Full factorial optimization of α-aminophosphonates synthesis using diphenylphosphinic acid as efficient organocatalyst

Diphenylphosphinic acid was used as an efficient and simple catalyst for the synthesis of the α-aminophosphonates by multicomponent Kabachnik-Fields reaction in one pot of aromatic aldehyde, aniline and diethylphosphite. Three physicochemical factors including catalyst amount, reaction time and medium temperature were optimized using a full factorial experiment design (FFD). Additionally, a quadratic polynomial regression model was applied for the analysis of the experimental data at a confidence level of 95% with p-values < 0.05. The high signification effect of the reaction time and the medium temperature on the α-aminophosphonates synthesis were confirmed by the statistical analysis. Besides, the diphenylphosphinic acid amount showed an effect on the reaction yield. ANOVA exhibited that the coefficient determination of this model up to 99.25%. This eco-friendly procedure was extended for the preparation of series of the α-aminophosphonates in ethanol as green solvent, giving the desired products with high chemical yields up to 90%.

Due to the overwhelming development of the α-aminophosphonates in synthetic and biological fields, the efficient catalysts are widely requested for their preparation and increase their productivity. Unfortunately, few investigations were dedicated to developing this multicomponent reaction under green conditions; many reactions used costly catalysts, a stoichiometric amount of catalysts, long reaction time, and production of by-products. The last one can cause a considerable ecological problem related to their chemical properties. Therefore, the development of a new effective catalytic process using a low-cost and eco-friendly catalyst is considered a valuable approach to preparing these compounds.
In the continuation of our ongoing research interest for novel synthetic derivatives of organophosphorus compounds [38][39][40][41][42], herein, we report the successful employ of diphenylphosphinic acid as an efficient catalyst in multicomponent condensation reaction aromatic aldehyde, aniline, and diethylphosphite. However, the diphenylphosphinic acid was previously tested in multicomponent reaction and the desired product was obtained with 76% chemical yield [43]. Nevertheless, this catalytic process is sensitive to various operational parameters, including the catalyst amount, reaction time and medium temperature. Furthermore, studying the effect of each factor alone is considered a rather tedious and costly synthetic process (time, cost and energy depenses). For these reasons, we have opting to use the full factorial design for diminution of the experimental difficulties by the optimization of all the affecting parameters together at the same time to optimize the effectiveness of our proposed target under green conditions reaction.

Experimental design
A statistical approach was chosen to optimizing the synthesis reaction of α-aminophosphonates using diphenylphosphinic acid as a new and efficient catalyst under green conditions. A full factorial model of two levels with three operating factors was selected in a first approach (2 3 ), and each factor takes two values including a low and high level. Table 1 shows the selected operating factors and their levels in the experiment. All synthesis experiments were realized with three repetitions at the central point (C (P) ). The chemical yield (R%) was chosen as the answer (y) to achieve the optimal conditions of the synthesis reaction of α-aminophosphonates. Data analyzes were performed using statistical software (Minitab18), which allows us to determine the main effects and the interactions between the factors tested. In this study, the total number of experiments (E nbr ) performed was reported as follows: Here β is the number of operating factors, and C (p) symbolizes the number of center points used to test for quadratic terms between low and high levels; these central points were used to estimate the clarity and curving of the applied model. So, eleven (11) experiments were conducted in this investigation, including a combination of the factor levels studied. The results of the factorial design, given in terms of the theoretical response (y) and a regression model, can be expressed by Eq. (2): Here δ 0 is the result average value; δ 1 , δ 2 , and δ 3 correspond to the linear coefficients; and δ 12 , α 13 , δ 23 , and δ 123 interaction coefficients between the operating factors and η means the residual term. The symbols Q Cat , t and T° symbolize the tested variables in the model.
Unfortunately, the proline derivatives have shown lower reactivities, the use of the amido proline (E) and trifluoroacetoxy amido proline (F) furnish the α-aminophosphonate 4a with 38% and 11% yields, respectively (Table 2, entries 6 and 7). These results were probably due to the high acidity (E) and (F), exhibited by their electron-withdrawing effects. While a problem of the low solubility of the Schiff base (G) still the main cause for no progress of the reaction ( Table 2, entry 8).

Modeling and optimization of α-aminophosphonates synthesis
Full factorial optimization of the synthesis of α-aminophosphonates was performed as a matrix of 11 experiments under the influence of three operating factors with different levels, as shown in Table 3. The obtained results showed that the chemical yield (R % ) varied from 20 to 90%; this vast experimental zone can be seen as an improvement for this behavior as it could include the required optimal conditions. The normal probability plot, Pareto plot, surface plots, individual/interaction effects, and optimization plots of the fitted values were examined. Analysis of variance and p-value significance levels were estimated to verify the significance of the effect of operating factors on chemical yield. After discarding insignificant terms (i.e., Q cat *T°*t), the resulting model was reduced to determine all workable terms (Q cat, T° and t).
The ANOVA test was used to determine the significant effect of operating factors and their interactions on chemical yield (R%). Table 4 shows the F-ratio, p-value, sum of squares and mean square of each parameter. Data rank can be judged by its p-value, with values earlier than zero denoting greater significance. The p-value should be less than or equal to 0.05 to examine statistical significance with up to a 95% confidence level. In the case of the adopted model, the statistical treatment generated p-values and F-values (probability > F, indicating the insignificant probabilities), and therefore one could establish the significance of each variable. The variable under study could be more significant when the absolute F-value became greater and the p-value became lesser. Statistical testing of this model was performed using Fisher's statistical test or Student's t-test for analysis of variance. Accordingly, the quadratic regression shows that the assumed model had a very large F-value, on the order of 57.04, indicating a height signification of the model. The analysis of the experimental data indicates that more than 99% of the obtained data can be well predicted by the adopted model with an R 2 reaching 99.25% and R 2 adj of 97.51%, indicating that the terms included in recommended model have been measured remarkably enough to make satisfactory predictions.
This section aimed to define the optimal condition for maximum chemical yields of the synthesis of α-aminophosphonates. The correctness of the model was confirmed by comparing the experimental data as function of the predicted responses generated by the adopted model. The results obtained showed good agreement between the experimental chemical yields and the predicted values. The predicted response of the model was consistent with the experimental data. In this study, the influence of five independent factors on the response function was examined by a full factorial design to determine the optimal conditions. In this study, the influence of five independent factors on the response function was examined by a full factorial design to determine the optimal conditions. The mathematical relationship between five important variables and the response can be estimated by a quadratic polynomial equation (Eq. 3): The statistical data of the selected significant model terms are summarized in Table 3 to describe the chemical yields as a function of the operating parameters tested.

Main individual effects
The individual effects of each operational factor on the chemical yields of the synthesis of α-aminophosphonates under green conditions are summarized in Fig. 2. According to the results obtained, we found that the amount of catalyst (Q cat ) has a highly positive effect, which is essentially due to the good catalytic performance and high reactivity of diphenylphosphinic acid C, reinforced by its pKa values (2.30) as a Brønsted acid catalyst compared with the Pka of A and phosphoric acid B and D (3.3, 3.37 and 3.7). Also, the reaction time (t) and temperature (T°) have a medium positive effect, while the other terms were not significant, with a p-value higher than 0.05 as shown in the Pareto chart (Fig. 3) and Table 4. These results showed good agreement between the predicted and experimental values for the chemical yields as summarized in Table 3, the main reaction factors were the catalyst amount (Q cat ) with an effect of 33.50 > medium temperature effect (19.50) > the effect of reaction time (10.50).

Interaction effects between operating factors
The interaction effects between the investigated operating factors are shown in Fig. 4. The interactions between Q cat /T° and t/ Q cat were the most significant with a (3) (y)R% = 59, 25 + 5, 25t + 16, 75Q cat + 9, 75T • − 2, 25t * Q cat − 0, 25t * T • − 2, 75Q cat * T • + 30, 75CtPt negative effect of -5.5 and −4.5 respectively, which was confirmed by the non-parallel borders of the effects. Therefore, the interactions between reaction time (t) and medium temperature effect represented an insignificant effect, which was confirmed by limits, which were easily found at p values less than 0.05, this phenomenon can be explained by the absence of a synergetic effect between these operating factors.

Determination of optimum conditions
In our study, the main optimization goal was to determine the ideal conditions for the synthesis of α-aminophosphonates using diphenylphosphinic acid as an efficient organocatalyst. The request-target was the synthesis of α-aminophosphonates in their maximum values in a minimum time in order to obtain the high chemical yield. The obtained results indicated that the highest chemical yield R %Exp (90.00%) was achieved when each factor value was placed at the optimal level, which was in good agreement with the predicted chemical yield R %pred (93.51%). Fig. 5 exhibits the 3D surface plots of chemical yield evolution as a function of Qcat/T° and t /Qcat for the synthesis of α-aminophosphonates. As can be observed, the chemical yields (R%) highly increase with the increasing amount of diphenylphosphinic acid, at the same time, this phenomenon can be explained by the interaction between the effects of the studied factors. The best chemical yields of the α-aminophosphonate synthesis were obtained under optimum conditions are shown in Table 5. It is anticipated that this behavior may open the way to applying this model for the synthesis of a matrix of MCRs on a series of variously substituted aromatic aldehydes and anilines with electron-withdrawing and electron-donating groups.

Applied of the optimal conditions
Based on the optimal conditions of the factorial experiments study, we have investigated the effectiveness and limitations of the MCRs on a series of variously substituted aromatic aldehydes and anilines with electron-withdrawing and electron-donating groups. The reaction proceeds in the presence of diphenylphosphinic acid (10 mol.%) in ethanol at 40 °C within 30 min. The results summarized in Table 6 showed the high efficiency of diphenylphosphinic acid as Brønsted catalyst in Kabachnik-Fields reaction. The use of aniline with benzaldehyde, 3-methoxybenzaldehyde, and 4-nitrobenzaldehyde leads to the α-aminophosphonates 4a, 4b and 4c with excellent chemical yields (up to 90%). Similarly in the presence of toluidine with 1-naphtylbenzaldehyde, dioxobenzaldehyde and 4-fluorobenzldehyde, the 4d, 4e and 4f are obtained in excellent yields (90%, 91% and 80%). The methyl-trifluoro aniline partially decreases the nucleophilicity of aniline giving the desired products 4g, 4h and 4i with 88, 78 and 87%.
According to the obtained results and based on our previous work, we propose a mechanism for the synthesis of α-aminophosphonates via multicomponent condensation reaction in one pot of aromatic aldehyde, amine and diethylphosphite catalyzed by a diphenylphosphinic acid. It was reasonably supposed that in the first step the catalyst plays a crucial role to activate electrophilically the carbonyl carbon of the aldehyde which promotes the nucleophilic attack by the amine to form the imine intermediate. Because of its formation is a reversible process, it is trapped immediately by the catalyst which prevents hydrolysis of the imine substrate to the amine and aldehyde by water formed. The coordination of catalyst active the imine and renders it more electrophile for facilitate the nucleophilic attack of the diethylphosphite which leads to the formation of the desired α-aminophosphonates with simultaneous release of the catalyst (Scheme 1).

Conclusions
In conclusion, we have described a novel and highly efficient protocol for the synthesis of α-aminophosphonates via multicomponent condensation reaction under green conditions, using diphenylphosphinic acid as Bronsted acid and eco-compatible organocatalyst. The full factorial experiment design was successfully used to establish the optimal conditions for optimizing the reaction yield. The regression analysis showed a good correlation between the obtained reaction yields (R% Exp ) and predicted yields (R% Pred ), which confirmed the validity and practicability of the model, with high and significant R 2 values up to 99.25%. The statistic treatment indicated that the diphenylphosphonic acid amount, reaction time, and medium temperature have high signification positive effects on the α-aminophosphonates synthesis. The application of the optimization conditions on a series of variously substituted aromatic aldehydes and aromatic amines with electron-withdrawing and electron-donating groups showed the effectiveness of this catalyst gave the α-aminophosphonates in chemical yields.