smallest size compared to those with Sc and Y, and are due to the steric hindrance of the functional groups.Structures exhibiting a larger volume are also generally more stable.The adopted Bader charge analysis provides a metric for characterizing the bondings among the involved species.The coordinative character of the metal-ligand bond depends mostly on the metallic species but is modulated by the functional groups in agreement with earlier findings on zeolitic imidazolate frameworks.68Within the linkers, covalent bonds are formed among the C atoms of the phenyl ring except for the one bound to the functional group which acquires a positive fractional charge in the presence of the electronegative terminations OH, NO 2 , and NH 2 .Furthermore, an ionic bond is formed between the carbon and oxygen atoms in the CO 2 units binding the BDC molecule to the metal node.In terms of electronic structure, all considered MOFs are semiconductors with band gaps ranging from 1.2 to 3.4 eV.These values, obtained with the PBE functional, represent an underestimation based on which we can speculate that these systems will absorb ultraviolet radiation.For the band gaps, we find a large influence of the functional groups, with electronegative terminations leading to about 50% reductions compared to the H-passivated reference.The analysis of band structures and pDOS confirm this trend and furthermore reveals the formation of gap states in the presence of OH and NH 2 terminations.
to account