Synthesis, Thermal, Structural Analyses, and Photoluminescent Properties of a New Family of Malonate-Containing Lanthanide(III) Coordination Polymers

Five new Lanthanide(III) complexes of malonic acid (HOOC-CH2-COOH); {[Gd(C3H2O4)(H2O)4]·NO3}n (1), {[Tb(C3H2O4)(H2O)4]·NO3}n (2), {[Ho(C3H2O4)(H2O)4]·NO3}n (3), [Er(C3H2O4)(C3H3O4)(H2O)2]n (4), and {[Eu2(C3H2O4)2(C3H3O4)2(H2O)6]·4H2O}n (5) were synthesized and characterized by elemental, infrared spectral, and thermal analyses. The structures of compounds 1–5 were determined by single crystal X-ray diffraction technique. The X-ray analysis reveals that compounds 1, 2, and 3 are isostructural and crystallized in the orthorhombic space group Pmn21. The lanthanide(III) ions are coordinated by four carboxylate and four water oxygen atoms adopting a distorted square antiprism geometry. The LnO8 square antiprisms are linked into infinite layers by malonate (C3H2O42-) dianions sandwiching sheets of nitrate counter ions. Compound 4 contains ErO8 square antiprisms linked into a two-dimensional network by hydrogen malonate (C3H3O4-) anions and malonate dianions. The europium complex, 5 is dinuclear having the two europium(III) ions (Eu1 and Eu2) bridged by carboxylate groups of hydrogen malonate ligands. The europium ions in 5 are nine-coordinate and exhibit a distorted monocapped square antiprism geometry. All the structures are consolidated by O–H⋯ O hydrogen bonds. The photoluminescence spectra of 1–5 exhibit characteristic emissions in the visible region. The IR spectra and thermal data are consistent with the structural results. The room-temperature effective magnetic moments for 1–4 are in good agreement with those expected for the free ions, while the data for 5 indicates that low-lying excited states contribute to the observed moment. The compound 1 was further subjected to quantum computational calculations to explore its optoelectronic properties including; density of states (DOS), dielectric function, refractive index, extinction coefficient, and absorption spectrum, to highlight the possible applications of such materials in the optoelectronics.

In order to enhance the fundamental knowledge of structural chemistry of lanthanide-carboxylate frameworks and in view of our continuous interest in this direction (Hussain et al., 2014(Hussain et al., , 2015a(Hussain et al., ,b, 2018, we report here the syntheses, characterization, crystal structures, photoluminescence, and magnetic properties of five novel lanthanide coordination polymers involving malonate ligand. They include; The optoelectronic properties including density of states, dielectric function, refractive index, extinction coefficient, and absorption spectrum, were also investigated for complex 1 with the help of DFT calculations. Owing to the bigger size of lanthanide complexes, they are very difficult to deal quantum chemically. Nonetheless, there are some previous computational studies including the structures and reactions (Eisenstein and Maron, 2002), bonding characteristics (Adamo and Maldivi, 1997), determination of ligand-field parameters (Ishikawa et al., 2003), effective core potential studies (Cundari et al., 1995), and details of computational methods applied in lanthanide and actinide chemistry etc (Dolg, 2015). To the best of our knowledge, this is the first report that describes the formation of lanthanide complexes including a nitrate ion and dinuclear Eu 3+ or Er 3+ complexes containing a hydrogen malonate anion, and their photoluminescent properties.

Synthesis of Complexes
The compounds 1-3 were synthesized by reacting 0.225 g (0.5 mmol) of M(NO 3 ) 3 ·6H 2 O (M = Gd, Tb, Ho) dissolved in 5 mL de-ionized water and 0.156 g (1.5 mmol) of malonic acid in 20 mL ethanol. The solutions were stirred for 2 h at room temperature. The pH of the reaction mixture was adjusted between 5 and 6 with 0.1 M NaOH solution. The solutions were filtered and kept at ambient temperature (or in the refrigerator) for crystallization. The crystals appeared in the solution after 2-3 weeks. The complexes 1, 2, and 3 were obtained as light yellow, colorless, and light pink crystals, respectively. They were separated by vacuum filtration and rinsed with ethanol. Yield: ∼50%.

Synthesis of [Er
Malonic acid (0.104 g, 1 mmol) and ErCl 3 ·6H 2 O (0.137 g, 0.5 mmol) were separately dissolved in 20 mL ethanol and 10 mL deionized water, respectively. The solutions were mixed and stirred for 2 h in a round-bottom flask at room temperature. During stirring, 0.1 M NaOH solution was used to maintain the pH of the mixture between 5 and 6. After 10 days, pink crystals of 4 appeared in solution, which were isolated by filtration and rinsed with methanol. Yield: 49%.

Synthesis of {[Eu
To a solution of 0.183 g (0.5 mmol) of EuCl 3 ·6H 2 O in 10 mL deionized water was added 0.104 g (1 mmol) of malonic acid dissolved in 25 mL ethanol. The solutions were mixed in round bottom flask and stirred for 3 h at room temperature at a pH of 5-6 maintained by using 0.1 M NaOH solution. After 2 weeks, colorless crystals of 5 were recovered by filtration and rinsed with methanol. Yield: 43%.

Physical Measurements
Elemental analyses were carried out on a Varion Micro Cube, Elementar, Germany. FTIR spectra were recorded over the frequency range 4,000-250 cm −1 on a Perkin Elmer FTIR 180 spectrophotometer using KBr pellets. Thermal analyses were performed from room temperature to 1,000 • C at heating rate of 10 • C min −1 in air on a Thermo-gravimeter Analyzer/Differential Scanning Calorimeter model SDT Q 600 (TA Instruments, USA). The excitation and emission spectra were recorded on photoluminescence spectrometer FLS 180 (Edinburg Instruments). The magnetic susceptibility measurements were conducted on Evans balance (Sherwood Scientific Ltd. UK) at room temperature and Hg[Co(SCN) 4 ] was used as a calibrant. The diamagnetic corrections for the component atoms were determined using Pascal constant (Kahn, 1993;Earnshaw, 2013) and details of the method is given the Supporting Information.

Crystal Structure Determinations
Intensity data for compounds 1-5 were collected on a Bruker APEXII CCD diffractometer at 150 K using MoKα radiation (λ = 0.71073 Å). An empirical absorption correction was carried out using SADABS (Sheldrick, 2014). The crystal structures were solved by direct methods with SHELXS-97 (Sheldrick, 2008) and refined by full-matrix least-squares on F 2 using SHELXL-2014 (Sheldrick, 2015). For molecular graphics, ORTEP 3 was used (Farrugia, 2012). The C-bound H atoms were geometrically placed (C-H = 0.99 Å) and refined as riding atoms. The O-bound H atoms were located in difference maps and refined freely as riding atoms in their as-found relative positions or with gentle restrains. One of the water molecules of crystallization in 5 is disordered over two adjacent locations and its H atoms could not be located. The constraint Uiso(H) = 1.2U eq (carrier) was applied in most of the cases. Details of the data collection and refinement details are summarized in Table 1.

Synthesis
The reaction of M(NO 3 ) 3 ·6H 2 O (M = Gd, Tb, Ho) with three equivalents of malonic acid (C 3 H 4 O 4 ) in the presence of NaOH in water-ethanol medium afforded the crystals of {[M(C 3 H 2 O 4 )(H 2 O) 4 ]·NO 3 } n complexes (1-3). The presence of nitrate was not detected in any of the previously reported structures of lanthanide-malonate complexes. Similar reactions of MCl 3 ·6H 2 O (M = Er, Eu) and malonic acid in 1:2 molar ratio gave the crystalline complexes [Er (C 3 The chloride ion did not participate in coordination demonstrating the greater affinity of Ln(III) ions for O than Cl. In every case, the pH of the reaction solution was adjusted to 5-6 in order to avoid the isolation of insoluble hydroxides. The compounds were isolated by slow evaporation of the reaction solution. The composition of the complexes was established from elemental and thermal analyses and verified by X-ray crystallography. All five complexes crystallized as polymeric substances.

IR Spectroscopy
The FTIR spectra of 1-5 are shown in Figures S1-S5. In the IR spectrum of malonic acid two intense bands at 1,737 and 1,706 cm −1 are observed due to ν as (COO), while the symmetric stretches of carboxylate groups appear at 1,418 and 1,398 cm −1 . The signals at 2,992, 2,948, and 3,398 cm −1 are associated with C-H and O-H stretching vibrations, respectively. The CH 2 rock is detected at 771 cm −1 .
In the IR spectra of all complexes the asymmetric and symmetric stretching bands of the carboxylate groups were observed around 1,600 and 1,300 cm −1 , respectively (Deacon and Phillips, 1980;Rodríguez-Martín et al., 2002;Chrysomallidou et al., 2010;Hussain et al., 2018). There is a significant drop in frequencies of these bands relative to that of free malonic acid indicating the coordination of malonate ions. The broad peaks near 3,600 and 3,400 cm −1 correspond to the O-H stretching modes. The rocking vibration of coordinated H 2 O (ρ(H 2 O) was found at 837 cm −1 in complexes 1-3 and at 803 cm −1 in 4 and 5. The medium band around 950 cm −1 is ascribed to bending vibration, δ(O-C-O) of the carboxylate group. The M-O bonds absorbed at 276, 285, and 290 cm −1 for complexes 1, 2, and 3, respectively, which prabably represent the ν(M-O water ) vibrations (Chrysomallidou et al., 2010). These absorptions confirmed the formation of complexes as they were not observed in the ligand spectra. The spectral results are in agreement with the reported literature (Marrot and Trombe, 1994;Doreswamy et al., 2003;Chrysomallidou et al., 2010;Mathew et al., 2012).
The bands at 819 cm −1 in 1-3 mark the presence of nitrate ions (Alhoshani et al., 2019). The absence of a band around 1,700 cm −1 for complexes 1-3 indicates the deprotonation of COOH and coordination of carboxylate dianions to the metal ions. However, the peaks at 1,697 and 1,714 cm −1 in 4 and 5, respectively, correspond to C=O stretches of protonated carboxylic acid (COOH) (Chrysomallidou et al., 2010) as it is evident from crystal structures that the hydrogen malonate ions are present in these compounds.

Thermal Analysis
The simultaneous TG-DSC curves for complex 1 are shown in Figure 1. These curves express the mass losses in three consecutive steps. The first decomposition step occurs between 100 and 200 • C that is attributed to the departure of four coordinated water molecules (experimental weight loss = 19%, calculated = 18.3%). This is evidenced by an endothermic peak of DSC at about 160 • C. After the removal of water, the complex does not show sufficient thermal stability and starts releasing malonate ligand around 200 • C. The decomposition of the malonic group is completed at 400 • C with a weight loss of about 27% (calculated value 25.9%). The combustion of malonate is accompanied by two exothermic transitions in DSC. In the third stage nitrate is lost (as a nitrogen oxide) in the range of 400-650 • C leaving behind ½Gd 2 O 3 as a residue (experimental = 46%, calculated = 46.1%). The DSC plot shows an endothermic dip at about 600 • C attributable to the removal of nitrate.
A close similarity to 1 is noted concerning the TG-DSC profiles of compounds 2 and 3, presented in Figures S6, S7, respectively. However, instead of 650 • C for 1, the decomposition is completed at 900 and 600 • C for 2 and 3, respectively. The DSC curves show endothermic and exothermic peaks that all are in agreement with the mass losses observed in the TG curves. The final residues in case of 2 and 3 correspond to 46 % ½Tb 2 O 3 (calculated = 46.3%) and 47% ½Ho 2 O 3 (calculated value 47.1%), respectively. The similarity of the thermal patterns suggests that the decomposition mechanism is the same for the three compounds.
As illustrated in Figure S8, for compound 4 the first mass loss of 8% occurs between 140 and 170 • C, attributed to dehydration (calculated weight loss = 8.8 % for the removal of two water molecules) and is associated with an endothermic peak at 168 • C. The loss of water at relatively higher temperature indicates the absence of water molecules of crystallization in the complex. After exclusion of coordinated water molecules, the anhydrous compound is stable up to 370 • C. The second weight loss of 45% occurs due to the removal of two malonic groups in the temperature range of 370-900 • C (calculated 50.2%), leaving Symmetry codes: (i) x-½, 1-y, z-½; (ii) -x+2, y, z; (iii) x, y-1, z; (iv) -x+3/2, -y+2, z+1/2.
behind 47% ½Er 2 O 3 as residue (calculated = 46.8%). The DSC curve depicts two exotherms presumably due to combustion of organic moieties at 400 and 625 • C. The thermal behavior of complex 5 is described in Figure S9. The decomposition begins with the loss of two water molecules of crystallization in the temperature range 90-130 • C (experimental weight loss = 8%; calculated = 8.1%). The second weight loss of 12% was observed in the range of 150-200 • C and is ascribed to the elimination of three water molecules coordinated with metal atom. Thus, the thermogram clearly distinguishes the presence of uncoordinated and coordinated water molecules in the complex. After 225 • C, the malonate ligands are lost reducing the mass by 41% (calculated = 45.8%). The final residue is 39% that is associated with ½Eu 2 O 3 (calculated 39.4%). In the DSC plot an endotherm at about 150 • C corresponds to the dehydration step, while the exotherms at about 300 and 410 • C represent the combustion of the malonate ligands. The shapes of the TGA curves for 1-5 are similar to those of the other malonatecontaining Ln 3+ complexes described in the literature (Muraishi et al., 1991;Doreswamy et al., 2003;Chrysomallidou et al., 2010;Delgado et al., 2016) suggesting that the stability of the complexes is comparable to the reported ones.

Description of Crystal Structures
Single-crystal X-ray structural analysis revealed that compounds 1, 2, and 3 crystallize in the polar, orthorhombic space group Pmn2 1 and are isostructural. Therefore, complex 1 is taken as an example to present and discuss the structures in detail with any significant differences for 2 and 3 noted, where ever applicable. Selected bond distances and bond angles for 1 are presented in Table 2, while for 2-5 in Tables S1-S4, respectively. The hydrogen bonding details for 1-5 are given in Tables S5-S9, respectively.
The asymmetric unit of 1 shown in Figure 2 consists of a Gd 3+ ion (site symmetry m), a malonate (C 3 H 2 O 2− 4 ) ligand (with the central C atom lying on a crystallographic mirror plane), four water molecules (two lying on a mirror plane) and a nitrate counter ion (the N atom and one of the O atoms have m site symmetry). The cationic complex is polymeric with each Gd 3+ ion coordinated by four O atoms from three different malonate groups and by four water molecules adopting a fairly regular square anti-prismatic geometry. Each square face of GdO 8 coordination polyhedron consists of two malonate  O atoms and two O atoms of water molecules, but their dispositions are different (Figure 3). In the O1/O1 i /O3/O5 face, the water O atoms are "trans" (lying across the square diagonal), whereas in the other, O2 ii /O2 iii /O4/O4 i , they are "cis" (adjacent). The angles subtended at the Gd atom by them vary in the range of 72.01 to 144.61 • . The malonate ligand is bonded to three different symmetry-related metal atoms yielding a two dimensional coordination polymer. It forms a six-membered chelate ring with one Gd 3+ ion, while the remaining two carboxyl oxygen atoms bind in a unidentate mode to the other two metal ions. In this way, the coordination mode of the bridging malonate group can be described as µ 3 -κ 2 O,O'κO",κO"' (Delgado et al., 2016). The six-membered chelate ring is well described as a boat conformation, with C1 × 2 and O2 × 2 exactly coplanar by symmetry and C2 and Gd1 displaced in the same sense by 0.610 (6) Å and 0.623 (7) Å, respectively.
The mean Gd-O bond distance in 1 is 2.390(4) Å ( Table 2). The comparable distances for Tb in 2 (Table S1) and for Ho in 3 (Table S2) are 2.377(3) and 2.352(4) Å, respectively. This trend agrees well with that expected in terms of the lanthanide contraction effect (Bünzli, 2014). In each case, the M-O m (m = malonate) bonds are shorter than the M-O w (w = water) bonds, which can be explained electrostatically in terms of stronger attraction to the delocalized negative charge on the malonate O atoms. The M-O bond lengths fall within the range observed for other Ln 3+ complexes of malonate (Hernández-Molina et al., 2003;Cañadillas-Delgado et al., 2006;Delgado et al., 2016). The C1-O1 and C1-O2 bond lengths (Table 2) in the malonate ligand are almost equal, indicating delocalization of charge. The dihedral angle between the square planes is 2.84(16) • and the metal ion is displaced from the O1 and O2 planes by 1.248(2) and −1.330(2) Å, respectively.
In the extended structure of 1, the ligands bridge the metal ions into infinite cationic sheets of the formula [Gd(C 3 H 2 O 4 )(H 2 O) 4 ] + propagating in the (010) plane (Figure 4). Each malonate ligand links with three metal ions and the shortest Gd· · · Gd separation within a layer is 6.1705(9) Å, slightly less than the shortest inter-layer separation of 6.7470(7) Å [The corresponding data for 2 = 6.1498(7) and 6.7359(5) Å, respectively, and for 3 = 6.1179(11) and 6.7123(10) Å, respectively]. The nitrate counter ions occupy the inter-layer sites and the inter-sheet bonding is consolidated by O-H· · · O hydrogen bonds (Table S5), with malonate O atoms, water molecules and nitrate-O atoms all acting as acceptors. The hydrogen-bonding patterns in the terbium (Table S6) and holmium (Table S7) compounds are essentially identical to that in 1.
Complex 4 crystallizes in the unusual orthorhombic space group Fdd2. The asymmetric unit of 4 depicted in Figure 5 contains one erbium(III) ion (site symmetry 2), a malonate ligand, a hydrogen malonate anion and two water molecules. To balance the charge of Er 3+ , the malonate species must represent statistically disordered malonate (C 3 H 2 O 2− 4 ) and hydrogen malonate (C 2 H 3 O − 4 ) ions, with half of the O2 oxygen atoms in the crystal bearing a proton. The coordination polyhedra of Er 3+ ion is a square antiprism defined by two chelating ligands (bonding via O1 and O3), two monodentate malonate ligands (via O4) and two water molecules. In both square faces (O1/O1 i /O3/O3 i and O4 ii /O4 iii /O5/O5 i ), the water molecules are located at "trans" positions ( Figure S10). The dihedral angle between these planes is 0 • (by symmetry) and the metal ion is displaced from them by −1.303(2) and 1.186(2) Å, respectively. The average Er-O bond length is 2.334(4) Å ( Table S3) that agrees well with the reported values (Delgado et al., 2016). The chelate conformation is an asymmetric boat, with C2 and Er1 deviating from C1/O1/C3/O3 (r.m.s. deviation = 0.001 Å) by 0.324(6) and 0.827(6) Å, respectively. The C3-O3 and C3-O4 bond lengths in the ligand are almost the same, indicating the delocalization of charge. However, C1-O2 is much longer than C1-O1 as a result of its disordered protonation, as described above. It is notable that O2 (the protonated O atom) does not coordinate to the metal ion. The coordination mode of the C1/O1/O2 carboxyl group is η 1 (monodentate) and that of C3/O3/O4 is µ 2 -η 1 :η 1 (bridging). In the extended structure of 4 the malonate ligands are bound in chelating form on one side (through O1 and O3) and as a bridging entity (via O4) from the  other side (µ 2 -κ 2 O,O'κO" coordination mode). The repeating units are cross-linked to generate a dense two-dimensional network, with no evidence of channels or pores. A part of the chain propagating in the (110) direction is expressed in Figure 6.
The structure of the compound does not match with any of the earlier reported structures of Ln 3+ complexes involving the hydrogen malonate ligand (Wenmei et al., 1992;Marrot and Trombe, 1994;Delgado et al., 2016).
Numerous O-H· · · O hydrogen bonds (Table S9) consolidate the packing: the bonds from the O8 and O11 carboxyl groups (one to another ligand O atom and one to a water molecule) have notably shorter H· · · O separations than the bonds arising from the water molecules.

Comparative Structural Analysis
The crystal structures of several lanthanide compounds containing malonate ligand have been reported, which describe the ability of the malonate ion to adopt monodentate, chelating, and bridging coordination modes. The six-membered chelate ring through the two carboxylate groups is quite common in the lanthanide complexes (Delgado et al., 2016). In the present series of complexes, the malonate 2− ligand adopts two types of coordination modes; µ 3 -κ 2 O,O'κO",κO"' (1-3) and µ 2 -κ 2 O,O'κO" (4,5) leading to 2D network structures.
In the majority of the complexes, the metal ions exhibit the coordination number nine, and the common geometries are tri-capped trigonal prism and distorted monocapped square antiprism (Delgado et al., 2016). In [Pr 2 (mal) 3 (H 2 O) 6 ] and its dihydrate, the coordination environment is distorted capped tetragonal antiprism (Chrysomallidou et al., 2010).
The structures of the complexes presented here (1-5) do not possess similarity to any of the previously reported structures. Four of the five complexes exist as mononuclear 2D polymers, while the fifth (5) is dinuclear. Two complexes (4 and 5) are non-ionic as usual, but three (1-3) contain nitrate as a counter ion, which are so far unprecedented. In complexes 1-4, the metal ions are eight-coordinated. The increase in coordination number from eight (for Gd 3+ -Er 3+ ) to nine (for Eu 3+ ) is due to its larger size compared with the others. The change in coordination number from nine to eight can be related to the lanthanide contraction (Bünzli, 2014).

Photoluminescence Properties
The excitation and emission spectra of 1-5 were recorded in the solid state at room temperature. All these compounds 1-5 exhibited luminescence in the visible region but most excellent results were obtained for compounds 2 and 5. The excitation spectrum of 2 was recorded to monitor the strongest emission of terbium ( 5 D 4 → 7 F 5 ) at 548 nm. The spectrum of 2 ( Figure 9A) exhibited ligand excited peaks between 230 and 270 nm which correspond to the S 0 → S 3, S 2 of the ligand transitions. The peaks in the terbium spectrum were observed at 318, 341, 351, 365, and 379 nm which correspond to the 7 F 6 → 5 H 7, 5 D 0,1 , 7 F 6 → 5 D 2 , 7 F 6 → 5 D 3 , 7 F 6 → 5 L 10 , and 7 F 6 → 5 G 6 transitions, respectively. The excitation spectrum of 5 was recorded to monitor the strongest emission of europium ( 5 D 0 → 7 F 2 ) at 619 nm. The spectrum of 5 ( Figure 9B) also exhibited broad band between 230 and 275 nm that represents the ligand excitations S 0 → S 3 and S 0 → S 2 . The excitation peaks of europium are located at 300, 317, 360, 381, 393, 413, and 461 nm attributed to the 7 F 0 → 5 F J , 7 F 0 → 5 H J , 7 F 0 → 5 D 4 , 7 F 0 → 5 L 7 , 7 F 0 → 5 L 6 , 7 F 0 → 5 D 3 , and 7 F 0 → 5 D 3 transitions, respectively. The major ligand excitation signal S 0 → S 1 expected at 370 nm might be superimposed on strong peaks 7 F 6 → 5 L 10 and 7 F 0  → 5 L 7 in 2 and 5, respectively. The excitation spectra of 2 and 5 depict that the ligand absorbs at shorter wavelength (230-−280 nm) for excitation which helps to sensitize the symmetry forbidden f-f transition of Tb(III) and Eu(III) ions, respectively. The emission spectrum of 2 under the excitation wavelength of 365 nm is shown in Figure 10A which exhibits five characteristic f-f emission peaks of terbium at 496, 548, 584, 626, and 654 nm attributed to the 5 D 4 → 7 F 6 , 5 D 4 → 7 F 5 , 5 D 4 → 7 F 4 , 5 D 4 →7F 3 , and 5 D 4 →7F 2 transitions, respectively. The strongest emission is observed by electric dipole transition at 548 nm ( 5 D 4 → 7 F 5 ) due to the induced effect of the coordinated ligand, which confers to the intense green luminescence output from the solid sample when irritated under UV light (Hou et al., 2013;Bogale et al., 2017a,b). In some previously reported terbium carboxylate polymers, the intensity of this emission is quenched in the presence of Fe 3+ and nitroaromatics, and can be used as a sensor for the detection of metal ions and nitro compounds (Bogale et al., 2017a,b). The magnetic transition at 490 nm ( 5 D 4 → 7 F 6 ) is relatively very weak with intensity ratio 1:6 ( 5 D 4 → 7 F 6 : 5 D 4 → 7 F 5 ) that is almost insensitive to the coordinated environments (Bogale et al., 2017a,b). These peaks have been observed in other terbium complexes (Zhao et al., 2004;Hou et al., 2013Hou et al., , 2014. The emission spectrum of 5 under the excitation of 381 nm is shown in Figure 10B which exhibits five characteristic f-f emission peaks of europium 560 nm ( 5 D 1 → 7 F 1 ), 597nm ( 5 D 0 → 7 F 1 ), 619 nm ( 5 D 0 → 7 F 2 ), 661 nm ( 5 D 0 → 7 F 3 ), and 560 nm ( 5 D 0 → 7 F 4 ). Among them an induced electric dipole transition 5 D 0 → 7 F 2 is the most intense which is hypersensitive to the chemical environment in the vicinity of Eu(III) ion and responsible for the strong red emission when irradiated under UV light (Hou et al., 2014). The magnetic dipole transition at 597 nm ( 5 D 0 → 7 F 1 ) that is less sensitive to the coordinated environment is relatively weak compared with the electric dipole transition. The Eu(III) transition rule states that the magnetic dipole transition ( 5 D 0 → 7 F 1 ) will be more intense when there exists a center of inversion. The intensity of electric dipole transition 5 D 0 → 7 F 2 transition will be decreased as the site symmetry of Eu(III) ion increases (Hou et al., 2014). By comparing the intensity of 5 D 0 → 7 F 2 (619 nm) and 5 D 0 → 7 F 1 (597nm) for 5, the intensity ratio is about 4:1 which suggests that europium ion exists in the low symmetry environment and there is no center of inversion as revealed by the X-ray structural analysis of compound 5 (Gu and Xue, 2006). The excitation and emission spectra of 3 ( Figure S12) exhibited sharp peaks with broad bases at 370 ( 5 I 8 → 3 G 6 ) and 570 nm ( 5 S 2 , 5 F 4 → 5 I 8. ), respectively. In addition, few broad peaks are observed between 400 and 500 nm in the emission spectrum of 3 which are difficult to designate. The emission spectra of 1 ( Figure S13B) and 4 ( Figure S14B) are different from 2, 3, and 5. No characteristic peaks of gadolinium and erbium are observed in the emission spectra of 1 and 4 except broad emission bands at 560 and 470 nm, respectively. Plush and Gunnlaugsson reported that a dinuclear europium(III) bismacrocyclic complex (Plush and Gunnlaugsson, 2007) showed significant enhancement in europium(III) emission when titrated with malonic acid at pH 6.5. When this dinuclear complex was titrated with other dicarboxylates such acetate, succinate, aspartate, and glutarate acids at the same pH, the Eu(III) emission on all occasions was quenched (Plush and Gunnlaugsson, 2007). Thus, we believe that malonic acid is most suitable to produce excited states that help to sensitize the lanthanide luminescence compared with the other aliphatic dicarboxylates.

Magnetic Properties
The room temperature magnetic moments of complexes 1-5 are provided in Table 3. The experimental µ eff values for these complexes are near to the Hund (except for 5) and Van Vleck (Van Vleck, 1932) values for the applicable free Ln(III) ion. The non-zero moment for 5 can be ascribed to the contribution of low-lying excited states to the magnetism, as observed in other europium(III) complexes (Ferenc et al., 2013a,b). These data indicate that the energies of the 4f orbitals in the title compounds differ a little from the free lanthanide(III) ions due to the fact that 5s 2 and 5p 6 orbitals are completely filled and strongly shield the 4f orbitals. Thus, it supports the assumption of the electrostatic nature of metal-ligand bonding in these compounds (Sinha, 2012;Kettle, 2013  parameters including Brillouin Zone (BZ) sampling and energy cut-offs are given in the Supporting Information. All the computational calculations were performed using Cambridge Serial Total Energy Package (CASTEP) in Material Studio (Carter et al., 2006). A detailed comparison of optimized geometry and experimental single crystal geometry of compound 1 is presented in Table S10 and Figure S16, which indicates the reliability of our chosen geometry in the present investigation.

Density of States (DOS)
In order to understand the structure-property relationship, we have calculated total density of states (TDOS) and partial density of states (PDOS) for compound 1. The TDOS and PDOS projected into individual states contributions of the molecule were calculated for compound 1 as shown in Figure 11. The total DOS shows a lot of structural patterns that can be better understood by looking at the PDOS. It can be seen that in deep valence band the contributions of s-and p-states from oxygen atoms are significant in the range of −25 to −3 eV, which indicates significant ligand contributions in the molecular structure. On the other hand, around the Fermi-level the contributions from p-and f -states are significant. Hybridization effects can also be analyzed using PDOSs from Figure 10. The significant contributions of p-states of O atoms and f -states of Gd atoms around −0.5 eV indicates the strong bonding character or energy states hybridization of gadolinium atoms with oxygen atoms of ligands.

Optical Properties
In the past, the photophysical and electroluminescence properties of rare earth metals have been studied very keenly because of their many technological applications i.e., optical amplifiers, luminescent solar concentrators, and active waveguides (Kenyon, 2002;Kido and Okamoto, 2002; FIGURE 12 | The calculated optical properties of 1, including real and imaginary parts of the dielectric function, refractive index, and extinction.  Armelao et al., 2010;Katkova and Bochkarev, 2010;Heffern et al., 2013;Reisfeld, 2015). Along similar lines, we have calculated some important optical parameters, including real and imaginary parts of dielectric function, refractive index, extinction coefficient and absorption spectrum in the solidstate for 1 using periodic boundary conditions. The real and imaginary parts of the dielectric function are presented in Figure 12. The dielectric function is the response of the material to the alternating electric field. Experimentally, dielectric function is calculated using dielectric techniques e.g., dielectric relaxation spectroscopy (DRS). In the present investigation, the optical functions of compound (1) are calculated for photon wavelength up to 800 nm to the direction of polarization vector [100]. For compound 1, its real and imaginary parts of the dielectric function show peaks of maximum dielectric function values (real = 2.2 and imaginary = 1.5) in the range of 200 nm to 300 nm, which indicates that the maximum interaction of light occurs in this range. The refractive index and extinction coefficients also show the highest values of n (1.52) and k (0.64) at similar wavelengths as that of dielectric function in the UV region. These values indicate by how much the value is bent when entering the material.
Moreover, we have also calculated the UV-Visible spectrum for compound 1 by using the PBE-GGA method for solid-state crystal structure. In addition to the commutated UV-Visible spectrum, we have also experimentally recorded the UV-Visible spectrum in ethanol solution. Both the calculated and experimental spectra are illustrated in Figure 13. It is important to mention that the experimental spectrum is only available in the range of 190-400 nm due to the limits of our spectrophotometer. Owing to the above situation and to make a comprehensive comparison of computed and experimental UV-Visible spectra, we have also presented the enlarged part of the computationally generated UV-Visible spectrum in the range of 150-400 nm as shown in Figure 13. A comparison of computationally generated and experimental UV-Visible spectra shows that they are in reasonable agreement with each other. The maximum absorption wavelengths in both spectra are found to be around ∼215 nm. Moreover, the absorption ranges for both the spectra are between 175 and 300 nm. The experimental spectrum for compound 1 shows one shoulder peak which might be due to the fact that it has been measured in ethanol while the computationally generated spectrum is in the solid state. The absorption values display maximum amplitudes in the range of 200-250 nm with good absorption coefficients in the ultraviolet region that could be valuable for the possible application of compound 1 as a UV sensor. Thus, we believe that these optical properties can be very helpful to offer a theoretical basis for the experimental analysis of photophysical properties in future, and to get new physical insights from the molecules to materials.

CONCLUSIONS
Five new lanthanide-malonate coordination polymers (1-5) with two-or three-dimensional connectivity have been synthesized and their crystal structures were determined by X-ray crystallography. The complexes 1-4 are monoculear and the central Ln 3+ ions are eight-coordinate assuming square antiprism geometry. Complex 5 is dinuclear with the nine-coordinated Eu 3+ ions possessing the mono-capped square antiprism polyhedra. The malonate and hydrogen malonate ligands show typical versatility in their chelating, bridging, and combined bonding modes to the different metal ions. So far as we are aware, all three are new crystal structure types. Most of the known compounds such as, [Gd 2 (C 3 H 2 O 4 ) 3 (H 2 O) 6 ]n·2nH 2 O (Cañadillas- Delgado et al., 2006) [Er 2 (C 3 H 2 O 4 ) 3 (H 2 O) 5 ]n·2nH 2 O, (Delgado et al., 2016), and [Eu 2 (C 3 H 2 O 4 ) 3 (H 2 O) 6 ]n·2nH 2 O (Hernández-  contain dianionic malonate ligands, while only a few reports are available on the hydrogen malonate complexes (Wenmei et al., 1992;Marrot and Trombe, 1994). The IR spectra also indicate the presence of hydrogen malonate ligand in 4 and 5. The results of the thermogravimetric analysis verified the composition of the investigated complexes. The photoluminescence spectra of 2 and 5 exhibit characteristic emission of Tb(III) and Eu(III), respectively. Additionally, we have used the first principle calculations for compound 1 to explore its optoelectronic properties. The prediction of dielectric function, refractive index, extinction coefficient and absorption spectrum shed light on prospective applications as optical materials. The maximum dielectric function and other absorption coefficients in the UV region for compound 1 indicate its potential application as a UV sensor. A comparison of computationally generated and experimental UV-Visible spectra shows that they are in reasonable agreement with each other having maximum absorption around ∼215 nm. Thus, we strongly believe that the present set of synthesis, characterization, and computational insights will evoke the significant interests of scientific community in the chemistry of rare-earth coordination polymers.

AUTHOR CONTRIBUTIONS
XC, SA, and IK devised the project, the main conceptual ideas, and proof outline. SH synthesized the compounds, performed analyses and wrote the manuscript. SM carried out the computational and theoretical work. ME collected the crystal date and helped in structure solutions. WH refined and drew images of the structures and wrote the crystal description.