Evaluation of Acidity Constants and Evolution of Electronic Features of Phenol Derivatives in Different Compositions of Methanol/Water Mixture

is work was devoted to evaluation of acidity constants of 28 phenol derivatives in 11 different compositions of methanol/water solvent mixtures. e �nsager reaction �eld model was applied to any molecule of phenol derivatives dissolved in binary mixture of methanol/water, and the quantum chemical descriptors of the solute were calculated. Multiple linear regression was used to perform the reliable QSPR models in order to predict the acidity constants of the solutes. It was explored that the solvation of phenol derivatives in solvent of binary mixture of methanol/water shows a different behavior as the composition of methanol varies. Four different mechanisms proposed for solvation in 0–100 volume percent of methanol solvent. It was seen that the dipoledipole interactions increase as the amount of methanol increases in solvent mixture, which implies the contribution of highly negative oxygens of methanol on hydrogen bondings between solute and solvent cavity. e orbital energies are a major electronic descriptor on solvation processes.is proposes that the charge exchange between frontier orbital energies of anions and the solvent molecules is the major event occurring in solution in order to stabilize the produced anions.


Introduction
It is well known that the toxicity and pharmaceutical property of an organic molecule strongly depend on its acidic character [1,2].e acidity constants play fundamental roles in many other analytical procedures such as solvent extraction, complexometry, and ion transport.erefore, the knowledge about acidic properties of chemical substances could elucidate their toxicities, pharmaceutical activities, and analytical roles.Some of the fundamental theories of classical physical organic chemistry are based on how an acid-base equilibrium could be affected by changing the chemical structures of the molecules involved in the reaction [3].Constructing quantitative structure-activity/property relationship (QSAR/QSPR) techniques are of promising computational tools for predicting acidity constants of new and even nonsynthesized chemicals [4].e QSPR techniques relate chemical properties of a class of compounds to their encoded molecular structure parameters named molecular descriptors [5,6].e chemical properties of interest could be boiling and melting points, acid-base behavior, chromatographic retention indices, partitioning phenomena, reaction kinetics and equilibriums, and so on.
Molecular descriptors play fundamental roles in the QSAR/QSPR studies.Finding new molecular descriptors with higher correlation toward activity/property is in the frontier of QSAR/QSPR researches.In this regard, electronic descriptors obtained from quantum chemical calculations have found major popularity and there is a challenge between calculation complexity and accuracy in order to select the quantum chemical calculation methods for example, semiempirical and ab initio [7].
Phenol derivatives have widely been concerned with the medicinal issues.ey are widely used as general antiseptics in medical and dental practice, agriculture, cosmetics, and food industry due to their potent fungicide, bactericide, and antioxidant and anti-in�ammatory properties [8][9][10][11][12][13][14][15].ey are also used as potent vanilloid receptor agonists and in medical practice as an expectorant [16].Nonetheless, the exact mechanism of their interactions in body still remains unclear.Herein, attempts were made to conduct a quantum mechanical study on electronic interactions between some phenol derivatives and their body-like environment.In this regard, the variation of acidity constants of 28 phenol derivatives in solvent of methanol/water as function of electronic descriptors would be monitored.Informative electronic features, which might be helpful in the understanding of their biological activities mechanism in the body, would be explored.
In this paper, a QSPR study was conducted on acidity constants of 28 phenol derivatives in many different compositions of methanol/water solvent.ree different categories of electronic descriptors including charges, dipoles, and orbital energies were applied to construct the QSAR models.In order to explore the informative electronic descriptors determining the acidity of phenol derivatives the evolution of electronic descriptors governing the acidity of the phenol derivatives in methanol/water against the solvent composition were monitored.In this regard, quantum descriptors of any individual molecule in solvent were calculated.Multiple linear regression (MLR) analysis was employed to obtain the structure-property relationships between the acidity constants and molecular quantum descriptors.

Method
A Pentium IV personal computer with windows XP operating system was used.All molecular structures (Z-matrix) were built and initially optimized in HyperChem version 6.03 (Hypercube, Inc.).For full optimization of molecular structures and calculation of quantum chemical descriptors, Gaussian 98 soware was used.Variables selection was performed by using SPSS soware version 11.5.0 (SPSS Inc., 2001) by employing the multiple linear regression method.e electronic properties of several phenol derivatives (Table 1) were used in binary mixtures of methanol/water as solvents.eir corresponding experimental acidity constants were taken from [17][18][19].All molecular structures were built in Hyperchem Soware for Structural Chemistry.Gaussian 98 was operated to optimize the chemical structures in the solvent.e chemical structures were optimized with 6-31G basis set for all atoms at HF level of theory.e idea which states that the effect of solvents on the energies of organic compounds oen is reasonably related to the dielectric constant of the solvent, which was used quantitatively in the work of some researchers [20,21], was followed [21].In this manner �nsager reaction �eld model in which solute is placed in a cavity surrounded by a continuous dielectric constant medium was applied [21].
e average value of the dielectric constants of the solvent mixture was used as an input in order to account for the solvent effects on the molecular structures.No molecular symmetry constraint was applied; rather full optimization of all bond lengths and angles was carried out at the level of HF/6-31G.e calculated electronic descriptors for each molecule are classi�ed into three categories of charges, dipoles, and orbital energies.In Table 2 a list of detailed electronic descriptors used in this work can be found.In this study 18 electronic descriptors have been used to characterize the solvation of phenol derivatives in methanol/water solvent.ese electronic descriptors were used to describe stability, reactivity, chemical potential, and other related properties of the molecules [22][23][24].
For each molecule 18 electronic descriptors were calculated.In addition, the amount of solvent components (volume percent of methanol in water), VP, and the value of dielectric constant DC were used [25].erefore, the descriptor data matrix of each molecule composed of 20 columns.

Results and Discussion
e twenty-eight chemical structures of phenol derivatives (Table 1) in eleven different volume percents of methanol/water mixtures (308 entries in overall) were optimized and their corresponding electronic descriptors were calculated.e preliminary regression analysis made in this work indicates that the data set of 308 entries need to be divided (split) into four sets.In other words, the solvation processes of phenol derivatives in different solvent mixtures of methanol/water obey four different mechanisms (Figure 1).It was found that the 28 molecules of phenol derivatives in 0-40, 50-60, 70-90, and 100 volume percent (hereaer known as �rst, second, third, and fourth series, resp.) of methanol in methanol/water solvent show totally different solvation behaviors.
In this work, the most important variables in any of the mentioned series are selected by a stepwise selection procedure, which combines the forward selection and backward elimination approaches.is procedure considers �rst the descriptive variable most highly correlated with the response.If the inclusion of this variable results in a signi�cant improvement of the regression model, evaluated with an overall F-test, it is retained and the selection continues.In a next step the variable that gives the largest signi�cant decrease of the regression sum of squares, evaluated with a partial F-test is added.Aer each forward selection step a backward elimination step is performed.In this step a partial F-test for the variables, already in the equation, is carried out.If a variable is no longer contributing signi�cantly to the regression model, it is removed.e procedure stops at the moment that no variables ful�ll the requirements anymore to be removed or entered.Aer this selection procedure classical MLR can be applied on the retained variables to build a predictive model.e stepwise variable selection-based MLR analysis was used to obtain the structure-property relationships for the any of four solution series.In Table 3, the summary of obtained models was shown.e high  2 ,  2  LOO ,  2 LMO values of any model and their closeness to each other explain the predictive power and stability of the proposed models as well.e models show that the selected molecular structural parameters cover all the three different electronic classes of the suggested descriptors including local charges, dipoles, and orbital energies.
e widely used approach to establish the robustness of the resulting models is called Y-randomization [26].e values of   were randomly attributed to the molecules and the MLR modeling was repeated with the randomized data.e randomization was repeated one hundred times for any of the �rst, second, third, and fourth series, separately, and their corresponding maximum values obtained for the  2 were 0.087, 0.124, 0.126, and 0.213, respectively.e T 3: e summary of QSAR models of phenol derivatives in 0-100 volume percents of methanol in solvent mixture obtained by using quantum descriptors.

Model no.
Volume LOO is the leave-one-out cross-validated square of correlation coefficient.e  2  LMO is the leave-many-out cross-validated square of correlation coefficient.
statistical qualities of these models are much lower than the original ones (Table 3).erfore, it can be considered that our models are reasonable.ese models were used to reproduce the acidity constants of the phenol derivatives in four different series of methanol/water mixtures.Results are shown in Table 1.
Although the experimental values of the acidity constants cover a divers range from   = 3.51 through   = 14.9 values, it seems that our proposed models have a good promising on predicting acidity constants (see Table 1).
Concerning the proposed models for the all series, the selected variables are hardness HD, the ratio of gap of energy between highest occupied (HOMO) and lowest unoccupied molecular orbital (LUMO) to HOMO value HLG/HOMO, square value of total dipole moment of molecule  2 , volume percent of methanol in solvent mixtures VP, root mean square value of local charges  rms , sum of local negative charges on the molecule SNC, the LUMO to HOMO ratio LUMO/HOMO, root mean square value of dipole moment  rms , and the gap of energy between highest occupied and lowest unoccupied molecular orbital HLG, which are calculated based on procedure was stated in our previous work [27].
In order to inspect the relative importance and contribution of each descriptors in the constructed QSAR models, the value of mean effect (MF) was calculated for each descriptors by the following equation and it is shown in Figure 2: where MF  is the mean effect for considered descriptor ,   is the coefficient of descriptor ,   denotes the value of descriptor  of molecule ,  is the number of descriptors in the model, and  is the number of molecules in the data sets.e value of mean effect shows the relative contribution of each descriptor on the predicted response.
From Figure 2, It can be estimated that in the �rst series (0-40%) although the charges (SNC,  rms ) and dipole ( 2 ) are involved on evaluation of acidity, orbital energies (HD, HLG/HOMO) show signi�cant contribution on proton dissociation.In the second series (50-60%), dipole interactions show higher contribution than the �rst one, but still the role of orbital energies (HD, LUMO/HOMO) in solvation processes is dominant.e third series (70-90%) prefer to govern the solvation through dipole-dipole interaction than orbital energies.In the last series (100%), charges and dipoles do not show any contribution on acidity of phenol derivatives whereas the only involved descriptor is orbital energies descriptor of HLG.e fact that the orbital energies have major impact on acidity of phenol derivatives in all ratio of methanol/water mixtures might be due to the relation of orbital energies with the binding energies as the chemical binding takes place (Figure 3).It is believed that chemical bindings lead to charge transfer between solvent and produced anions.In other words, solvent tries to stabilize the anions through the charge transfer from their frontier orbital energies.is �nding is along with the simple model proposed by Sourav et al., in which they demonstrate that the hardness is related to the binding energy of the molecule being formed in solution and their corresponding molecular cations and anions as well [28].A close look at Figure 3 reveals that the contribution of dipole interactions in solvation of phenol derivatives increases as the amount of methanol in solvent increases.But, no dipole interactions can be seen to show contribution on proton dissociation when the solvent is pure methanol.It is hard to give an exact explanation on such a variation of dipole-dipole interactions with the solvent composition, but it may imply the contribution of highly negative oxygens of methanol on hydrogen bondings between solute and solvent cavity through strong dipoledipole interactions.

Conclusion
Considering the electronic effects of solvent of methanol/ water mixtures, a variety of quantum chemical descriptors including electrical charges, dipoles, and orbital energies in solvent for the whole molecule of any phenol derivatives were calculated.Using multiple linear regression method, four proper models were established to predict the acidity constants of phenol derivatives in solvent of methanol/water within an acceptable range of statistical parameters of the correlation.It was revealed that the solvation of phenol derivatives in solvent of binary mixture of methanol/water show different behavior as the composition of methanol varies.Four different mechanisms proposed for methanol composition of 0-40, 50-60, 70-90, and 100 volume percent of methanol in solvent.It was found that the orbital energies are major electronic descriptor on solvation processes proposing charge transfer from frontier orbital energies of anions toward the solvent molecules in solvent cavity to stabilize the produced anions.Also, it was shown that the dipole-dipole interactions increase as the amount of methanol increases in solvent mixture with nonzero volume percent of water.It seems that the dipole-dipole interaction which is likely to be due to hydrogen bondings between solute and solvent cavity increases with the amount of methanol in solvent composition.

F 1 :
Plot of leave-many-out cross-validation acidity of phenol derivatives in 11 compositions of methanol/water solvent.Analysis reveals four different categories of their solvation process in the solvent.

F 2 :
e mean effect percent of contributed descriptors in four different series of solvation of phenol derivatives in methanol/water solvent.
2 is the square of correlation coefficient for calibration.c F is the Fischer value of the correlation.
a N is the number of molecules in data set.b d  2 LMO : Correlation coefficients of leave-many-out cross-validations   : Acidity constant MF  : Mean effect value for considered descriptor of    : Coefficient of descriptor    : e value of descriptor  of molecule .Number of descriptors in the model : Number of molecules in the data set. Superscripts: