Much attention has recently been paid to the establishment of environmentally friendly more acceptable routes, including removal of toxic reagents, minimization of by-product formation, low cost, green and easy procedure. Batteries play an important role as a power source in our everyday life such as mobile phones, microgrids, satellites, etc. Among the various metal ion batteries, lithium-ion batteries are comparatively mature technology having high energy density, power density and good long cycle life ,but the high cost and low availability of certain materials are its main disadvantages . Due to low cost and high natural abundance of sodium, the sodium ion batteries (SIBs) have gained much attention in recent years as an economically interesting alternative to lithium ion batteries for the future exploration  . Recently, various cathode materials for sodium ion batteries have been studied, viz., olivine-type sodium metal phosphates, prussian blue, Na3V2(PO4)3/carbon, Cu-doped P2-Na0.5Ni0.33Mn0.67O2 encapsulated with MgO and titanium substituted P2-Type Na0.67Fe0.5Mn0.5O2  - . For anode materials in SIBs, carbon-based materials (such as graphene, hard carbon, carbon nanosheet and hollow carbon nanospheres), Na+ intercalation pseudocapacitance in TiO2/graphene nanocomposites, amorphous phosphorus/carbon, carbon coated K0.8Ti1.73Li0.27O4 and carbon-coated NaTi2(PO4)3 have been investigated  - . Nanostructured and nanocomposites of organic conducting polymers have been studied in energy storage areas due to their numerous active sites which can generate green batteries with large capacity, high energy and long cycle life    . A group of researchers reported the electrochemical performance of organic tetralithium salts of 2, 5-dihydroxyterephthalic acid having different morphologies viz., nanosheets, nanoparticles and bulk, as both positive and negative electrode of rechargeable lithium-ion batteries . They observed that nanosheets morphologies exhibited the best electrochemical performance with discharge capacities of 223 and 145 mAh∙g−1 at 0.1 and 5 C rates, respectively. Other organic electrode materials, such as, sodium salt of terephthalate and its various derivatives have been used as anode materials in sodium-ion batteries, which were prepared using simple acid-base chemistry . These materials showed outstanding electrochemical activity . In addition, tin, antimony and phosphorus easily formed alloy with sodium, which exhibited excellent electrochemical performance as an anode material for Na-ion batteries    . Very recently, Li et al. described the sodium-ion storage on CuS nanosheets anchored into reduced graphene oxide as anode for SIBs . These materials showed high specific capacity, high initial Coulombic efficiency, superior rate performance and excellent long-term cycle stability, suggesting that Na chemistry for ion battery systems will be feasible for energy storage applications for the next generation. As derivatives of terephthalic acid, the 2-aminoterephthalic acid (H2ATA) have been used for organic building block for assembly of metal-organic framework compounds (for example, isoreticular metal-organic framework-3, IRMOF-3), in which –NH2 groups of organic linker do not involve in the construction of framework structure  . Most importantly, this uncoordinated amine group can serve as an active catalyst site for a variety of organic reactions      and also show as a selective adsorbent for harmful gases . Karabacak et al. described the experimental and theoretical vibrational and electronic analysis of 2-aminoterephthalic acid . Recently, Renault et al. reported the application of dilithium 2-aminoterephthalate as organic Li-battery anode material . The resulting electrodes showed stable capacities (ca. 180 mAh∙g−1) and excellent rate capabilities with battery performance at 500 mA∙g−1. The above results encouraged us to carry out the detailed theoretical calculations of 2-aminoterephthalate (H2ATA) and its sodium salts, aim to find out a sustainable, green and low-cost route towards the construction of sodium ion batteries.
In this study, we report the theoretical calculations of H2ATA, disodium 2-aminoterephthalate (Na2ATA) and its sodium inserted complexes (trisodium 2-aminoterephthalate, Na3ATA and tetrasodium 2-aminoterephthalate, Na4ATA) using Density Functional Theory (DFT) with the hybrid B3LYP method to calculate a wide variety of molecular properties such as optimized structure, binding energy (ΔE) per sodium and spectroscopic properties. NBO (natural bond orbital) analysis and global reactivity descriptors of 2-aminoterephthalic acid, disodium 2-aminoterephthalate and its inserted sodium complexes (Na3ATA and Na4ATA) were also performed to evaluate the strength of donor-acceptor interaction energy and chemical reactivity of this compound. Electronic properties and UV-Visible spectra were also calculated. To our knowledge, there has been no systematic theoretical study of 2-aminoterephthalic acid and its sodium salts using Density Functional Theory (DFT).
2. Computational Details
The geometries of the model complexes were optimized at the hybrid B3LYP  method based on Becke’s three-parameter functional of density functional theory (DFT) calculations using 6-311++G(d,p) basis set. Several structural configurations were considered for comparison of their stability. Geometry optimization was taken to be converged if the maximal atomic force was smaller than 0.00045 hartree/Bohr. Geometries of individual species ligand, metal and metal-complexes were optimized. No geometric constraint was imposed in all the calculations. After optimizing the geometry of each coordination complex, the metal−ligand binding energy ΔE was calculated as .
where, Ecomplex, Emetal and Eligand are the energies of the sodium terephthalate complex, the metal ion and terephthalate ligand, respectively. Therefore, states to the binding energy of the complex per sodium.
The vibrational frequency analyses were performed for all optimized structures (no imaginary frequencies), and indicating that the structures are stable minima on the potential energy surface. It is known that DFT potentials systematically overestimate the vibrational wavenumbers. These discrepancies are corrected either by computing anharmonic corrections explicitly or by introducing a scaled field or by directly scaling the calculated wavenumbers with a proper factor. The raw vibrational frequencies were scaled by a factor of 0.9580, which produced good agreement with the experiment for a wide range of systems. All calculations were performed using the Gaussian 16 program package . Gauss View 6.0.16 was used for the visualization of the optimized structures and simulated vibrational spectra.
Electronically excited state calculations were performed to examine the UV-visible spectra of the H2ATA molecule and its sodium salts. The vertical excitation energies were obtained using the time-dependent density functional theory (TD-DFT) at the level of B3LYP with the 6-311++G(d,p) basis set, after the ground-state optimization. Molecular orbital analysis was also done to calculate the HOMO-LUMO energy gap. Natural bond orbital analysis was performed to provide the appropriate scheme for the metal-ligand interactions. The global reactivity descriptors were also analyzed to describe the molecular reactivity.
3. Results and Discussions
3.1. Geometry of H2ATA
The three different optimized conformers of H2ATA together with their energy with respect to the most stable structure are illustrated in Figures 1(a)-(c). Figure 1(a) is the most stable structure with minimum energy conformer where the C=O groups are on the same side. The second (Figure 1(b)) and third (Figure 1(c)) conformers are more than 0.76 and 11.81 kJ/mol, respectively, higher in energy than conformer 1a. The optimized geometrical parameters in both gas phase and different solvents are listed in Table 1. The bond lengths of both C-COOH (1) and C-COOH (2) in gas phase are slightly shorter (ca. 0.02Å) than experimental results (Table 1) . Due to solvent effects, this bond length decreases almost by 0.018 Å than experimental. The C-NH2 bond lengths both in gas phase and different solvents are calculated about 0.005 Å shorter than experimental result. There are no significant effects of solvents. Due to Coulombic interaction between O and H of COOH bond, C-O bond was calculated larger than C=O bond. The C=O bond is 0.005Å larger than experimental results and no such significant difference was found in other solvents. The calculated bond angles of two carboxylates are found to be 1.83˚ and 1.68˚ shorter than experimental results . It is also noticed that the calculated bond angles in different solvents varies by 1.50˚ and 1.44˚ respectively. These calculated values are good agreements with the experimental results  except the NH2 bond angles which are predicted shorter by 1.78˚ in gas phase and almost 2.90˚ in different solvents.
Figure 1. Theoretical optimized minimum energy conformer of the H2ATA. Grey, white, blue and red circles represent carbon, hydrogen, nitrogen and oxygen, respectively.
Table 1. Comparison of the theoretical (optimized) and experimental geometric parameters of H2ATA in gas phase and different solvents.
[a] DMF = dimethylformamide, DMSO = dimethyl sulfoxide, EtOH = ethanol, EtSH = ethanethiol, FA = formamide, NBA = n-butylamine, ACN = acetonitrile. [b]d = bond length, d(Cg-C) = d(Cring-C), θ = bond angle.
3.2. Geometries of Sodium Salts
The three different optimized structures of disodium 2-aminoterephthalate (Na2 ATA), sodium inserted complexes trisodium (Na3ATA) and tetrasodium (Na4 ATA) 2-aminoterephthalate were shown in Figures 2-4 and the results were summarized in Table 2. A significant change of bond lengths of C-N and Cring-C were observed in disodium, trisodium and tetrasodium salts of H2ATA. The C-N bond lengths of tetrasodium salt were 0.055 Å larger than disodium salt. A significant change of bond angle of NH2 was observed in disodium and its sodium inserted complexes and about 8.18˚ larger in disodium complex compare to trisodium and tetrasodium complex.
Different conformers of the C8H5NaxNO4 (x = 2, 3 or 4) were investigated by DFT calculations (Figures 2-4). In the case of C8H5Na2NO4, there is a negligible
Figure 2. Structures of disodium 2-aminoterephthalate (Na2ATA). The three different conformations of Na2ATA together with their energy with respect to the most stable structure. Grey, white, blue, red and purple circles represent carbon, hydrogen, nitrogen, oxygen and sodium atoms, respectively.
Figure 3. Structures of trisodium 2-aminoterephthalate (Na3ATA). The three different conformations of Na3ATA together with their energy with respect to the most stable structure.
Figure 4. Structures of tetrasodium 2-aminoterephthalate (Na4ATA). The three different conformations of Na4ATA together with their energy with respect to the most stable structure.
Table 2. Geometrical parameters of Na2ATA, Na3ATA and Na4ATA (optimized lowest energy structure).
energy difference for the rotation of the carboxylate group in the meta position as compared to the amino group, but a relative increase in energy of 1.06 kJ/mol and 50.68 kJ/mol if the sodium is placed between the ortho-carboxylate and the amino group (Figure 2(b) and Figure 2(c)). The sodium ion naturally found in the unreduced carboxylate group, whereas retaining the energetically favorable location for one sodium atom near to the amino group.
According to Table 3, the binding energy, enthalpy and Gibbs free energy of Na2ATA complex exhibit value on −694.94, −543.44 and −407.46 kJ/mol respectively and this suggests the thermodynamically most stability of the complex. The binding energies of Na3ATA and Na4ATA in the range of −543.44 to −407.46 kJ/mol, also suggest the thermodynamical stability. The per sodium energy difference of Na2ATA is smaller (151.46 and 287.48 kJ/mol) compare to Na3ATA and Na4ATA, indicating the higher stability of the Na2ATA complex. The binding energies, enthalpies and Gibbs free energy of disodium inserted complexes (Na3ATA and Na4ATA) are also tabulated in Table 3.
3.3. FTIR Spectra
The calculated infrared (IR) absorption frequencies of the compound and its sodium complexes in gasphase are listed in Table 4 and the spectra are shown in Figure 5. The calculated wavenumbers are scaled by a factor of 0.9580. The strong bands at 3615 and 3611 cm−1 of free H2ATA assigned to O-H stretching
Table 3. Binding energy (ΔE), enthalpy (ΔH) and Gibbs free energy (ΔG) of Na2ATA, Na3ATA and Na4ATA (optimized lowest energy structure).
Table 4. Characteristic IR bands (cm−1) for H2ATA, Na2ATA, Na3ATa and Na4ATAa.
[a] ν = stretching vibration, νasy = asymmetric and νsy = symmetric.
Figure 5. Theoretical IR spectra of (a) free H2ATA, (b) Na2ATA and (c) Na4ATA.
vibrations of carboxylic groups, were disappeared on metal carboxylate formation . The strong bands at 1711 and 1670 cm−1 of free H2ATA in FT-IR due to C=O stretching vibration are shifted to 1491 and 1394 cm−1 in the disodium 2-aminoterephthalate complex, Na2ATA, correspond to asymmetric νasy(C-O) and symmetric νsy(C-O) vibrations, respectively . On the other hand, both trisodium 2-aminoterephthalate (Na3ATA) and the tetrasodium 2-aminoterephthalate, Na4ATA, exhibited four bands at ca.1574 and ca.1522 cm−1, and at ca.1361 andca.1342 cm−1, due to asymmetric νasy(C-O) and symmetric νsy(C-O) vibrations, respectively (Table 4). The FTIR spectra of H2ATA and its sodium salts exhibited two bands at ca. 3550 and ca. 3390 cm−1 due to the amino group . In addition, all compounds showed band at ca. 1230 cm−1 which may be assigned to the C-N stretching vibrations .
3.4. Natural Bond Orbital (NBO) Analysis
The NBO analysis was known to be effective tools for chemical elucidation of hyperconjugative interaction and electron density transfer from the filled lone pair electron . Density Functional Theory with the hybrid B3LYP method was used for NBO calculation to examine the various second-order interactions between the filled orbitals of one subsystem andunoccupied orbital of another subsystem. NBO analysis of disodium, trisodium and tetrasodium 2-aminoterephthalate was carried out to evaluate the strength of donor-acceptor interaction energy, E(2) of these complexes and the results are summarized (disodium and tetrasodium only) in Table 5. The results showed the most effective interaction between the anti-bonding electrons of carbon (C4-C5) and carbon (C1-C6) of the π-conjugated system of the benzene ring. The results showed that the major interaction energies of this compound appeared from the interaction between the lone pair electrons of the O atom and antibonding orbitals of carbon atoms of the two carboxylate ions as well as sodium ions. There is also a significant
Table 5. Second order perturbation theory analysis of Fock matrix in NBO for the Na2ATA and Na4ATA in gas phasea.
[a] LP = lone pair, LP* = antibonding lone pair, BD = bonding pair, BD* = antibonding.
interaction noticed with the lone pair electrons of nitrogen (amino group) to the anti-bonding of C4-O5.
3.5. Electronic Properties and UV-Visible Spectrum of H2ATA, Na2ATA and Sodium Inserted Complexes
The time-dependent DFT (TD-DFT) on electronic absorption spectrum of H2 ATA, Na2ATA, Na3ATA and Na4ATA in gas phase were calculated using B3LYP/6-311++G(d,p) method. The major possible transitions, calculated frontier orbital energies, oscillator strengths (ƒ), excitation energies (eV) and molecular orbital (MO) major contributions listed in Table 6 and Table 7 respectively. The energy gap between the orbitals demonstrated the molecular chemical stability which is critical parameters in determining the molecular electrical
Table 6. Calculated wavelengths (λ), oscillator strengths (ƒ) and excitation energies (E) of H2ATA, Na2ATA, Na3ATA and Na4ATA at gas phase using TD-DFT/B3LYP/6-311++G(d,p) level of theory.
Table 7. Frontier molecular orbital energetic parameters of free H2ATA, Na2ATA, Na3ATA and Na4ATA at gaseous statea.
[a] ΔEgap = Energy gap, I = ionization potential, A = electron affinity.
transport properties owing to electron conductivity . The chemical and spectroscopic properties of the molecules are mainly depending on the energy gaps. The frontier molecular orbitals show the electron density for predicting the most reactive position in π-electron systems and also explain several types of reaction in conjugated system . The frontier molecular orbitals (HOMO and LUMO) of free H2ATA are shown in Figure 6. In free H2ATA molecule, the LLCT (Ligand to ligand charge transfer) bands are mainly observed at 185 nm, 224 nm and 365 nm indicating π→π* and n→π* transitions. However, TD-DFT data demonstrated that LLCT bands appeared at 185 - 224 nm. The sharp band appeared at ~224 nm. The molecular orbital contribution (56%) at this band in the gas phase showed the major transitions occurred between the highest occupied molecular orbital (HOMO) to lowest unoccupied molecular orbital+1 (LUMO+1) and the energy gap between HOMO and LUMO+1 was 5.52 eV for H2ATA. An electronic system with a larger HOMO-LUMO gap should be less reactive than one having a smaller gap. The HOMO-LUMO (ΔEgap) gap of the present studied molecule H2ATA is 3.86 eV (Figure 6), indicating the high reactivity. Whereas in the metal complexes, Na2ATA and Na4ATA, the major transitions occur at 267 nm and 199 nm, respectively, due to LLCT (π→π*) transition. The molecular contribution (55%) at 267 nm band for Na2ATA exhibited the major transitions occurred between the highest molecular orbital-3 (HOMO-3) to lowest unoccupied molecular orbital+1 (LUMO+1).
3.6. Global Reactivity Descriptors of H2ATA, Na2ATA and Its Sodium Inserted Complexes (Na3ATA and Na4ATA)
The global reactivity descriptors, e.g. electronegativity (χ), chemical potential (μ), global hardness (η), global softness (s), electrophilicity index (ω) were determined by the conceptual density functional theory on the basis of Koopmans’s theorem . The global reactivity descriptors of the titled molecule and its sodium salts were calculated. Global reactivity descriptors were calculated using the energies of frontier molecular orbitals EHOMO and ELUMO as χ = −1/2(ELUMO + EHOMO), μ = −χ = 1/2(ELUMO + EHOMO), η = 1/2(ELUMO − EHOMO), ѕ = 1/2η and ω = μ2/2η. The energies of frontier molecular orbitals, (ELUMO and EHOMO) and global reactivity descriptors of H2ATA Na2ATA, Na3ATA and Na4ATA are listed in Table 6 and Table 7. The studied molecules, H2ATA and
Figure 6. The frontier molecular orbitals (HOMO and LUMO) of H2ATA.
Table 8. Quantum chemical descriptors of free H2ATA, Na2ATA, Na3ATA and Na4ATAa.
[a] χ = electronegativity, μ = chemical potential, η = global hardness, ѕ = global softness, ω = electrophilicity index.
Na2ATA showed a higher HOMO-LUMO gap in gas phase signifying harder molecule. The free H2ATA exhibited higher value for global electrophilicity index, hardnessand electronegativity than Na2ATA (Table 8).
In summary, we investigated the structural and vibrational properties of 2-aminoterephthalic acid, disodium 2-aminoterephthalate and inserted sodium complexes using density functional theory (DFT/B3LYP) methods with 6-311++G(d,p) basis set. The calculated binding energy, enthalpy and Gibbs free energy of Na2ATA revealed that this compound is thermodynamically more stable than other inserted sodium complexes such as Na3ATA or Na4ATA. NBO analysis of disodium 2-aminoterephthalate exhibited the major interaction energy of the O atom with the carbon atoms of the two carboxylate ions as well as its sodium ions. The UV-visible spectrum of the 2-aminoterephthalic acid indicated that molecular orbital contribution (56%) occurred between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital+1 (LUMO+1), whereas, in the case of disodium salt, molecular orbital contribution (55%) occurred between the highest molecular orbital-3 (HOMO-3) and lowest unoccupied molecular orbital+1 (LUMO+1). In terms of the global reactivity descriptors, H2ATA showed higher electronegativity than Na2ATA. The present computational study of the 2-aminoterephthalic acid and its sodium salts provide strong encouragement for future exploration of functionalized terephthalic acid derivatives as useful material for the safe, low cost, non-toxic, green and easy technology for the production of sodium ion batteries for industrial application.
Financial support of this work by the Centre for Advanced Research in Sciences (University of Dhaka, Dhaka, Bangladesh) is greatly appreciated.
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