Understanding the Lack of Reactivity of 2,4-Dihydroxybenzaldehyde Towards the Biginelli Adduct Using Density Functional Theory Molecular Modeling

: The Biginelli reaction is a multicomponent reaction for obtaining dihydropyrimidinthiones quickly, with multiple substitution patterns. The reaction mechanism remains unclear. Three possible pathways proposed for the reaction are the iminium route, an enamine intermediate, and the Knoevenagel pathway. However, when thiourea was used, no theoretical calculations were reported. Thus, based on the literature, the iminium pathway was used to obtain evidence explaining the lack of reactivity of 2,4-dihydroxybenzaldehyde towards the Biginelli adduct, compared with 4-hydroxybenzaldehyde. This computational study, carried out using the B3LYP / 6-31 ++ G(d,p) level of theory, showed an increment of 150 kJ / mol in the activation energy of the slowest pathway, due to the presence of a hydroxyl group in position 2 (ortho) of the aromatic aldehyde, decreasing its reactivity. Natural bond orbital (NBO) calculations suggest that the determinant steps are simultaneous, i.e., the polarization of the carbonyl group and its corresponding protonation by the hydrogen of the SH fragment of the thiourea tautomer. The activation enthalpy values suggest that the nucleophile attack takes place later on the compound 2,4-dihydroxybenzaldehyde compared to 4-hydroxybenzaldehyde-TS, conﬁrming that the OH group in position 2 hinders the condensation reaction. The results show that the nucleophile attack corresponds to a late transition state for the compound 2,4-dihydroxybenzaldehyde, proving that the OH group in position 2 hinders the condensation reaction.


Introduction
Also known as Biginelli adducts, 3,4-Dihydropyrimidinones (DHPMs), are compounds derived from pyrimidine, in which carbon C-4 is entirely saturated, eliminating the characteristic aromaticity of Sigma-Aldrich Co. (Ciudad de Mexico, Mexico). Commercially available solvents (acetone, chloroform, and methanol) were used after purification; then, the products were dried according to standard procedures. In a flask fitted with a stirring system, the corresponding aldehyde (1.0 equiv.) was placed together with 3-oxobutanoic acid methyl ester (1.1 equiv.) and thiourea (1.1 equiv.). All products were obtained under microwave-assisted reactions on a CEM Discovery BechMate system with 100 W potency, and the temperature was 100 • C for each reaction in an open-vessel system. The reaction time was determined for each adduct by TLC. Each adduct was monitored every 5 min; the end of the reaction was established once the starting material was consumed and a total reaction yield was calculated. The solid product was vacuum filtered and washed with solvent.

Characterization of Compounds
Characterization of the compounds 1 H NMR, 13 C NMR, and DART MS was carried out using their melting point (mp), as follows (see

Theoretical Methods and Molecular Modeling
The potential energy surface (PES) of all species involved in the reactions of 4hydroxybenzaldehyde and 2,4-dihydroxybenzaldehyde with MAA and thiourea was studied employing DFT and transition state theory (TST). The interchange-correlation functional of Becke, Lee, Yang, and Parr, jointly basis set 6-31++G(2d,p), was employed by the use of Gaussian 09 for Linux [25]. Because the reactions were carried out free of solvents, they were modelled in the vacuum. The minimum energy surface (MES) was generated using the following convergence criterion: maximum displacement 0.0018 Å and maximum force: 0.00045 Hartree/Bohr. Three mechanisms were studied, iminium route, enamine intermediate route, and Knoevenagel pathway without solvent; however, only the mechanism with the lowest activation energy was analyzed herein.
The stationary points, minimum energy structure, and saddle point were verified employing frequency calculations, using statistical mechanics. Additionally, unimolecular and bimolecular transition states were obtained using the quadratic synchronous transit method (QST) with two (QST2) or three (QST3) structures. The calculation of intrinsic reaction coordinates (IRC) in all cases confirmed these structures. This method allowed the verification of first-order nature; it means that the reactant or reactants connect to products through a simple reaction coordinate. Thermodynamic magnitudes, such as zero-point energy (ZPE), absolutes entropies, S(T) enthalpy, and H(T), were obtained from quantum mechanics and statistic mechanics, using partition functions. The velocity coefficient, activation energy (Ea), activation enthalpy (ΔH ‡), and Gibbs energy (ΔG ‡) were

Theoretical Methods and Molecular Modeling
The potential energy surface (PES) of all species involved in the reactions of 4-hydroxybenzaldehyde and 2,4-dihydroxybenzaldehyde with MAA and thiourea was studied employing DFT and transition state theory (TST). The interchange-correlation functional of Becke, Lee, Yang, and Parr, jointly basis set 6-31++G(2d,p), was employed by the use of Gaussian 09 for Linux [25]. Because the reactions were carried out free of solvents, they were modelled in the vacuum. The minimum energy surface (MES) was generated using the following convergence criterion: maximum displacement 0.0018 Å and maximum force: 0.00045 Hartree/Bohr. Three mechanisms were studied, iminium route, enamine intermediate route, and Knoevenagel pathway without solvent; however, only the mechanism with the lowest activation energy was analyzed herein.
The stationary points, minimum energy structure, and saddle point were verified employing frequency calculations, using statistical mechanics. Additionally, unimolecular and bimolecular transition states were obtained using the quadratic synchronous transit method (QST) with two (QST2) or three (QST3) structures. The calculation of intrinsic reaction coordinates (IRC) in all cases confirmed these structures. This method allowed the verification of first-order nature; it means that the reactant or reactants connect to products through a simple reaction coordinate. Thermodynamic magnitudes, such as zero-point energy (ZPE), absolutes entropies, S(T) enthalpy, and H(T), were obtained from quantum mechanics and statistic mechanics, using partition functions. The velocity coefficient, activation energy (Ea), activation enthalpy (∆H ‡), and Gibbs energy (∆G ‡) were calculated from transition state theory (TST) assuming the transmission coefficient to be equal to 1, using equations previously described [26][27][28].

Transition State and Mechanism
Even when Biginelli reactions are one of the most used reactions in organic synthetic literature, the reaction mechanism remains unclear. Several attempts have been made to elucidate the mechanism. In this sense, three possible pathways proposed for the reaction of aromatic aldehyde, urea, and methyl acetoacetate: Iminium route, enamine-intermediate, and Knoevanagel pathway ( Figure 2) [13]. Some works have reported theoretical calculations that supplied sharp pieces of evidence that the iminium route is likely to occur when urea used as reagent [17,18,29,30]. However, no theoretical calculations had reported when thiourea was used. Thus, based on literature, the three pathway described above were studied to get some evidence that explained the unreactivity of 2,4-dihydroxybenzaldehyde to Biginelli adduct. Also, only the mechanism with the lowest activation energy was analyzed herein. The kinetic mechanism of iminium route studied for both compounds because of the structural similarity between 4-hydroxybenzaldehyde, 2,4-dihydroxybenzaldehyde. Figure 1 shows the reactions involved in the selected compounds. According to literature, the first step (1) in the iminium route is the nucleophilic addition of thiourea to aromatic aldehyde, followed by dehydration of the adduct formed in step 1; this compound (3) reacts with MAA to yield the 5 compounds, which produces a six-member ring and dehydrated to form the Biginelli adducts.

Transition State and Mechanism
Even when Biginelli reactions are one of the most used reactions in organic synthetic literature, the reaction mechanism remains unclear. Several attempts have been made to elucidate the mechanism. In this sense, three possible pathways proposed for the reaction of aromatic aldehyde, urea, and methyl acetoacetate: Iminium route, enamine-intermediate, and Knoevanagel pathway ( Figure 2) [13]. Some works have reported theoretical calculations that supplied sharp pieces of evidence that the iminium route is likely to occur when urea used as reagent [17,18,29,30]. However, no theoretical calculations had reported when thiourea was used. Thus, based on literature, the three pathway described above were studied to get some evidence that explained the unreactivity of 2,4dihydroxybenzaldehyde to Biginelli adduct. Also, only the mechanism with the lowest activation energy was analyzed herein. The kinetic mechanism of iminium route studied for both compounds because of the structural similarity between 4-hydroxybenzaldehyde, 2,4-dihydroxybenzaldehyde. Figure 1 shows the reactions involved in the selected compounds. According to literature, the first step (1) in the iminium route is the nucleophilic addition of thiourea to aromatic aldehyde, followed by dehydration of the adduct formed in step 1; this compound (3) reacts with MAA to yield the 5 compounds, which produces a six-member ring and dehydrated to form the Biginelli adducts.

Bond Order Analysis
The process of bond rupture and formation in the transition state for the slowest stage of the reaction in the iminium pathway was studied employing natural bond orbitals (NBOs) where Wiberg bond indexes were calculated using the NBO 5.0 program, which operates within the Gaussian 09W software package [31]. These parameters allow the yield of the relative change rate of the bond and the development percentage (%) of each bond, which indicates whether the coordinate is "early" or "late" in the slowest step (Equation (1)). It can be noted that these calculations were made only for the slowest stages in both cases.
where δBi is the relative variation of the bond index and defined by Equation (2): , The superscripts R , TS , and P represent the reactant, transition state, and products, respectively. The synchronicity parameter is used to explain whether a concerted reaction proceeds synchronously,

Bond Order Analysis
The process of bond rupture and formation in the transition state for the slowest stage of the reaction in the iminium pathway was studied employing natural bond orbitals (NBOs) where Wiberg bond indexes were calculated using the NBO 5.0 program, which operates within the Gaussian 09W software package [31]. These parameters allow the yield of the relative change rate of the bond and the development percentage (%) of each bond, which indicates whether the coordinate is "early" or "late" in the slowest step (Equation (1)). It can be noted that these calculations were made only for the slowest stages in both cases. %E where δBi is the relative variation of the bond index and defined by Equation (2): The superscripts R , TS , and P represent the reactant, transition state, and products, respectively. The synchronicity parameter is used to explain whether a concerted reaction proceeds synchronously, where all events have the same progress along the reaction coordinate (Sy = 1), or whether the reaction is entirely asynchronous (Sy = 0) (Equation (3)).

Chemistry
The methodology was used from the procedures reported by Stadler and Kappe [32] and Manhas et al. [33], with an environmentally friendly approach using microwave conditions, a solvent-free system, and low-cost acid catalyst [30]. The results are shown in Table 1.  [34]. None of the Lewis acids used in previous syntheses favored exclusively some of the reactions that developed, and presented different behaviors among them, although they presented the same by-products. The use of piperazine as a catalyst leading to the acquisition of a solid-phase product with a yield of 72% with a reaction time of 15 minutes. The spectroscopic analysis showed the presence of dienamine produced by the condensation between piperazine and methyl acetoacetate. This result led us to explore the reaction mechanism using theoretical methods (DFT) and molecular modeling. Table 2 shows the kinetic and thermodynamic activation parameters obtained at B3LYP/6-31++G(2d,p) for all reaction pathways in the iminium route; Scheme 1 reveals the free energy profile for each TS along with the reaction pathway. The reaction was studied in six (6) steps as follows: The first step corresponds to the condensation reaction between thiourea and the benzaldehyde. In this step, it was found that the tautomerization of thiourea had an equilibrium constant in the order of 10 −2 ; therefore, there is a significant population of thiol tautomer.

Thermodynamic Parameters for 4-Hydroxybenzaldehyde and 2,4-Dihydroxybenzaldehyde
Step 2 corresponds to the reaction of the thiol tautomer of the previous step with the benzaldehyde through six-member TS.
Step 3 corresponds to the elimination of water from the product obtained in the second step.
Step 4 corresponds to the keto-enol tautomerization reaction of MAA; this enol reacts in step five with the compound originated in step 3; subsequently, the compound generated in step 5 reacts through an intramolecular mechanism generating a cyclic compound (step 6) which finally lost a water molecule forming the DHPMT compound (1-5). Table 2. Kinetic and thermodynamic activation energies obtained in each stage of the Biginelli reaction, studied at the B3LYP/6-31++G(2d,p) level of theory for 4-hydroxybenzaldehyde and 2,4-dihydroxybenzaldehyde.
Step According to Scheme 1, there is an evident difference in the activation free energy of stage 2 observed for each compound. This stage is faster for the 4-hydroxybenzaldehyde compound than for 2,4-dihydroxybenzaldehyde. The high free energy value for this last compound (approximately 239 kJ/mol) means that, in practice, the condensed product was not obtained; therefore, as it is a determining stage compared to other stages, it prevents the formation of the final product. According to the structural similarity of these compounds, the results suggest that the presence of the OH group in the ortho position of the aldehyde hinders the introduction of thiourea for condensation to take place. The rest of the stages are more feasible for both compounds, with relatively low activation free energy in each case. According to Scheme 1, there is an evident difference in the activation free energy of stage 2 observed for each compound. This stage is faster for the 4-hydroxybenzaldehyde compound than for 2,4-dihydroxybenzaldehyde. The high free energy value for this last compound (approximately 239 kJ/mol) means that, in practice, the condensed product was not obtained; therefore, as it is a determining stage compared to other stages, it prevents the formation of the final product. According to the structural similarity of these compounds, the results suggest that the presence of the OH group in the ortho position of the aldehyde hinders the introduction of thiourea for condensation to take place. The rest of the stages are more feasible for both compounds, with relatively low activation free energy in each case. Figure 3 shows the structures of minimum energies for R, TS, and P for each case studied. The condensation reaction with thiourea occurs through a six-member cyclic transition state, of a concerted nature, unlike what is reported in the literature for the case of urea as the reagent, where it is considered that the reaction occurs in several stages. Within the level of theory used herein, it was found that the TS of six members is approximately 70 kcal/mol lower than the corresponding TS of 4 members. Processes 2019, 7, x FOR PEER REVIEW 8 of 12 Geometric parameters such as bond length, dihedral angles, and imaginary frequency associated with the transition vector in the TS are shown in Tables 3 and 4. In both cases, there is an increase in the distance of bonds C10-O11 and H21-S22, and a decrease in interatomic distances for bonds O11-H21 and N15-C1O. These results suggest that this reaction stage is carried out through polar-TS, where the hydrogen HS protonates to the carbonyl group of the benzaldehyde, which is polarized later to be attacked by the NH atom of the thiourea compound through a concerted process. The values of the dihedral angles in both cases suggest transition states far from planarity.  Geometric parameters such as bond length, dihedral angles, and imaginary frequency associated with the transition vector in the TS are shown in Tables 3 and 4. In both cases, there is an increase in the distance of bonds C10-O11 and H21-S22, and a decrease in interatomic distances for bonds O11-H21 and N15-C1O. These results suggest that this reaction stage is carried out through polar-TS, where the hydrogen HS protonates to the carbonyl group of the benzaldehyde, which is polarized later to be attacked by the NH atom of the thiourea compound through a concerted process. The values of the dihedral angles in both cases suggest transition states far from planarity. The distance N6-C1 in TS, which represents the nucleophilic attack on the reaction center for the 2,4-dihydroxybenzaldehyde compound, is more significant for the 4-hydroxybenzaldehyde which provides additional evidence that the OH group at position 2 of the aromatic ring prevents a fundamental approach of the nucleophile to the reaction center. The decrease in the polarity of the TS, when the 4-hydroxybenzaldehyde compares to 2,4-dihydroxybenzaldehyde compound, suggests that the presence of the OH group in position ortho decreases the polarization of the TS and therefore the rate of the reaction.

Reaction Mechanism and Geometric Parameters
The influence of the OH group on the reduction of TS polarization is supported by the values of the NBO charges shown in Table 5. The high dispersion of charges can be observed in atoms C11, O12, H22, and S23 from 4-hydroxybenzaldehyde. These results would confirm the hypothesis that the OH group in position 2 in 2,4-dihydroxybenzaldehyde prevents the nucleophile substitution by disadvantaging the polarization of the carbonyl group, the transfer of the proton to this group, and consequently, an increase of activation energy at this stage. Table 5. Wiberg bond indexes of R, TS, and P, for the Biginelli reaction of 4-hydroxybenzaldehyde and 2,4-dihydroxybenzaldehyde in gas phase obtained from B3LYP/6-31++G(2d,p). The Wiberg bond indexes were calculated with the purpose of studying the evolution of the reaction, along with the coordinates involved in product formation. The evolution of the bonds and the order of synchronicity are shown in Table 5 for each studied stage. In both reactions, the determining stages are the polarization of the H3-S4 bond and the protonation of the carbonyl group of the benzaldehyde substituted, respectively. However, the difference in the evolution of these bonds for both compounds is remarkable. In the case of the 4-hydroxybenzaldehyde, the partial formation of the O2-H3, and N6-C1 bonds, as well as the polarization of the C1-O2 bond during the TS is noteworthy. In contrast, the bond order for the 2,4-dihydroxybenzaldehyde compound is much smaller, confirming that the last TS interaction occurs subsequently and, therefore, the condensation reaction is slower.

4-hydroxybenzaldehyde
On the other hand, the synchronicity of the reaction confirms the decrease of the TS polarity in this case and, consequently, a lower reactivity.
The magnitude of the interaction between the respective aromatic compounds and the tautomer of thiourea can be estimated by observing the interactions between orbital boundaries of both compounds. Figure 4 shows the highest occupied molecular orbital (HOMO) for thiourea and the lowest occupied molecular orbital (LUMO) of the substituted benzaldehydes. It can see that the decrease in distance between C10 and N19 implies subsequent interaction among the OH group, with the N atom causing a strong electronic repulsion amid two electronegative groups; this secondary interaction an effective interaction, making the formation of the condensation product difficult.

Conclusions
The methodology used, free of solvents, allowed us to yield derivatives with reaction times lower than those reported in the literature. The non-reactivity of 2,4-dihydroxybenzaldehyde was evaluated experimentally using different catalysts and reaction conditions, without success; thus, to explain the lack of 2,4-dihydroxybenzaldehyde, molecular modeling was necessary. According to the thermodynamic activation parameters, stage 2, which corresponds to the condensation between thiourea (tautomer) and the corresponding aromatic aldehyde, is crucial for determining the reactivity of hydroxylated benzaldehydes towards the Biginelli reaction. The presence of a hydroxyl group in position two at the reaction center (carbonyl group) increases activation energy by approximately 150 kJ/mol; consequently, the reactivity of these compounds decreases. The NBO calculations suggest that the determining pathways are, simultaneously, the polarization of the carbonyl group and its corresponding protonation by hydrogen of the SH fragment of the thiourea tautomer. The results show that the nucleophile attack corresponds to a late transition state for the compound 2,4-dihydroxybenzaldehyde, proving that the OH group in position 2 hinders the condensation reaction.

Conclusions
The methodology used, free of solvents, allowed us to yield derivatives with reaction times lower than those reported in the literature. The non-reactivity of 2,4-dihydroxybenzaldehyde was evaluated experimentally using different catalysts and reaction conditions, without success; thus, to explain the lack of 2,4-dihydroxybenzaldehyde, molecular modeling was necessary. According to the thermodynamic activation parameters, stage 2, which corresponds to the condensation between thiourea (tautomer) and the corresponding aromatic aldehyde, is crucial for determining the reactivity of hydroxylated benzaldehydes towards the Biginelli reaction. The presence of a hydroxyl group in position two at the reaction center (carbonyl group) increases activation energy by approximately 150 kJ/mol; consequently, the reactivity of these compounds decreases. The NBO calculations suggest that the determining pathways are, simultaneously, the polarization of the carbonyl group and its corresponding protonation by hydrogen of the SH fragment of the thiourea tautomer. The results show that the nucleophile attack corresponds to a late transition state for the compound 2,4-dihydroxybenzaldehyde, proving that the OH group in position 2 hinders the condensation reaction.

Conflicts of Interest:
The authors declare no conflict of interest.