Spectroscopic and Structural Study of a New Conducting Pyrazolium Salt

The increase in conductivity with temperature in 1H-pyrazol-2-ium 2,6-dicarboxybenzoate monohydrate was analyzed, and the influence of the mobility of the water was discussed in this study. The electric properties of the salt were studied using the impedance spectroscopy method. WB97XD/6-311++G(d,p) calculations were performed, and the quantum theory of atoms in molecules (QTAiM) approach and the Hirshfeld surface method were applied to analyze the hydrogen bond interaction. It was found that temperature influences the spectroscopic properties of pyrazolium salt, particularly the carbonyl and hydroxyl frequencies. The influence of water molecules, connected by three-center hydrogen bonds with co-planar tetrameters, on the formation of structural defects is also discussed in this report.


Introduction
Solid proton conductors are attractive materials due to the possibility of their application as an electrolyte in fuel cells for portable electronics and transportation [1]. These solid materials with good proton conductivity and negligible electronic conductivity are often referred to as solid electrolytes. They allow the passage of electrical current through the material by the movement of protons. According to present knowledge, the conductivity of solids by polyatomic protonic species, such as H 3 O + and NH 4 + , is relatively low. Therefore, proton conduction based on the movement of H + attracts researchers' attention [2]. There are many advantages of facilities using solid electrolytes as compared to liquid electrolytes [3,4]; for example, the only by-products of the reaction occurring in fuel cells based on solid electrolytes are water and heat. This advantage allows the production of pollution-free electrochemical devices, such as the compact power batteries used in mobile and laptops.
Recent studies reveal the numerous requirements for a proton conductor to be used as an electrolyte in a fuel cell [5,6]. For instance, the conduction should be selective to protons, and the electrolyte must be an electrical insulator to prevent the internal short circuit of the cell. Additionally, proton conductors must be thermally stable, which prevents decomposition on heating with the loss of its conductivity. Proton conductors with thermal stability allow the construction of fuel cells with minor corrosion problems.
Some inorganic salts, such as hydrogen sulfates (CsHSO 4 ), reveal high proton conductivity close to 10 −1 S·cm −1 at high temperatures [7,8]. Organic polymers such as Nafion are also good proton-conducting materials, with conductivity close to ∼ 10 −1 S·cm −1 [9], and are currently used in proton exchange membrane fuel cells (PEMFCs) in the USA space program and for transport applications [10,11]. Recently, heteroaromatic triphosphate, 2,4,6triphosphono-1,3,5-triazine (TPT), was used in the synthesis of novel proton conductors (1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MTPT), M = Ce, Zr, Fe) via polymerization with metal ions. Besides TPT, a new class of imidazole-based organic proton conductors has been developed lately [12,13]. Many proton-conducting salts are based on heterocyclic bases and aromatic acids, such as imidazolium salts of benzoic, salicylic, orthophthalic, and terephthalic acids [14,15]. Nevertheless, the hydrogen bonds formed in such solids were weak and medium strength, and their mechanism of conductivity is based on the Grotthuss mechanism. On the other hand, the number and location of the carboxylic group influence the thermal stability and electrical conductivity of the proton conductors [15]. For example, imidazolium orthophthalate and terephthalate revealed high thermal stability with values of 464 and 422 K, respectively, and imidazolium orthophthalate also presented good electrical conductivity (10 −1 S·m −1 ) [14]. There are many proton-conducting salts with high proton conductivity. They fulfill only a few requirements for application as an electrolyte in a fuel cell. For example, several materials exhibit good conductivities but contain crystal water or hydrated protons. They will lose water and conductivity on heating such as hydrated acid or ion-exchanged ceramics [16,17]. It was shown that the oscillation of hydrogen atoms in hydrogen bonds corresponds to a net transport of charge. The cooperative proton transfer phenomenon, followed by reorientation of donating and accepting groups, is a Grotthuss-type conductivity [18,19]. Thus, the transfer phenomenon is similar to an internal acid-base reaction. Proton transfer needs activation energy. If the proton donating and accepting groups are chemically identical, X-H···X, the proton transfer is energetically cost-free. In the case where the proton donating and accepting groups are chemically different X-H···Y, the proton-transfer needs extra activation energy, as in the case of transfer of a proton from a NH + group to carboxylic group COO − . Based on our previous studies on conducting materials, we consider a new conducting pyrazolium salt of hydrated 1,2,3-benzene tricarboxylic acid. It was shown previously that due to the presence of water molecules in the crystal lattice of imidazolium selenate dihydrate, the three-dimensional hydrogen bond exists [20]. There are also some inorganic acid hydrates with high proton conductivity stable up to 350 • C. These salts include, for instance, H 2 Ti 4 O 9 ×1.2H 2 O or zirconium sulfate phosphonates [21]. The conductivity of such salts is related to the water content.
The main goal of this study is to extend the knowledge of a conductivity phenomenon within a new hydrated pyrazolium salt. In the first part of this study, we carried out thermal, optical, and structural analyses. In the second part, the geometrical and topological parameters of the salt under investigation were analyzed in terms of the quantum theory of atoms in molecules (QTAiM) and density functional theory (DFT) methods. In protonconducting systems, intermolecular interactions play a crucial role. Therefore, a study of their role in the real system and theoretical models has outstanding significance. To the best of our knowledge, the QTAiM theoretical calculations and Hirshfeld Surface approach have not been applied so far to analyze the HBs' interactions in pyrazolium hemimellitate hydrate.

Thermal Properties Analysis
Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA were used to study the thermal properties of the substrates and the product. The pur hemimellitic acid (Hem×H2O) decomposes in a broad temperature range from 400 to 650 K ( Figure S4). The endothermic peaks observed in the DSC thermogram with the minima at 440, 470, and 600 K represent dehydration, melting, and acid decomposition [22]. Py razole (Pyr) decomposes in one stage below 450 K ( Figure S5). The DSC thermogram o pyrazole shows two sharp endothermic peaks at 340 and 470 K, attributed to its melting and decomposition. Several overlapping endothermic peaks with the minima at 400, 435 and 600 K can be observed in the DSC thermogram of the PyrHem×H2O (Figure 4). They are related to the dehydration, melting, and decomposition of the compound. The melt ing range of PyrHem×H2O is between 393 and 443 K. The formation of gas bubbles wa noted when the sample was heated above 420 K. It seems most likely that decarboxyla tion of anion moiety proceeds [23]. The salt has a different and more complex decompo sition profile compared to pure acid (Hem×H2O) and pyrazole (Pyr). It decomposes in a few consecutive overlapping stages between 350 and 650 K. These steps may be related to the dehydration, decarboxylation, and decomposition of pyrazole and acid, or its anhy dride. However, it is not possible to define these stages precisely, as they overlap.  Table 1.

Thermal Properties Analysis
Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) were used to study the thermal properties of the substrates and the product. The pure hemimellitic acid (Hem×H 2 O) decomposes in a broad temperature range from 400 to 650 K ( Figure S4). The endothermic peaks observed in the DSC thermogram with the minima at 440, 470, and 600 K represent dehydration, melting, and acid decomposition [22]. Pyrazole (Pyr) decomposes in one stage below 450 K ( Figure S5). The DSC thermogram of pyrazole shows two sharp endothermic peaks at 340 and 470 K, attributed to its melting and decomposition. Several overlapping endothermic peaks with the minima at 400, 435, and 600 K can be observed in the DSC thermogram of the PyrHem×H 2 O (Figure 4). They are related to the dehydration, melting, and decomposition of the compound. The melting range of PyrHem×H 2 O is between 393 and 443 K. The formation of gas bubbles was noted when the sample was heated above 420 K. It seems most likely that decarboxylation of anion moiety proceeds [23]. The salt has a different and more complex decomposition profile compared to pure acid (Hem×H 2 O) and pyrazole (Pyr). It decomposes in a few consecutive overlapping stages between 350 and 650 K. These steps may be related to the dehydration, decarboxylation, and decomposition of pyrazole and acid, or its anhydride. However, it is not possible to define these stages precisely, as they overlap. Molecules 2021, 26, x FOR PEER REVIEW 5 of 18

Intermolecular Interactions Analysis
The analysis of intermolecular interactions in the studied hydrated pyrazolium hemimellitate crystal was carried out using the Hirshfeld surface, fingerprint plots, and the quantum theory of atoms in molecules (QTAiM). The Hirshfeld surface of a molecule in a crystal is constructed by partitioning the crystal space into regions in which the electron distribution of the sum of spherical atoms of the molecule dominates the corresponding sum over the crystal. It can be described using the molecular weight-function w(r): where ρA(r) is a spherically averaged electron density of various atoms centered on the nucleus A. The Hirshfeld surface is defined as the region around a molecule where the weight function ≥0.5. The contribution to electron density from the promolecule to the procrystal exceeds that of all other molecules in this region in the crystal. The Hirshfeld surfaces and fingerprint plots for the hemimellitic ion, the water molecule, and the pyrazolium ion are shown in Figure 5. The Hirshfeld surfaces are defined by points where the contribution in the electron density of the target molecule equals the contribution of all other molecules. The dominant interaction (H⸱⸱⸱O and O⸱⸱⸱H) corresponds to the area presented at Hirshfeld surface: red for the highest contribution through green to blue for points with smaller contribution. Based on the analysis of the Hirshfeld surface and fingerprint plots, the hydrogen bonding patterns can be identified. On the fingerprint plot, each point corresponds to a unique (di, de) pair. The parameters di and de present the distance from the Hirshfeld surface to the nearest nucleus outside and inside the surface, respectively [24,25]. All (di, de) pairs are presented in

Intermolecular Interactions Analysis
The analysis of intermolecular interactions in the studied hydrated pyrazolium hemimellitate crystal was carried out using the Hirshfeld surface, fingerprint plots, and the quantum theory of atoms in molecules (QTAiM). The Hirshfeld surface of a molecule in a crystal is constructed by partitioning the crystal space into regions in which the electron distribution of the sum of spherical atoms of the molecule dominates the corresponding sum over the crystal. It can be described using the molecular weight-function w(r): where ρ A (r) is a spherically averaged electron density of various atoms centered on the nucleus A. The Hirshfeld surface is defined as the region around a molecule where the weight function ≥0.5. The contribution to electron density from the promolecule to the procrystal exceeds that of all other molecules in this region in the crystal. The Hirshfeld surfaces and fingerprint plots for the hemimellitic ion, the water molecule, and the pyrazolium ion are shown in Figure 5. The Hirshfeld surfaces are defined by points where the contribution in the electron density of the target molecule equals the contribution of all other molecules. The dominant interaction (H···O and O···H) corresponds to the area presented at Hirshfeld surface: red for the highest contribution through green to blue for points with smaller contribution. Based on the analysis of the Hirshfeld surface and fingerprint plots, the hydrogen bonding patterns can be identified. On the fingerprint plot, each point corresponds to a unique (d i , d e ) pair. The parameters d i and d e present the distance from the Hirshfeld surface to the nearest nucleus outside and inside the surface, respectively [24,25]. All (d i , d e ) pairs are presented in colors, which correspond to areas presented at the Hirshfeld surface: red for the highest contribution through green to blue for points pointed out the smallest contribution.
interaction is 37.3%, whereas O-H … O amounts to 9.1%. The total contribution of O⸱⸱⸱H interaction is 46.2% of all interactions between the anion and the closest environment. The water molecule plays a role as a proton donator and an acceptor; the total O⸱⸱⸱H interaction is 59.9%, and this contribution is related to the O-H⸱⸱⸱O interactions. The pyrazolium ion is connected by N-H⸱⸱⸱O with two hemimellitate ions, and the O···H interaction is responsible for over 40.4% of all interactions between the pyrazolium ion and the closest environment. The structure is stabilized by N-H⸱⸱⸱O (36.8%) and C⸱⸱⸱H (3.3%) interactions. Pyrazolium ions are also stabilized by the C-H … O (5.9%) interaction.

Figure 5.
On the left, the Hirshfeld surfaces for the hemimellitate ion (a), the water molecule (b), and the pyrazolium ion (c) mapped with di; mapping range: red (short distance) through green to blue (long-distance). In the middle, fingerprint plots (de versus di) for these features involving specific pairs of atoms; on the right, histograms showing the percentage of different types of interactions taking place in the studied salt.
To analyze the hydrogen bond interactions, various descriptors originating from Bader's quantum theory of "Atoms in Molecules" (AIM) are used [26,27]. Koch and Popelier [28] proposed criteria for the description of the D-H⋅⋅⋅A hydrogen bond (where A is a proton-acceptor center). The electron density at the bond critical point BCP (ρH⋅⋅⋅A) The intermolecular H···O and O···H contacts in N-H···O, C-O − ··· H, and O-H···O can be analyzed. For these bonds, the fingerprint plot shows a pair of spikes at the bottom left of the plot, the upper one (d i < d e ) associated with the donor atom, the lower one (d i > d e ) with the acceptor. The carboxylate anion is a proton-accepting center, whereas carboxyl groups are proton-accepting and proton-donating centers. The contribution of N-H···O interaction is 37.3%, whereas O-H ···O amounts to 9.1%. The total contribution of O···H interaction is 46.2% of all interactions between the anion and the closest environment. The water molecule plays a role as a proton donator and an acceptor; the total O···H interaction is 59.9%, and this contribution is related to the O-H···O interactions. The pyrazolium ion is connected by N-H···O with two hemimellitate ions, and the O···H interaction is responsible for over 40.4% of all interactions between the pyrazolium ion and the closest environment. The structure is stabilized by N-H···O (36.8%) and C···H (3.3%) interactions. Pyrazolium ions are also stabilized by the C-H···O (5.9%) interaction.
To analyze the hydrogen bond interactions, various descriptors originating from Bader's quantum theory of "Atoms in Molecules" (AIM) are used [26,27]. Koch and Popelier [28] proposed criteria for the description of the D-H···A hydrogen bond (where A is a proton-acceptor center). The electron density at the bond critical point BCP (ρ H···A ) should be within a range of 0.002-0.040 a.u. The corresponding Laplacian of electron density at the BCPs (∇ 2 ρ BCP ) should be within a range of 0.024-0.139 a.u. Additionally, there are energetic descriptors of BCPs such as electron energy density at BCP (H C ) and its components, potential electron energy density (V C ), and kinetic electron energy density (G C ). The equation gives relationships between topological parameters at the critical point: The Rozas group [29] proposed a classification of hydrogen bonds using the electron energy density and Laplacian of electron density at the BCPs. Weak and moderate Hbonds are characterized by ∇ 2 ρ BCP > 0 and H C > 0, which indicates them as closed-shell interactions. Suppose H C is negative, corresponding to the interaction between the proton and proton acceptor within the hydrogen bridge. In that case, the interaction may be treated as strong hydrogen bonds. The Laplacian of the electron density for interacting pairs of atoms is negative as well. The negative Laplacian for H-bonds indicates their covalent character. If Laplacian is positive and H C is negative, strong hydrogen bonding is partially covalent [30]. For a very strong hydrogen bond interaction, ∇ 2 ρ BCP and H C values are both negative. It has been shown that ρ BCP and ∇ 2 ρ BCP correlate with HBs' energy [31,32]. The increase in hydrogen bond strength is related to the growth of electron density at the bond critical points.
For the 1H-pyrazol-2-ium 2,6-dicarboxybenzoate monohydrate, geometrical and topological parameters of intermolecular contacts, i.e., O-H···O, N-H···O, and C-H···O ( Figure 6) are presented in Table 2. The QTAiM analysis of electron densities at the H···O bond critical points showed that ρ BCP is in a range of 0.0296 to 0.0340 a.u., and Laplacian varies 0.1087 to 0.1268 a.u. A small ρ BCP value indicates the depletion of the electronic charge in the internuclear region. The water molecule plays the role of proton acceptor center (oxygen atom) and proton donator. The most significant electron density at the proton-acceptor O-H···O bond critical point is observed for interaction between the hydroxyl proton of the carboxyl group and water oxygen (-COOH···OH 2 ). It means that HBs' interaction is more substantial for -COOH···water interaction than for -COO − ··· water interaction. The shortest H···O distances are observed for -COOH···water interaction. There are also -COO − ··· H-N and N-H···OH 2 interactions. The most significant electron density at the bond critical point and the shortest bond length were observed for -COO − ··· H-N interaction. The shortest contact exists connecting the oxygen atom of the water molecule and the hydrogen atom of the carboxylic group. The kinetic and potential electron energy densities at BCP (G C , V C ) are close to each other for -COO − ··· H-N interaction. The analysis of V C and G C shows that G C is always greater than the modulus of V C . It means that H C , the total electron energy density at BCP, is greater than zero. Thus, one can expect that intermolecular interactions are of medium strength.   Figure 6.  corresponding to the H···O bond critical point (BCPs), the electron density at BCP ρ BCP ; Laplacian of electron density at BCP, ∇ 2 ρ BCP ; total electron energy density at BCP, H C and the components of the H C : kinetic electron energy density, G C ; potential electron energy density, V C . The atomic labeling is presented in Figure 6.

Electrical Properties Analysis
For PyrHem×H 2 O, the temperature dependence (273-393 K) of the electrical conductivity has been investigated from 1 Hz to 10 MHz. The sample was a cylindrical pellet made of powdered crystallites. The frequency dependence of the real part of complex conductivity is presented in Figure 7. In the temperature range from 273 to 313 K, the conductivity increases almost linearly with frequency. Measured ac conductivity values are very low and hardly change with temperature changes. Moreover, in a given range of frequency measurements, no plateau was observed to provide information about the value of the dc conductivity. As the temperature rises above 313 K, the frequency relationship of ac conductivity changes, which is typical of the ion conductor response. A plateau appears at the lowest frequencies, corresponding to the dc conductivity. Figure 8 shows the impedance dependence in the form of Nyquist plots (imaginary part Z" of total impedance Z* on the real part Z') collected at temperatures T = 358 K and T = 383 K for PyrHem×H2O. The entire response contains a reply from the two parts of the sample: grain interior (crystallite) and grain boundaries. They can be easily distinguished from the total measured impedance using the proper fitting procedure. For fitting the experimental data, the Cole-Cole formula for double RC parallel equivalent circuits connected in series was used: In the temperature range from 273 to 313 K, the conductivity increases almost linearly with frequency. Measured ac conductivity values are very low and hardly change with temperature changes. Moreover, in a given range of frequency measurements, no plateau was observed to provide information about the value of the dc conductivity. As the temperature rises above 313 K, the frequency relationship of ac conductivity changes, which is typical of the ion conductor response. A plateau appears at the lowest frequencies, corresponding to the dc conductivity. Figure 8 shows the impedance dependence in the form of Nyquist plots (imaginary part Z" of total impedance Z* on the real part Z') collected at temperatures T = 358 K and T = 383 K for PyrHem×H 2 O. The entire response contains a reply from the two parts of the sample: grain interior (crystallite) and grain boundaries. They can be easily distinguished from the total measured impedance using the proper fitting procedure. For fitting the experimental data, the Cole-Cole formula for double RC parallel equivalent circuits connected in series was used: where R 1 denotes the resistance of the first contribution, R 2 is the resistance of the sum of two contributions (the crystalline and grain boundaries), C 1 and C 2 mean electrical capacities of circuits 1 and 2, α 1 and α 2 are Cole-Cole parameters, and ω = 2πν is the angular frequency of the measuring field. Such an approach is commonly used to analyze complex impedance responses in polycrystalline samples and ceramics [33,34]. The two contributions from bulk material (crystallite) and grain boundaries are visible at lower temperatures. As the temperature rises, the shape of the measured response gradually becomes more homogeneous ( Figure S6). The fitting procedure values of total impedance were used to calculate the dc conductivity of PyrHem×H2O. The dc conductivity versus the inverse temperature, in the form of the Arrhenius plot, is presented in Figure 9. The Arrhenius law has described it: where σ0 means the pre-exponential factor, Ea is the activation energy, and k is the Boltzmann constant. In the temperature range from 323 to 347 K, the conductivity is characterized by high activation energy Eσ1 = 5.05 eV. Next, at the temperature range 347 The fitting procedure values of total impedance were used to calculate the dc conductivity of PyrHem×H 2 O. The dc conductivity versus the inverse temperature, in the form of the Arrhenius plot, is presented in Figure 9. The Arrhenius law has described it: (4) where σ 0 means the pre-exponential factor, E a is the activation energy, and k is the Boltzmann constant. In the temperature range from 323 to 347 K, the conductivity is characterized by high activation energy E σ1 = 5.05 eV. Next, at the temperature range 347 K ≤ T ≤ 354 K and 354 K ≤ T ≤ 360 K, the activation energy decreases to the value of E σ2 = 2.68 and 1.23 eV, respectively. Above 360 K, dc conductivity is almost temperatureindependent. The step decrease of conductivity above 388 K can be related to the degradation of the sample due to melting and the degradation of PyrHem×H 2 O. The maximum conductivity amounts to 8.2 × 10 −3 S·m −1 at 388 K for the investigated proton-conducting material. It can be seen that the temperature at which the change in the slope of Arrhenius law is observed is in the temperature region where the dehydration process takes place. TGA measurements (Figure 4) show that the weight loss in the temperature range from 318 to 388 K is 5%. It is in good agreement with the endset temperature (354 K) of the endothermic peak with a minimum of 400 K. Water molecules that have emerged from the crystal lattice cause structural defects. An increase in proton conductivity is then possible.  Figure 10 shows the infrared spectra of hemimellitic acid hydrate Hem×H2O (a) and PyrHem×H2O (b) recorded at room temperature. The most prominent experimental vibrational bands with theoretically calculated frequencies are collected in Table S1. In the spectrum of Hem×H2O, there is a broad absorption in the range 3200-2200 cm −1 due to the stretching vibration of the hydrogen-bonded O-H group. Another band characteristic of the acid species is O-H out of plane vibration, which appears as a broad, medium intensity band with a maximum at 898 cm −1 . The calculated γO-H frequency is 889 cm −1 . It is worth mentioning that H-bond formation affects the stretching and deformational vibrational modes of the proton donating group as N-H and O-H bond and the modes of the proton accepting center, i.e., the C=O group and O-H of a water molecule. The carbonyl stretching band appears at 1727 and 1701 cm −1 . According to theoretically calculated frequencies of vibrational modes, the lower frequency band (1701 cm −1 ) is due to the C=O stretching vibration of the C=O group, which interacts with a water molecule.

Vibrational Analysis
For PyrHem×H2O, in the range 3200-2800 cm −1 , there are bands related to the N-H stretching modes of charged amine derivatives (νC=NH+). In the range of 2800-1900 cm −1 , multiple combinational bands are present. The bands denoted as A (2768 cm −1 ), B (2619 cm −1 ), and C (1912 cm −1 ) are associated with νOH stretching vibrations of a hydroxyl group bonded by hydrogen bonds [20,[35][36][37]. The bands A, B, and C are due to Fermi resonance between the νOH stretching vibration, the overtone of the out-of-plane bending vibrations 2γOH, and the combination of the out-of-plane γOH and in-plane δOH bending modes [38].   (Figure 1). In the spectral range 500-900 cm −1 , the HB interaction leads to the formation of bands related to out-of-plane mode γO-H ⸱⸱⸱ O [39]. For PyrHem×H2O, the hydroxyl O-H moiety of -COOH carboxylic groups interact with water molecules, forming O-H … O hydrogen bonds (Figure 2). The band at 897 cm −1 was ascribed to out-of-plane O-H bending mode based on normal modes' theoretical calculations (see Table S1). A moderately intense, broad IR band at 951 cm −1 is due to the O-H bending of the hydrogen-bonded hydroxyl group of the carboxylic moiety. Decreasing intensity of this γO-H…O band with temperature in IR spectra of PyrHem×H2O was observed ( Figure 11). At 303 K intensity ratio, I770/I951 is 4.03, at 343K it is 5.18, and at 363K it is 15.87, while at 373 K, the band at 951 cm −1 is almost invisible. It means that the hydrogen bond between the hydroxyl group of the carboxylic moiety and water molecule is broken with increasing temperature. Figure 11 shows the temperature evolution of the carbonyl band. The intense absorption band of the C=O group is present at 1737 cm −1 at 293 K. Under the influence of temperature, the bandwidth broadening and a fine structure of the carbonyl band are revealed. There are two doublets: at 1741, 1737 cm −1 and 1732, 1728 cm −1 . The temperature dependence of the positions of the bands 1737 and 1728 cm −1 is presented in Figure 12. This variation in band position correlates very well with changes in activation energy in electrical conductivity measurements (Figure 9).  [20,[35][36][37]. The bands A, B, and C are due to Fermi resonance between the ν OH stretching vibration, the overtone of the out-of-plane bending vibrations 2γ OH , and the combination of the out-of-plane γ OH and in-plane δ OH bending modes [38]. The formation of the amine salt results from the transfer phenomenon of a proton from the Lewis acid unit to the Lewis base. Bands at 1579 and 1380 cm −1 are due to the out-of-phase and in-phase COO − stretching vibrations of the carboxylate COO − group, respectively [14,15].

Vibrational Analysis
The crystal structure of PyrHem×H 2 O revealed that both O-H···OH 2 and C-O − ··· + H-N interactions exist (Figure 1). In the spectral range 500-900 cm −1 , the HB interaction leads to the formation of bands related to out-of-plane mode γ O-H···O [39]. For PyrHem×H 2 O, the hydroxyl O-H moiety of -COOH carboxylic groups interact with water molecules, forming O-H···O hydrogen bonds (Figure 2). The band at 897 cm −1 was ascribed to out-of-plane O-H bending mode based on normal modes' theoretical calculations (see Table S1). A moderately intense, broad IR band at 951 cm −1 is due to the O-H bending of the hydrogen-bonded hydroxyl group of the carboxylic moiety. Decreasing intensity of this γ O-H··· O band with temperature in IR spectra of PyrHem×H 2 O was observed (Figure 11). At 303 K intensity ratio, I 770 /I 951 is 4.03, at 343 K it is 5.18, and at 363 K it is 15.87, while at 373 K, the band at 951 cm −1 is almost invisible. It means that the hydrogen bond between the hydroxyl group of the carboxylic moiety and water molecule is broken with increasing temperature. Moreover, the position of the band 1702 cm −1 at high temperatures may indicate that carbonyl groups interact with water molecules. The theoretical calculations for Hem×H2O showed that the band associated with the C=O stretching vibration of the C=O group, which interacts with a water molecule, should be observed around 1701 cm −1 . The observed splits of the carbonyl band in the IR spectrum of PyrHem×H2O can be related to the phenomenon of involvement of the mobile water molecules in the electrical conductivity. Their diffusion process occurs within the dynamic network of hydrogen bonds, which may cause a non-equivalence in the carbonyl groups in the crystal lattice.   Moreover, the position of the band 1702 cm −1 at high temperatures may indicate that carbonyl groups interact with water molecules. The theoretical calculations for Hem×H2O showed that the band associated with the C=O stretching vibration of the C=O group, which interacts with a water molecule, should be observed around 1701 cm −1 . The observed splits of the carbonyl band in the IR spectrum of PyrHem×H2O can be related to the phenomenon of involvement of the mobile water molecules in the electrical conductivity. Their diffusion process occurs within the dynamic network of hydrogen bonds, which may cause a non-equivalence in the carbonyl groups in the crystal lattice.  Moreover, the position of the band 1702 cm −1 at high temperatures may indicate that carbonyl groups interact with water molecules. The theoretical calculations for Hem×H 2 O showed that the band associated with the C=O stretching vibration of the C=O group, which interacts with a water molecule, should be observed around 1701 cm −1 . The observed splits of the carbonyl band in the IR spectrum of PyrHem×H 2 O can be related to the phenomenon of involvement of the mobile water molecules in the electrical conductivity. Their diffusion process occurs within the dynamic network of hydrogen bonds, which may cause a non-equivalence in the carbonyl groups in the crystal lattice. Figure 13a presents temperature-dependent Raman spectra of PyrHem×H 2 O in a spectral range of 1800-1500 cm −1 . The room temperature spectrum consist of a prominent band at 1760 cm −1 (ν C=O ) and 1583 cm −1 (ν C=C ). Above the 354 K, a new band at 1640 cm −1 arises (Figure 13a). According to theoretical calculations, it is due to the deformational vibration of the water molecule δ O-H . It may indicate that dynamic water molecules appear in the crystal lattice. This phenomenon influences the band's position and intensity associated with C = O vibrations (Figure 13b,c).
Data collection. A colorless pillar crystal (AcOEt) of 0.20×0.16×0.06 mm was used to record 13,154 (Cu Ka-radiation, θ max = 76.68 • ) intensities on a Rigaku SuperNova Dual Atlas diffractometer [40] using mirror-monochromatized Cu Kα radiation from a high-flux microfocus source (λ = 1.54184 Å). Accurate unit cell parameters were determined by least-squares techniques from the θ values of 5946 reflections, θ range 2.77-76.06 • . The data were corrected for Lorentz polarization and for absorption effects [40]. The 2613 total unique reflections (R int = 0.033) were used for structure determination.

DSC/TGA Analysis
Thermogravimetric analyses (TGA) were performed on a Mettler Toledo Star TGA/DSC unit (Greifensee, Switzerland). Samples weighing 2-3 mg were placed in aluminum oxide crucibles and heated from 50 • C (323 K) to 900 • C (1173 K) at a 10 K min -1 under an argon flow rate of 40 mL·min -1 . Differential scanning calorimetry (DSC) measurements were performed on a Mettler Toledo Star DSC system (Greifensee, Switzerland). A sample (2-3 mg) was placed in an aluminum crucible, sealed, and then heated from 25 • C (298 K) to 480 • C (753 K) at a heating rate of 10 K min -1 under an argon flow rate of 40 mL·min -1 .

FT-IR and Raman Spectroscopy
Bruker Equinox 55 spectrometer connected with FT-IR Hyperion 2000 microscope was used to obtain FT-IR spectra in the spectral range from 450 to 4000 cm −1 . The spectral resolution equals 2 cm −1 . The spectra were measured using the KBr pellets technique. The Raman spectrum was recorded on a Jobin-Yvon HORIBA LabRAM HR 800 spectrometer equipped with a CCD detector. Raman spectra were recorded from 50 to 3700 cm −1 with the excitation line λ ext = 633 nm and the spectral resolution better than 2 cm −1 . The laser power was kept below 1 mW to avoid thermal and photochemical degradation of the sample. A cryostat made by Linkam Corp. was used to investigate the vibrational spectra versus temperature from 278 to 378 K.

Impedance Spectroscopy
The electric properties of the investigated materials were studied using the impedance spectroscopy method. Salt was powdered in the agate mortar. The received powder was pressed at room temperature under 30 MPa to form cylindrical pellets (~0.4 mm thick and 5 mm in diameter). Next, the electrodes were placed at the proper surface using Hans Wolbring GmbH silver paste. The real and imaginary parts of the electric impedance of the prepared samples were measured in the frequency range from 1 Hz to 10 MHz using the computer-controlled Alpha A High-Frequency Analyzer (Novocontrol GmbH). The temperature of the sample was stabilized by the Quatro Cryosystem with an accuracy of 0.1 K.

Computational Methods
The intermolecular interactions were analyzed using the Hirshfeld surface and fingerprint plots analysis. The calculations were carried out using the CrystalExplorer 3.0 program [46]. Normal mode calculations were performed with the Gaussian09 sets of codes [47]. The initial geometry of the pyrazolium hemimellitate was taken from X-ray data, and it was further applied in the geometry optimization. DFT methods with functional WB97XD [48] combined with the 6-311++G(d,p) standard basis set were used. Thus, the calculations were performed at WB97XD/6-311++G(d,p) level of approximation, including the vibrational frequencies. The results of optimizations correspond to energy minima since no imaginary frequencies were found. The method, as mentioned above, overestimates the calculated harmonic frequencies. For this reason, the scaling factors have been proposed in the literature to correct for anharmonicity. The predicted vibrational wavenumbers were scaled down by a single factor of 0.957. Gaussian output wfn files were used as inputs for the QTAiM program to calculate the topological properties of the salt. The bond critical points were located (BCPs and RCPs), and their properties, such as electron densities at critical points (ρ BCP and ρ RCP ) and their Laplacians (∇ 2 ρ BCP and ∇ 2 ρ RCP ), were calculated. The additional characteristics of BCPs were analyzed, such as total electron energy density at BCP (H C ) and its components, potential electron energy density (V C ), and kinetic electron energy density (G C ) [49].

Conclusions
In this paper, we examined the conductive, thermal, and spectroscopic properties of the new proton conductor, 1H-pyrazol-2-ium 2,6-dicarboxybenzoate monohydrate with a maximum conductivity of 8.2 × 10 −3 Sm −1 at 388 K. The intermolecular interactions analysis shows that the dominant interactions in the investigated salts are hydrogen bonding. The hydrogen bond between the hydroxyl group of the carboxylic moiety and water molecule is broken with increasing temperature. Free water molecules appear in the crystal lattice. The process of proton diffusion takes place in a dynamic network of hydrogen bonds with the participation of water molecules.
Supplementary Materials: The following are available online. Figure S1: The molecular packing in the crystal PyrHemxH 2 O, showing sheets (layers) parallel to the bc plane. The H atoms not involved in hydrogen bonds have been omitted for clarity, Figure S2: Non-classic C-H···O hydrogen bonds linking types into layers parallel to the bc plane. The symmetry codes are explained in Table 1, Figure S3: π ··· π interactions between pyrazolium rings. The molecules are shown in two orthogonal projections. Hydrogen atoms have been omitted for clarity, Figure S4: TGA/DTG curves (top panel) and DSC curves (bottom panel) of Hem×H 2 O, Figure S5: TGA/DTG curves (top panel) and DSC curves (bottom panel) of Pyr, Figure S6: Scaled complex impedance plots -Z"(Z') plot for the measured pyrazolium hemimellitate, Table S1: Experimental and calculated (WB97XD/6-311++G(d,p)) IR stretching and bending frequencies of the O-H, N-H, and C=O groups.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.