Synthesis, structural characterization, and computational study of (E)-N′-(3,4-dimethoxybenzylidene)furan-2-carbohydrazide

2.1 Syntheses and characterization

Fourier Transform Infrared Spectroscopy (FTIR) spectra were recorded using a Shimadzu 8201 spectrophotometer with KBr technique in the 4000–400 cm⁻¹ region calibrated by polystyrene. Electron Spray Mass Spectrometer (ES–MS) and High Resolution mass spectrometer (HRMS) were recorded on a Micro mass LCT orthogonal acceleration time-of-flight (TOF) mass spectrometer (positive ion mode). Proton nuclear magnetic resonance (¹H NMR) spectra were recorded at 400 MHz and Carbon-13 nuclear magnetic resonance (¹³C NMR) spectra at 100 MHz on a BrukerDPX400 spectrometer. Chemical shifts are denoted in ppm relative to internal solvent standard.

2-Furoic hydrazide (0.0158 mol) and 3,4-dimethoxybenzaldehyde (0.0158 mol) were heated under reflux in ethanol (20 mL) until a solid precipitate was formed (30 min). The mixture was allowed to cool to room temperature and the solvent removed under reduced pressure. The solid was washed successively with cold ethanol, filtered and then recrystallized from cold ethanol to give the pure product in 85% yield and mp 132–134 °CC. IR (KBr) cm⁻¹: 3178 (NH str.), 1104 (N—N), 1658 (C⚌O), 1507 (C⚌C), 1561 (N⚌C), 1020 (C—O). MS (ESI) m/z: [M⁺, Na⁺], 297.0, HRMS (TOF-ES⁻) m/z calculated for C₁₄H₁₅N₂O₄ [M + H]⁺ 275.1032, found 275.1027. ¹H NMR (400 MHz, CDCl₃) δ 10.0 (s, 1H, NH), 8.3 (s, 1H, CH), 7.5 (s, 2H, aromatic ring), 7.3 (d, J = 3.1 Hz, 1H, OCH, furan ring), 7.1 (d, J = 7.8 Hz, 1H, furan ring), 6.8 (d, J = 8.2 Hz, 1H, aromatic ring), 6.5 (d, J = 1.2 Hz, 1H, furan ring), 3.9 (s, 6H, 2 OCH₃). ¹³C NMR (100 MHz, CDCl₃) δ 154.7 (C⚌O), 151.4 (C⚌N), 149.4 (OCCH, furan ring), 148.8 (OCCH, furan ring), 126.6, 122.9, 115.8, 112.4, 108.3 (aromatic and furan rings), 56.0 (OCH₃), 55.9 (OCH₃). Spectra of ¹H NMR, ¹³C NMR, MS(ESI) and HRMS spectra are available in the ESI file.

2.2 Crystallographic analysis

X-ray single crystal data were collected at $\text{230}\text{K}$ using graphite monochromated $\text{Mo}-\text{K}\mathrm{\alpha }\text{(}\mathrm{\lambda }=\text{0.7107}\text{Å)}$ radiation on a Bruker SMART APEX CCD diffractometer. Data reduction was carried out using SAINT (Bruker, 2003) and the structure was solved using SHELXS-97 (Sheldrick, 2008). Full matrix refinement on F² was performed with SHELXL-97 (Sheldrick, 2008) and all calculations were carried out using the SHELXTL package (Sheldrick, 2008). The non-H atoms were refined anisotropically and H atoms were included in calculated positions, except for those bonded to N, which were found by Difference Fourier Methods and refined isotropically. It was necessary to collect the data at 100 K. The crystal data are summarized in Table 1. X-ray diffraction pattern as a function of 2θ is given in Fig. 1. The crystal structural data is deposited at Cambridge Crystallographic Data Centre (CCDC) in CIF format as data for publication in scientific journal under the CCDC 794422 number.

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Fig. 1 XRD pattern of (E)-N′-(3,4-dimethoxybenzylidene)furan-2-carbohydrazide as a function of 2θ. Miller indices are given in purple color.

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4.1 Molecular geometry

The new product (E)-N′-(3,4-dimethoxybenzylidene)furan-2-carbohydrazide 3 was synthesized via condensation of 2-furoic hydrazide 1 and 3,4-dimethoxybenzylidene 2 in refluxing ethanol (Scheme 1). The formation of 3 was confirmed by spectral data (¹H NMR, ¹³C NMR, FTIR, MS and X-ray crystallography.

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Scheme 1 Synthesis of (E)-N′-(3,4-dimethoxybenzylidene)furan-2-carbohydrazide 3.

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The 3D molecular structure of 3 is depicted in Fig. 2a and b. Fig. 2a represents the experimental X-ray crystal structure with the numbering scheme while 2b displays the optimized B3LYP/6311 + G(d,p) geometrical structure. Fig. 3 displays the orientation of molecules of 3 in the asymmetric unit of X-ray crystal viewed along the c-axis, where the red dotted lines represent the hydrogen bonds. Fig. 4 displays the crystal lattice of the two unit cells oriented along the a-axis.

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Fig. 2 (a) The experimental geometric structure of the title compound 3 in the unit cell with the numbering scheme (b) the theoretical geometrical structure as predicted by B3LYP/6-311 + G(d,p) level of theory.

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Fig. 3 Orientation of (E)-N′-(3,4-dimethoxybenzylidene)furan-2-carbohydrazide viewed along the c-axis in the crystal packing showing the oxygen and nitrogen in red and blue colors respectively and the intermolecular NH٠٠٠O hydrogen bondings in red colors. H atoms are omitted for clarity.

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Fig. 4 The crystal lattice of the unit cells oriented along the a-axis.

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X-ray crystallography showed the existence of a single significant molecular moiety (Z′) occurs four times (Z) in the asymmetric unit cell of 3, stated differently: Z′ is 1 and Z is 4. Compound 3 is a modified form of (E)-N′-(1-p-tolylethylidene)furan-2-carbohydrazide (Morjan et al., 2013) where the para-methyl group and meta-hydrogen of the phenyl ring are substituted by methoxy groups and the methyl group attached to the double bond is substituted by a hydrogen atom. Theoretical calculations showed that the title compound is perfectly planar regardless of the hydrogen atoms of the methoxy groups occupying meta and para positions on the phenyl ring, which is not in a full agreement with the experimental results. X-ray solid state structure showed that the furan moiety is slightly twisted, forming a dihedral angle O(1)—C(1)—C(5)—N(1) = 16.9° with the phenyl moiety in this compound. The observed and predicted hydrazone moieties constituents; C(7)—C(6)⚌N(2)—N(1)—C(5)—C(1), are in close agreement, with this region effectively planar and atoms about N—N in trans orientation.

The optimized geometrical parameters (bond lengths and bending angles) obtained using B3LYP with the 6-311 + G(d,p) basis set and the experimental geometric parameters are presented in Electronic supplementary information (ESI), Table S1, for comparative purposes. A Graph comparing the observed geometrical parameters; bond lengths and bending angles, with the calculated ones at B3LYP/6-311 + G(d,p) level of theory is given in Fig. 5. As seen from this comparison, the optimized geometric parameters of 3 are in good agreement with the experimental values with a correlation factors ${\text{R}}^{\text{2}}\text{=}\text{0.988}$ and ${\text{R}}^{\text{2}}\text{=}\text{0.977}$ in case of bond distances and bending angles, respectively. The slight differences observed between the calculated and experimental values result from the fact that the theoretical calculations were performed for isolated compound in the gaseous phase, while its experimental results were obtained for the solid phase of the title compound.

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Fig. 5 The observed geometrical parameters vs the calculated ones; the bending angle correlation between the observed values and the DFT calculated ones are displayed on the main axes (red color) while the correlation graph of the calculated DFT and experimental bond distances occupy the minor axes (blue color).

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The largest differences between the calculated B3LYP/6-311 + G(d,p) and the experimental values are found in the C—H and N—H bonds; 0.138–0.127 Å for the C—H bonds, 0.137 Å for the N(1)—H(1) bond. As a consequence of this findings and as extension to this work, 3 has been simulated by other three different levels of DFT; PBE0, HCTH and WB97XD, with 6-311 + G(d,p) basis set. The same unfortunate results, only with the C—H and N—H bond distances, are obtained. For instance C(6)—H(6) are 1.107 Å, 1.100 Å and 1.098 Å and N(1)—H(1) bond lengths are 1.027 Å, 1.017 Å and 1.014 Å as predicted by PBE0 (Adamo and Barone, 1998; Perdew et al., 1996), HCTH (Boese and Handy, 2001; Boese et al., 2000; Hamprecht et al., 1998) and WB97XD (Chai and Head-Gordon, 2008), respectively, implying a shortness of DFT functional in predicting bond lengths of bonding interaction between C and H atoms from one side, and N and H atoms from the other side.

In the case of bending angles, the most tangible variations were detected; 2.09° for the angle C(5)—N(1)—N(2), 2.0° for the angle O(2)—C(5)—C(1), 1.98° for the angle C(6)—N(2)—N(1), 1.22° for the angle C(9)—O(3)—C(13), 1.11° for the angle C(2)—O(1)—C(1), and 1.65° for the angle C(5)—N(1)—H(1).

The calculated C—C and C—O bond lengths, on average, deviate from X-ray diffraction data by $0.57\pm 0.15\%\text{Å}$ and $0.39\pm 0.24\%\text{Å}$ , respectively, giving rise to an error less than 0.01 Å in C ∼ C and less than 0.005 Å in C ∼ O theoretical bond distances estimations. The calculated and observed bond distances of C(5)—O(2) (1.235 Å and 1.234 Å, respectively) are in good agreement with the observed bond lengths of a typical carbonyl group in aromatic hydrocarbons. The calculated bond lengths of the C—C bonds in the furan heterocyclic ring (1.36 Å, 1.363 Å, 1.429 Å) and the observed ones in the same ring (1.340 Å, 1.344 Å, 1.42 Å) are much shorter than a typical C—C single bond (1.54 Å) and longer than a characteristic C⚌C double bond (1.34 Å). The same trend is noticed with the C—C bonds in the phenyl moiety where the observed bond distances varied between 1.363 Å and 1.44 Å while the same calculated geometrical parameters varied between 1.356 Å and 1.41 Å. Such behavior could be rationalized in terms of delocalization of the $\pi -\text{system}$ within the aromatic moieties involved and thus a hyperconjugated system is obtained.

The experimental and theoretical bond distances of N(2)—C(6) are 1.285(2) Å and 1.281 Å indicating a double bond nature of the bond. The experimental and theoretical C(5)—N(1) bonds are 1.347(19) Å and 1.381 Å, which are shorter than that of a typical C—N single bond by 0.123 Å and 0.089 Å, respectively, but longer than that of a typical C⚌N double bond by 0.057 Å and 0.091 Å, respectively (Allen et al., 1987), indicating the existence of a highly conjugated system. The N(1)—N(2) bond length is 1.384(17) Å, and 1.358 Å as predicted by X-ray and DFT, are shorter than that of a typical N—N single bond (1.45 Å) but longer than N⚌N double bond (1.25 Å). An energy calculation at the same level of theory on the strength of the N—N bond showed that the bond energy of N—N bond is 76.20 kcal mol⁻¹. This energy is around 36.20 kcal mol⁻¹ larger than the energy of a typical N—N bond but around 23.80 kcal mol⁻¹ lower than that of a typical N⚌N double bond. As a consequence of that, a suggestion of double bond nature between the nitrogen atoms in our compound is more favorable. Thus the assumption of highly conjugated system would be enhanced.

It is worth noting that the optimized dihedrals are very poorly correlated with the observed ones with the level of theory employed due to inconsistency among dihedrals; some of the optimized dihedrals are obtained as anhedrals. The observed and calculated ones are reported in ESI, Table S2. If the absolute values of both, the observed and the calculated dihedrals are considered, a close nice correlation will be obtained; R² = 0.998.

4.2 Geometrical structures

Due to double bond geometry and restricted rotation around N(2)⚌C(6) bond, compound 3 was expected to exhibit E/Z-stereoisomerism. In the ¹H NMR spectra the hydrazinamide NH was apparent, appearing as a broad singlet at δ = 10 ppm in CDCl₃, reflecting the existence of only one rotamer. NMR theoretical calculations were in agreement with the observed ¹H NMR data, where a singlet peak either in the gas phase or in CHCl₃ solvent due to resonance of hydrazinamide NH at δ = 9 and at δ = 11 ppm, respectively, was obtained for the E rotamer. The inter-conversion of E/Z rotamers in solution might be evident if the hydrazinamide NH appears as a doublet in the observed ¹H NMR. However, only the E-form (Figs. 2 and 3) around N(2)⚌C(6) was selectively separated as it is exclusively evident from X-ray crystallography. Figures of both the Z-isomer (5) and the rotational E/Z transition structure (TS2, Fig. 7) around N(2)⚌C(6) double bond at the B3LYP/6-311 + G(d,p) level of theory are reported in supplementary materials as mole files. The most important features of the rotational transition structure are that of perfect linearity of C(6)—N(2)—N(1) angle (180.0°) and the existence of one imaginary symmetrical bending vibrational mode ( $\nu =-416.63{\text{cm}}^{-1}$ ) centered at N(2) atom. In addition, the calculated bond distances N(1)—N(2) and N(2)—C(6) in the transition structure are 1.290 Å and 1.255 Å respectively, about 0.068 Å and 0.026 Å shorter than the B3LYP based lengths of the corresponding bond distances in the E-rotamers (3), and 0.094 Å and 0.030 Å smaller than that of the experimental one. This indicates that the bond between the nitrogen atoms is substantially double bond in character. As a consequence of that, the electron density is more localized in the transition structure rather than being more delocalized as in the E-form.

Potential energy surface calculations revealed the probability of the existence of four different stereoisomers; the E-form with O(2) and H(1) in anti and syn orientations (3 and 4, respectively) and also the Z-form in the same orientations (5 and 6), due to amide bond rotamers, as depicted in Scheme 2. Relative energies of the four structures with respect to 3, the most stable one, are: 3 (0.00 kcal mol⁻¹) < 4 (1.58 kcal mol⁻¹) < 6 (7.55 kcal mol⁻¹) < 5 (7.63 kcal mol⁻¹).

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Scheme 2 Predicted E and Z Stereoisomers of (E)-N′-(3,4-dimethoxybenzylidene)furan-2-carbohydrazide.

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4.3 Energy calculations

Energy calculations at the given functional and basis set proved that title compound 3 and its isomers are all real ground states. The structure labeled 3 (Scheme 2) is the global minimum while the others (labeled 4–6, Scheme 2) are local minima on the potential energy surface (PES).

Relaxed PES calculations with geometry optimization at each point over a rectangular grid with the selected internal coordinates; dihedral angles, have been accomplished by scanning a two dimensional potential energy surface based on dihedral angle calculations. Sparkle PM6 semiempirical level of theory was employed to estimate the two dimensional PES utilizing the dihedral angles; C(5)—N(1)—N(2)—C(6) and H1(N1)—N(1)—N(2)—C(6). The input case was that the torsional dihedral angles be stepped 256 scans by 15.0° step size. The Gaussian scan over the two selected torsional dihedral variables is displayed in Fig. 6 as a three dimensional surface. The global minimum corresponds to structure 3 while the maximum corresponds to a structure where the two rings are oriented in anti-position to each other and the aromaticity of the phenyl ring was broken due to ring opening.

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Fig. 6 Relaxed potential energy surface of (E)-N′-(3,4-dimethoxybenzylidene)furan-2-carbohydrazideviewed as predicted by semiempirical PM6 level of theory where energy in atomic units (au), dihedral 1 is C(5)—N(1)—N(2)—C(6) and dihedral 2 is (N1)H(1)—N(1)—N(2)—C(6).

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Fig. 7 Energy profile of (E)-N′-(3,4-dimethoxybenzylidene)furan-2-carbohydrazide (3) and its geometrical structures (4, 5 and 6) as predicted by B3LYP/6-311++G(2df,pd)//B3LYP/6-311 + G(d,p) level of theory.

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Evidently, the total energy of each isomer is lower than the energy sum of its constituent monomers. All energy calculations are performed at B3LYP/6-311++G(2df,pd)//B3LYP/6-311 + G(d,p), while the frequencies calculations are accomplished at B3LYP/6-311 + G(d,p) level of theories. Transition structures were tackled using quadratic synchronous transit (QST2 and QST3) approaches (Peng et al., 1996) with the same B3LYP/6-311++G(2df,pd)//B3LYP/6-311 + G(d,p) level of theories. Two molecular specifications, viz. the reactants and the products, are employed in QST2 calculations. On QST2 failure, quadratic synchronous transit-guided quasi-Newton approach (QST3) was the alternative. In QST3, three molecular specifications: reactants, products, and a first guess for the transition state, in that order, will be considered where atoms must be in the same order in all molecule specifications. The stationary points were verified as first order saddle points, and thus rotational energy barriers (REBs) between the E/Z-geometrical isomers were calculated. The transition structures which connect the minima have been identified by means of internal reaction coordinate (IRC) with a maximum number of 20 points on each side of the path and step size (0.3 amu^−0.5 bohr) between points. Geometries have been optimized at each point along the reaction path.

REBs were estimated as the free energy of activation at 298 K ( ${\mathrm{\Delta }}^{‡}{G}_{(298\text{K})}^o$ ) along the bath connecting the lower energetic isomer and the corresponding transition state. For instance the REB between the E-isomer 3 and the transition structure TS1 is 17.11 kcal mol⁻¹ and it is 32.1 kcal mol⁻¹ between rotamer 3 and TS2. Atomization energy, heat of formation at 0 K and at 298 K and Gibbs free energy at 298 K of each of 3 and its rotamers ( $D_o(M)$ , ${\mathrm{\Delta }}_f{H}_{(0K)}^o$ , ${\mathrm{\Delta }}_f{H}_{(298K)}^o$ and ${\mathrm{\Delta }}_f{G}_{(298K)}^o$ , respectively) in kcal mol⁻¹ were calculated according to the following equations:

A rough Energy profile manifesting REBs among isomers 3, 4, 5 and 6 is displayed in Fig. 7.

As it is obvious from Fig. 6, rotamers are thermodynamically feasible due to small energy differences among them. Nevertheless, from Table 2 and Fig. 6 we see the high energy barrier, have to be overcome, to pass from monomer 3 to 5 and the calculated rate constant would be very small; $k_{(298.15\text{K})}=6.48\times {10}^{-12}{\text{s}}^{-1}$ . In another meaning, in spite of thermodynamic feasibility, rotamers 3 and 5 (E/Z) are, mostly, kinetically, not allowed. This result is in complete accordance with the observed results, only the E rotamer is obtained. Moreover, If 5 has been formed, it would likely interconvert to give rotamer 4 ( $k_{(298.15\text{K})}=859.81{\text{s}}^{-1}$ ), which in turn, has high probability to interconvert to 3. Accordingly, one would safely infer that, monomer 3 might be the only existing rotamer.

4.4 Hydrogen bonds

Hydrogen bonds (HBs) are so widespread in chemistry and biology as a consequence of many important structural and functional rules. HBs can occur intramolecularly as well as intermolecular. Intermolecular hydrogen bondings (IHBs) represent an important class of modeling compounds consisting of more than one molecule to form H-bond dimers, trimers, tetramers or more. In fact, such molecules are usually characterized by the simultaneous presence of HB donor/accepter moieties (Gorski et al., 2012).

X-ray structure of 3 revealed the existence of N(1)—H(1)⋯O(2) IHBs interaction between two molecules, Fig. 3. This would indicate that the crystal structure of (E)-N′-(3,4-dimethoxybenzylidene)furan-2-carbohydrazide is stabilized to some extent by (N—H⋯O) hydrogen bonding that linked into chains between molecules of the compound as it is manifested in Fig. 3. The experimental H⋯O distance for the N(1)—H(1)⋯O(2) bond is 2.030 Å, slightly longer than the DFT (2.023 Å) prediction. Obviously, both the experimental and computed distances of the H-bonds in the dimeric form are significantly shorter than the van der Waals radius of H⋯O bond (2.90 Å), but they are still longer than a typical O—H covalent distance or the sum of their covalent radii of about 1.30 Å (Bondi, 1964).

It is found that the HBs significantly elongated C⚌O and N—H bond distances in the C⚌O⋯H—N hydrogen bond from 1.215 Å and 1.017 Å in the E-monomer to 1.225 Å and 1.024 Å respectively in the dimeric form of the title compound. Furthermore, our analysis of the charge distribution showed that hydrogen bonding significantly decreased the charge density on the carbon and oxygen atoms of the carbonyl moiety and on the hydrogen and nitrogen atoms of the hydrogen bond residue from −0.571, −0.399, 0.268 and −0.22 eu, respectively, in the E-monomer to −0.007, −0.275, 0.401 and −0.019 eu on the corresponding C⚌O⋯H—N atoms that constitute the hydrogen bond moiety in the dimer. Calculations revealed an intensification of positive charge density at the hydrogen atom. On the other hand, electron densities on C and O were significantly decreased due to charge transfer from the electron donor carbonyl oxygen to hydrogen electron acceptor residue of the hydrogen bonding moiety. The calculated bond length and electron density changes are consistent with each other.

The observed and calculated N(1)—H(1)⋯O(2) angles associated with the H-bonds, were found to be in good agreement with each other (161.7° and 162.7°, respectively). H-bonding energy (HBE) which is employed to estimate the stability of the dimer, shown that, the dimer is stabilized to a more extent than its monomers in the gas phase by 8.84 Kcal mol⁻¹. HBE is estimated using the equation: $\text{HBE}\text{=}\left({\text{E}}_{\text{adduct}}\text{-}{\sum }_i{\text{E}}_{\text{monomer}}-BSSE\right)\text{/n}$ (Van Duijneveldt et al., 1994; Morjan et al., 2013)., where E_adduct is electronic energy of the hydrogen bonding complex which is the dimer in this case, E_monomer is the electronic energy of 3 and n represents the number of H-bonds connecting monomers in the adduct in which n = 1 in the case of the dimer. BSSE is estimated as the difference between the monomer energies at the assigned basis set and the complex full set of basis functions. The BSSE calculated according to counterpoise method is 1.20 kcal mol⁻¹, so the corrected HB complexation energy will be 7.64 kcal mol⁻¹. In the BSSE counterpoise methodology, single point calculations of the monomers as fragments of the optimized dimer are conducted, followed by single point calculations of each monomer in presence of the ghost orbitals of the other one in the complex. Stated differently, BSSE correction to the binding complexation energy is the sum of deformation energies of all monomers required to deform them from their equilibrium geometry to the geometry they actually have in the complex.

In extension to this work, the strength of the H-bond has been investigated in solution using CPCM model (Cossi et al., 2003; Barone and Cossi, 1998) with the same level of theory and basis set used in the gas phase. In this model energy is computed in solution by making the solvent reaction field self-consistent with the solute electrostatic potential where a solute cavity is created via a set of overlapping spheres. The number of generated spheres was 34 with the volume of the generated cavity was $\text{374}{\text{Å}}^{\text{3}}$ with each of the employed solvent. Furthermore, the impact of dielectric continuum on the strength of HBs has been investigated in different solvents; chloroform (CHCl₃, ε = 4.7113), 1,2-dichloroethane (ε = 10.125) as well as in a variety of polar aprotic solvents; acetone (Me₂C⚌O, ε = 20.493), dimethylsulfoxide (DMSO, ε = 46.826) DMSO, ε = 46.826), acetonitrile (MeCN, ε = 35.688), diethylether (Et₂O, ε = 4.24), 2-hexanone (ε = 14.136), tetrahydrofuran (THF, ε = 7.4257), and formamide (ε = 108.94). Energies of compound 3 and its dimeric complexes in solutions corrected to zero-point energies and the estimated hydrogen bonding energies are reported in Table 3.

It is obvious from Table 3 and gas phase calculations that the dimers are more stable in solution. In another words, HB stabilization energy remarkably enhances in solutions, compared to its value in gas phase. It ranges from $17.10\text{kcal}{\text{mol}}^{\text{- 1}}$ in formamide to $20.16\text{kcal}{\text{mol}}^{\text{- 1}}$ in THF as being estimated by DFT calculations while its value in gas phase, disregarding BSSE, is $8.84\text{kcal}{\text{mol}}^{\text{- 1}}$ . Despite of the tangible HBE variation between gas phase and solutions, calculations made it clear that the stability of the crystalline structure of (E)-N′-(3,4-dimethoxybenzylidene)furan-2-carbohydrazide has been enhanced by IHB; N—H⋯O hydrogen bonding, linked into chains between monomers; Fig. 3.

HBE decreased with increasing the medium dielectric constant. It was found that the HBE could be, satisfactorily, expressed exponentially with the medium dielectric constant; represented by the equation HBE = 17.04 + 1.29 e⁻⁽ε^/12.05) R² = 0.973, the lower curve in Fig. 8. Apparently, if the first three HBE values corresponding to $\mathrm{\epsilon }$ values (108.94, 46.826 and 35.688) were disregarded, HBE would be linearly varied with $\mathrm{\epsilon }$ and could be satisfactorily represented by the equation HBE = −0.05ε + 18.18, R² = 0.982, the upper curve of Fig. 8. Data were manipulated and fitted whether exponentially or linearly by using Origin 9 package. Full fitting data of ɛ vs. HBE are reported in ESI; Tables S3 and S4.

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Fig. 8 The variation of hydrogen bonding energy with the dielectric continuum as predicted by B3LYP/6-311++G(2df,pd)//B3LYP/6-311 + G(d,p) level of theory using the CPCM model. The lower part of the figure represents the exponential dependence of HBE on solvent dielectric while the upper part depicts the linear variation of HBE.

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The calculations in the gas phase with the assigned level of theory and basis set showed the existence of intramolecular HB between O(1) and H(1) which is in disagreement with the observed X-ray results. The O(1)٠٠٠H(1) experimental and gas phase calculated distances are 2.428 Å and 2.264 Å. The corresponding bond distances in the dimer, trimer and tetramer forms of the titled compound calculated in the gas phase have been remarkably increased to be 2.368 Å, 2.381 Å and 2.406 Å, respectively. As a consequence of that, intramolecular-HB has disappeared. The same behavior of intramolecular-HB has been observed in solutions only in the case of the monomer and dimer but disappeared for trimers. Apparently the planarity of the monomer in the gas phase is responsible for such behavior. Planarity decreased in the case of dimer and trimer and thus the pronounced intramolecular HB. The dihedral torsional angle O(1)—C(1)—C(5)—N(1) has increased from 0.0° in the monomer to be around 3.2° in the dimer, 3.8° in the trimer, and 5.4° in the tetramer. Whether in the gas phase or in solution, the system became more compacted by increasing the number of monomers in the HB-adduct. As a consequence of that, twisting of the furanyl group to minimize crowding would be more feasible, thus, the afore-mentioned torsional angle increased. The O٠٠٠H distance became larger than the van der Waals radii of the two atoms and the probability of forming intramolecular-HB has been eliminated.

In addition to the expected inter/intramolecular HBs another kind of intramolecular HB with ethanol, the solvent used in synthesis would be expected. In fact neither of the IR nor of the ¹H-NMR showed a characteristic band of OH group of the solvent. In attempt to account for the inexistence of the solvent/monomer IHBs, the condensed Fukui Functions $f_{\text{(O)}}^{-}$ and $f_{\text{(H)}}^{+}$ which correspond to nucleophilic and electrophilic attack, respectively, were calculated at the B3LYP/3-21 + G(d) level of theory for both monomer 3 and the solvent in the gas phase. The results are reported in Table 4. Condensed Fukui Functions are calculated as in literature (Oláh et al., 2002).

According to the Hard Soft Acid Base principle (Pearson, 1968) which says that reaction is favored between electrophile/nucleophile of most nearly equal softness, the IHB between the nucleophilic oxygen atom of 3 with the electrophilic H-atom of hydroxyl group of the solvent is slightly less favored (ΔS_(O….HOEt) = 0.0472 au⁻¹) than that between monomers (ΔS_(O…..HN) = 0.0449 au⁻¹). The difference between the two deltas is relatively small (0.0023). This might imply that the IHBs between the O of the monomer and H of the solvent is also probable. In another interpretation, the probable IHBs through the O of the monomer and H of the solvent would be weak and would be easy to be removed. This might account for the usage of ethanol as a solvent and then in washing and recrystallizing of this compound. On the other hand, the O softness of the solvent (0.8799 au⁻¹) is closer to the softness of H in the solvent (0.2125 au⁻¹) rather than that of the H atom of the NH moiety in 3 (0.1204 au⁻¹). This would imply that either of the monomer/monomer or the solvent /solvent interaction would be more appreciable than that of solvent /monomer intermolecular attraction.

4.5 Vibrational frequency

Three Cartesian displacements of 34 atoms in 3 provide 102 internal and 96 vibrational modes corresponding to 3N-6 normal vibrational modes for nonlinear compounds where N is the total number of atoms in the compound. The vibrational modes of our compound have been estimated using FTIR and theoretically computed using B3LYP with the basis set 6-311 + G(d,p). Our compound has proved to be a global minimum ground state on the potential surface energy as it is already mentioned. It showed an inexistence of any imaginary bands in the DFT calculated spectrum. To generate the correct frequencies, the computed vibrational frequencies were scaled by 0.9613 as reported in literature. The vibrational bands assignments were accomplished by using Gauss-View molecular visualization program. Selected most observed and calculated characteristic vibrational modes in ${\text{cm}}^{-1}$ with their calculated relative intensities in a basis to 100 relative to the most intense peak in the case of calculated ones are provided in Table 5.

The vibrational modes of frequencies predicted by the B3LYP level of theory on 3 are in good agreement with the experimental values (R² = 0.992) while the dimeric HB complex reflected better agreement to the X-ray observations (R² = 0.999); Fig. 9. This result provides strong evidence that the HB-dimeric complex is the predominant structure rather than the monomeric one in the unit cell in the solid state.

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Fig. 9 Correlation of experimental and calculated vibrational modes of frequencies of (E)-N′-(3,4-dimethoxybenzylidene)furan-2-carbohydrazide monomer at the minor axes (blue colr), while that of the dimer at the major axes (red color).

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The relative deviation of the values predicted for the HB-dimer is 1.11 ± 0.75% while it is 4.77 ± 5.59% in the case of the E-monomer. Relative deviation is usually calculated using equation 6 where N is the number of vibrational modes involved in calculations, or in general, the number of times the calculations are made (Mkadmh et al., 2009).

As it is clear from Table 5 that the DFT computed vibrational modes of frequencies of the dimer are found either slightly overestimate or underestimate the observed x-ray values. Besides, they are roughly close to that of the E-monomer, yet, significant differences are noticed at certain regions. The most informative difference is observed for the N—H stretching band. The monomeric band observed at v = 3360 cm⁻¹ disappeared in crystalline sample, where it is observed at v = 3184 cm⁻¹ in the dimeric form of 3. The difference between the two calculated values (176 cm⁻¹) could be attributed here to the impact of the N—H⋯O intermolecular hydrogen bonding. The electrostatic H⋯O interaction weakened the N—H bond due to electronegativity difference where oxygen atom is more electronegative than nitrogen atom. In addition, the disappearance of the band at v = 3360 cm⁻¹ in the observed ones, strongly confirm the existence of the dimer, not the monomer, in the solid state.

The C⚌O band of the E/E-dimer appeared at v = 1650 cm⁻¹, 15 cm⁻¹ greater than the corresponding observed value and 26 cm⁻¹ lower than that of the monomer (v = 1676 cm⁻¹). This behavior could be referred to the dimerization that resulted as a consequence of IHB. The dimerization weakened the C⚌O bond, the sigma donor, lowering the stretching force constant, which in turn negatively influenced the symmetrical stretching frequency of the carbonyl bond. Besides, the absorption vibrational band of the carbonyl moiety whether in the dimeric or monomeric forms are still significantly lowered than that of a typical aliphatic C⚌O stretching frequency (1710 cm⁻¹). This behavior could be attributed to the conjugation with the furanyl moiety from one side and the resonance with the neighboring N atom from another side.

A similar trend is noticed in the case of C⚌N vibrational mode where the band is significantly shifted; red shifted, from v = 1611 cm⁻¹ in the monomer to v = 1572 cm⁻¹ the dimer. The dimer band is in better agreement with the experimental value (9 cm⁻¹ larger than the observed one) than that of the monomer.

The FT-IR spectrum showed absorption bands at 1104 cm⁻¹ which were assigned to N—N and calculated theoretically by B3LYP at 1120 cm⁻¹ for the monomer. The calculated stretching vibration mode of the N—N band for the dimer with B3LYP at 6-311 + G(d,p) basis set was somewhat shifted to the lower frequency appearing at 976 cm⁻¹, indicating that the N—N bond is slightly weakened in the dimer.

Despite the significant differences in the case of rocking bands; about 200 cm⁻¹ between the monomer and the dimer shown in Table 5, the values of the rocking bands between the two structures are slightly closed to each other. The band of rocking in plane for N—H and C—H are very close to each other; the bands are v = 1569 cm⁻¹, v = 1399 cm⁻¹ respectively for the monomer, and v = 1558 cm⁻¹, v = 1419 cm⁻¹ for the corresponding bands in the HB-complex.