Probing the solvent effects and protonation sites of 1-phenyl-4-(phenyldiazenyl)-1H-pyrazol-5-amine (PDPA): DFT calculations meet pKa profiling

3.1 Analysis PA and GB results

The calculated PA and GB values of the investigated species using the DFT method have been displayed in Table 1. The corresponding total energies, zero-point energy (ZPE), and the thermal corrections for energies, enthalpies, and Gibbs free energies (TCE, TCH, and TCG) have been collated in Table SM1 of the supplementary materials. Our preliminary DFT calculations for the parent PDPA-H molecule show that N2 and N5 are the least basic atoms with PA values of 189.2 and 189.2 kcal/mol, respectively; Whereas the competition between N1, N3, and N4 has been clearly observed. Based on these results, the PA and GB values of N1, N3, and N4 atoms have been considered in our discussion. It was found that N1 is more basic than N3 and N4. For the parent molecule, the PA and GB values of the N1 atom are higher than the corresponding ones for N3 and N4. The average PA and GB values of N1 and N2 atoms are 219.7 and 213.1 kcal/mol, respectively, compared with those of N3 (219.2 and 212.2 kcal/mol) and N4 (218.3 and 211.2 kcal/mol) atoms. The average PA and GB values indicate that all atoms have almost the same basicity, with the N1 atom being the most basic. These results agree with those obtained by pK_a calculation. These findings indicate that the PDPA molecule and its derivatives are moderate potent bases and their basicity is close to that of 5-metylhydantoin derivatives (PA=185-207 kcal/mol) (Safi and Frenking 2013), aniline (PA = 210 kcal/mol) (Jolly 1991), and triazepines derivatives (PA = 207 kcal/mol) (Safi and Lamsabhi 2007), with PA values of, 186.6-209.7 kcal/mol. It was also found that the basicity of the PDPA molecule is much higher than that of Helium (PA= 42.6 kcal/mol) and lower than that of methanide (PA = 416.8 kcal/mol) (Jolly 1991).

In general, our results show that the stronger the EDG power is, the more basic the center is, while the stronger the EWG power is, the less basic the center is (Grabowski 2001; Safi and Frenking 2013; Safi and Omar 2014). For the N1 atom, results in Table 1 demonstrate that the maximum PA values of ∼229 and ∼ 227 kcal/mol correspond to -NH₂ and -CH₃ derivatives, respectively. These results can be attributed to the higher ability of the lone-pair electrons on the N atom of the NH₂ group, as well as the inductive effect of the CH₃ group, leading to an increase the electron density of the N1 atom, and consequently increasing the tendency of the N1 atom to interact with the incoming proton. On the other hand, the lowest PA value of 213.5 kcal/mol belongs to -CN and -NO₂ derivatives, indicating that substitution of electron withdrawing groups decreases the electron density on the N1 atom, and consequently, decreases the propensity of the interaction of the N1 atom with the proton. A similar interpretation can also be used for GB results. These results can be confirmed by investigating the NBO results. Data in Table SM2 show that the maximum occupancies of the neutral and protonated N1 atom, ($\text{LP}{\left(1\right)}_{\text{N}1}$), of 1.9456 and 1.7682 a.u., respectively. Whereas the minimum occupancies for the same atom are 1.9386 and 1.6336 a.u., respectively. Therefore, the intrinsic basicity of N1 atoms of the investigated derivatives can be arranged as follows: PDPA-NH₂ > PDPA-CH₃ > PDPA-H > PDPA-Cl > PDPA-F > PDPA-CHO > PDPA -CN ≈ PDPA-NO₂.

For the N3 atom, an irregular decrease was observed in the PA and GB values of PDPA-NH₂ derivative compared to the parent molecule, see Table 1. In contrast, an unexpected increase in the PA and GB values of PDPA-CHO and PDPA-NO₂ derivatives compared to the parent molecule, which might be explained in terms of the formation of a weak IMHB between the proton and the oxygen atom of both -CHO and -NO₂ groups, resulting in reducing the potential of the positive charge of the incoming proton. For N4, the trends of PA and GB values are almost similar to N1, except for the PDPA-CHO molecule, which is 6.3 kcal/mol higher than that of PDPA-H. It is found that the PA of the PDPA-CHO derivative is higher than that of the parent molecule by 6.3 kcal/mol. For both N3 and N4 atoms, the presence of the phenyl group, which is directly bonded to the azo-dye group, has a crucial role in decreasing the basicity due to the delocalization effect.

The geometries of the neutral and protonated (at N1) forms of some investigated derivatives, including PDPA-H, PDPA-NH, PDPA-CHO, and PDPA-NO₂, have been shown in Fig. 1, while the other derivatives have been shown in Fig. SM2 of the supplementary materials. Full geometries of the protonated forms, at N2 and N3 atoms, are available from authors upon request.

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Scheme 1.

Schematic representation of the studied PDPA molecule and its derivatives. PDPA: Poly (2,5-dialkyl-phenylene) amine.

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Fig. 1.

Optimized structure of neutral and protonated forms at N1 atom of PDPA-H, PDPA-NH₂, PDPA-CHO and PDPA-NO₂ derivatives. Bond lengths, C5-N1, N1=N2 and N1-H⁺ in Å (black color), the ∠N2N1C5 bond angle in (°) (in red color) and the dihedral angle, φ_C5N1N2C6 in (°) are shown in blue color.

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A general inspection of the results obtained shows that the bond lengths and bond angles of the investigated derivatives exhibit the expected variation upon protonation. It is found that the most effective changes are located in the bond lengths and the bond angles neighboring the protonated nitrogen atom, while slight variations are observed for other bonds. The C₅=N₁ and N₁-N₂ bond distances lengthen with averages of, correspondingly, 0.050 and 0.003 Å, while the ∠N₂N₁C₃ angle increases with an average of 3.3°. In addition, the phenyl group attached to the pyrazole ring is twisted out of plane. It is also found that the average bond distances of $N_i\dots H_{}^{+} (i=1, 3, \text{and} 4)$, are 1.014, 1.027, and 1.023 Å, respectively, which agree with the PA results. This signifies that the interaction between the N1 atom and the incoming proton is the strongest one.

3.2 Analysis of single water-PDPA interactions

Frontier orbital theory (FOT) affirms that the most reactive molecular orbitals (MO) in the molecule are the highest occupied and the lowest unoccupied molecular orbitals (HOMO and LUMO). The energy gaps of the individual water and PDPA derivatives (ΔE) and those of water-PDPA interactions (ΔE₁ and ΔE₂) can be calculated using the following expressions Eq. (2).

The corresponding E_HOMO and E_LUMO and HOMO-LUMO energy gaps (ΔE, ΔE1 and ΔE₂) have been displayed in Table 2.

A larger E_HOMO value is known to accelerate the atom’s tendency to donate electrons, while a lower E_LUMO increases the atom’s propensity to accept electrons. Examination of Table 2 indicates that the PDPA-NH₂ derivative has the highest capability to donate electrons to water molecules, while the PDPA-NO₂ derivative has the lowest. Contrarily, the PDPA-NO₂ derivative has the maximum ability to accept electrons, while PDPA-NH₂ has the minimum. These results clearly indicate that as the substitution of EDG increases, the electron density of the lone pair of electrons on N1 increases, consequently increasing its ability to donate electrons to the LUMO of the water molecule. In contrast, the substitution of EWG decreases the electron density on N1 therefore increasing it’s ability to accept electrons from water molecules. It is also found that the studied PDPA derivatives are characterized by small energy gaps, which lie in the range of 3.565-3.732 eV, signifying that they are chemically reactive and kinetically unstable.

Insight of the above findings, the question to be addressed is whether the electron’s flow is more favorable. The results in Table 2 clearly indicate that $\Delta E_2< \Delta E_1$, signifying that the electrons flow can take place from the HOMO of PDPA derivatives to the LUMO of water. This means that the interaction between the H₂O and PDPA molecules might have occurred by the interaction of the lone pair of electrons of the N1 atom of PDPA derivatives and the hydrogen water molecule. It is also found that as the power of EDG increases, the N1…H interaction power increases. Contrarily, EWG substitution decreases the strength of the N1…H interaction. Therefore, it can be predicted that the strength of N1…H interaction can be arranged as follows: PDPA -NH₂ > PDPA -CH₃ > PDPA -H > PDPA -Cl > PDPA -F > PDPA -CHO _> PDPA -CN _> PDPA -NO₂.

The solvent effect was explicitly performed by the interaction of PDPA derivatives with single water molecules at the N1 atom through the formation of IMHB. Fig. 2 shows the geometrical structures of the PDPA-water complexes. The first inspection of Fig. 2 shows that the bond distance of N₁…H in the PDPA-water complexes lies between 1.926 – 2.379 Å. Among the investigated complexes, the longest N₁…H bond of 2.379 Å was found for the PDPA-NO₂.H₂O complex, which is attributed to the possible formation of another IMHB with 2.290 Å between the hydrogen water molecule and the oxygen NO₂ group. On the other hand, the shortest IMHB of 1.953 Å, corresponds to the PDPA-NH₂.H₂O complex.

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Fig. 2.

Optimized structure of PDPA-H₂O complexes and its derivatives as obtained using B3LY{/6-311++G(d,p) level of theory. The intermolecular hydrogen bond length and bond angle between PDPA and water N₃…H as shown in blue and red colors, respectively. Units are in Å for N₃…H bond length and in (°) for ∠N₁HO bond angles.

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In general, our results indicate that as the power of EWGs increases, the length of the IMHB decreases, which can be explained by the increase in electron density at the N1 atom and vice versa. It is also found that as the strength of EDG increases, the hydrogen bond angle, ∠N₁HO, increases. Contrary, as the strength of EWG increases, the ∠N₁HO decreases, see Fig. 2.

The intermolecular interactions between the water molecule and the PDPA derivatives can be represented by plotting the scatter plot of δ g^inter/intra (a.u.) vs. sign(λ₂)ρ (a.u.) and the corresponding RGD maps, see Fig. 3 and Fig. SM3 of the supplementary materials. As seen in Figs. 3 and SM3, the intermolecular region has been represented by red dots, while the intramolecular interactions have been represented by black dots. The density of the red region reflects the strength of the intermolecular interactions between water molecules and PDPA derivatives. The density of the red dot is directly proportional to the intermolecular interaction. It is obvious from Fig. 3 that minimum intermolecular interaction corresponds to the PDPA-NO₂.H₂O complex, which the maximum one belongs to, correspondingly, PDPA-NH₂.H₂O complex.

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Fig. 3.

Scatter plots of δg^inter/intra (a.u.) vs. Sign(λ₂)ρ (a.u) of some PDPA-water complexes. The corresponding RGD maps are superimposed at the top right of each panel. The red dots correspond to the intermolecular interactions, while the black dots correspond to the intramolecular interactions. The corresponding plots of the other species have been shown in Figure SM3 of the supplementary materials

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The above results have been confirmed by the estimation of the interaction energy ($E_{int}$) of the $\text{PDHP}+{\text{H}}_2\text{O }\rightleftarrows \text{PDHP}.{\text{H}}_2\text{O}$ reaction using the following expression:

Here, $E_{complex}$, $E_{PDPA}$ and $E_{H2O}$ are the single point energies with the corrected ZPE of PDPA-water complexes, PDPA derivatives and water molecule, respectively. The corresponding $E_{int}$ values have been listed in Table 3. The corresponding energies, ZPE and Thermal corrections have also been displayed in Table SM1.

Our results show that the average $E_{int}$ value is -5.0 kcal/mol, which belongs to moderate IMHB. The maximum $E_{int}$ value of -6.6 kcal/mol corresponds to PDPA-NH₂.H₂O, while the minimum one of -4.2 kcal/mol belongs to the PDPA-CN.H₂O complex, illustrating the significant role of the nature of substituted groups in the strengthening or the weakening the IMHB. Furthermore, a second-order NBO perturbation analysis clearly depicts the interaction between the lone pairs of electrons on the N1 atom of PDPA derivatives, $\text{LP}{\left(1\right)}_{\text{N}1}$ nonbonding orbital, and the ${\sigma }_{\text{H}-O}^{*}$ antibonding orbitals of water molecule ($\text{LP}{\left(1\right)}_{\text{N}1}$) → ${\sigma }_{\text{H}-O}^{*}$), resultsing in a stabilization energy (E^CT). This E^CT enhances system stabilization by intermolecular charge transfer. According to Table 3, the E^CT value ranges from 0.62 to 9.7 kcal/mol, ensuring a moderate strength IMHB. The existence of an additional electron transfer is also observed in the case of PDPA-NH₂.H₂O and PDPA-NO₂.H₂O complexes. The extra stabilization of the PDPA-NH₂.H₂O complex is due to the (($\text{LP}\left(2\right)$O) → ${\sigma }_{\text{N}-H}^{*}$) interaction, which is associated with an E^CT of 3.4 kcal/mol. On the other hand, the interaction between the nonbonding orbitals of oxygen nitro group with antibonding orbitals of the O-H of water molecule (($\text{LP}\left(2\right)$O) → ${\sigma }_{\text{H}-O}^{*}$), which is associated with E^CT of 1.6 kcal/mol, destabilizes the PDPA-NO₂.H₂O complexes.

Additional understanding of the nature of the IMHB in PDPA-water complexes can be obtained by analyzing the AIM results of Bader’s theory (Bader 1991). Analysis of the BCP’s properties was usually utilized to estimate the hydrogen bond strength (Nguyen and Chandra 1998; Lamsabhi 2008; Safi 2016). The most relevant results topological properties, including the electron charge, ρ_BCP(r), computed at the BCP (3,−1) for the IMHB and its related parameters, including Laplacian (∇ ²ρ(r)), Lagrangian and Hamiltonian kinetic energies (G(r) and H(r), and the potential electron density (V(r), have been displayed in Table 3. The corresponding molecular graphs have been shown in Fig. 3. It was discovered that ρ_BCP(r) and ${\nabla }_{{\rho }_{BCP}}^2\left(r\right)$ values fall within the hydrogen bond range with averages of 0.0253 and 0.0816 a.u., respectively, indicating that the investigated IMHB belongs to medium interaction (Nguyen and Chandra 1998; Lamsabhi 2008). The largest ρ_BCP(r) (0.0924 a.u.) was reported for the PDPA-NH₂.H₂O complex, while the smallest value (0.0395 a.u.) was for the PDPA-NO₂.H₂O complex. Our results in Table 3 strongly affirm that substitution of the EDGs increases the ρ_BCP(r) and its related topological parameters, while substitution of EWGs decreases the ρ_BCP(r) and its related topological parameters. Furthermore, the IMHB energy and its bond order (BO) were evaluated as E_HB = -V(r)/2) (Espinosa et al., 1998), and BO= |V(r)|/G(r) and their results have been displayed in Table 3. Our results show that the average value of the BO is 0.91, with maximum and minimum BO values corresponding to PDPA-NH₂.H₂O and PDPA-NO₂.H₂O complexes, respectively. It is also found that E_HB values are ranged from 1.6 to 6.9 kcal/mol, which confirm the results of E_int and E^CT, in agreement with similar systems (Nguyen and Chandra 1998; Lamsabhi 2008; Safi 2016).

The NCI’s plot is useful in illustrating the correlation between strong directional attractions with the localized atom-atom contacts and the molecular division having weak interactions. The color-filled RDG isosurfaces and the scatter plots of the Hessian of the electron density, Sign(λ₂)ρ_, for some PDPA-water complexes have been shown in Fig. 4, while the other plots have been shown in Fig. SM4 of the supplementary materials. Examination of RDG isosurfaces indicate three different regions, which correspond to (i) weak interaction forces (green color) that occur between the atoms in the molecule, (ii) strong field interactions (red arrow) belong to steric effect of the aromatic rings and (iii) hydrogen bond interactions (blue color). A close examination of the 3D-Isosurface of color scaling of weak interactions diagram (NIC, Fig. 4 (right)) indicates that the interactions between LP(1)N₁ (proton acceptor) and the proton donor (hydrogen water molecule) are stronger in case of NH₂ and CH₃ derivatives compared to the others. Except for the PDPA-NO₂.H₂O complex, the presence of another IMHB field is indicated by the presence of blue circle (assigned by a blue arrow). A weak IMHB field was also observed between the oxygen nitro group (-NO₂ derivative) and the hydrogen water in case of PDPA-NO₂. Also, another IMHB region was observed between the oxygen water molecule and the amino hydrogen atom in the case of PPDPA-NH₂.H2O complex. These results agreed with NBO results as discussed above.

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Fig. 4.

RDG maps (left) and Scatter plots of RDG (a.u.) versus Sign(λ₂)ρ (a.u) (right) of some PDPA-water complexes, including PDPA-H.H₂O, PDPA-NH₂.H₂O, PDPA-CHO.H₂O, and PDPA-NO₂.H₂O. Note: Molecular graphs based on QTAIM are superimposed (left images, orange points, and yellow lines). QTAIM: quantum theory of atoms and molecules.

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