THEORETICAL STUDY (AB INITIO AND DFT METHODS) ON ACIDIC DISSOCIATION CONSTANT OF XYLENOL ORANGE IN AQUEOUS SOLUTION

Analytical measurement of materials requires exact knowledge of their acid dissociation constant (pKa) values. In recent years, quantum mechanical calculations have been extensively used to study of acidities in the aqueous solutions and the results were compared with the experimental values. In this study, a theoretical study was carried out on xylenol orange (in water solution) by ab initio method. We calculated the pKa values of xylenol orange in water, using high-level ab initio (PM3), DFT (HF, B3LYP/6-31+G(d)) and SCRF methods. The experimental determination of these values (pKa,s) is a challenge because xylenol orange has a low solubility in water. We considered several ionization reactions and equilibriums in water that constitute the indispensable theoretical basis to calculate the pKa values of xylenol orange. The results show that the calculated pKa values have a comparable agreement with the experimentally determined pKa values. Therefore, this method can be used to predict such properties for indicators, drugs and other important molecules.


INTRODUCTION
The pM indicator is a visual one which can act as a chelating agent to give a dye-metal complex for end point detection in the complexometric analyses. It is different from its dye, in color, and also has a low stability constant than the chelate-metal complex. Over 200 organic compounds form colored chelates with ions in a pM range that is unique to the cation and the dye selected. To be useful, the dye-metal chelates will usually be visible at 10 -6 to 10 -7 M concentration. Many of these indicators also have the typical properties of acid-base indicators and the color changes are the result of the displacement of the H + by a metal ion [1]. The xylenol orange (3,3′-bis[N,Nbis(carboxymethyl)aminomethyl]-ocresolsulfonephthalein) is a weak polybasic acid which belongs to triphenylmethane dyes ( Figure 1). It is an excellent complexometric indicator and potentiometric reagent for determination of many metal ions which is used in analytical chemistry with bind to metal cations at both their amino and acidic groups [2,3]. It can be represented by the symbolic formula H 6 L. It shows the presence of six ionizable hydrogens in the aqueous solutions. The six possible forms of xylenol orange (XO) are distributed in the pH range from 2 to 12 [2]. Due to the existence of more than one chelating system and the various acidic and basic properties of the XO molecule, which can form various complexes, the investigation on this system can be difficult. XO is used as an indicator, with color change from lemon to yellow, for determination of Bi and Th at pH range 1 to 3, Pb and Zn at pH range 4 to 5 and also Cd and Hg at pH range 5 to 6 [1]. It is also introduced (in form of Al-XO complex) as a colored reagent for determining trace amount of fluoride. This method is based on the 128 decolorization of a complex of Al(III) with xylenol orange as an ultra [4].
It must be pointed out that the acid equilibrium constants (K most important molecular properties and has received considerable attention for understanding many chemical and biochemical processes. It depends on proton transfer and interprets the functional mechanism of ionizable groups in a protein at a molecular level. Accurate p are also important for understanding reaction mechanisms that do not involve proton transfer. For example, thermodynamic cycles that use p bond dissociation energies of metal hydrides and other compounds. Thes used for elucidating reaction mechanisms that involve hydrogen atom transfer/proton electron transfer [5]. For these reasons, there is a strong interest for the development of reliable methods for pK a prediction.
There are several experimental methods, like capillary electrophoresis [6] potentiometric titration [7], bromatographic [8] and IR, NMR or UV on components acidities. In addition to these experimental methods, both ab initio empirical levels of theory have been extensively employed to the study of acidities and the results have been compared with the experimental values. Therefore, there are some studies dealing with the acid-base properties of compounds in aqueous s 13]. Computational chemistry can be valuable tool for evaluating the right sequence of deprotonation. This explains the many attempts to develop reliable methods for the calculation of accurate absolute or relative p In this paper, a theoretical study carried out on the p initio and density functional theory (DFT) methods. Hartree functional geometry optimizations were performed with the Gaussian were reoptimized at the B3LYP (the Becke's three Yang-Parr correlation functional) type of DFT by using the basis set 6 geometries were employed for calculating the s reaction filed (SCRF) level [18]. pK a = ∆G 0 /2.303RT formula. decolorization of a complex of Al(III) with xylenol orange as an ultra-sensitive colored reagent It must be pointed out that the acid equilibrium constants (K a , pK a = -log K a ) is one of the properties and has received considerable attention for understanding many chemical and biochemical processes. It depends on proton transfer and interprets the functional mechanism of ionizable groups in a protein at a molecular level. Accurate pK also important for understanding reaction mechanisms that do not involve proton transfer. For example, thermodynamic cycles that use pK a data, are used to determine the hydricities and bond dissociation energies of metal hydrides and other compounds. These critical data can be used for elucidating reaction mechanisms that involve hydrogen atom transfer/proton-coupled electron transfer [5]. For these reasons, there is a strong interest for the development of reliable everal experimental methods, like capillary electrophoresis [6] potentiometric [8] and IR, NMR or UV-Visible spectrometric [9][10][11], for studying on components acidities. In addition to these experimental methods, both ab initio and semi empirical levels of theory have been extensively employed to the study of acidities and the results have been compared with the experimental values. Therefore, there are some studies base properties of compounds in aqueous solutions and gas phases 13]. Computational chemistry can be valuable tool for evaluating the right sequence of deprotonation. This explains the many attempts to develop reliable methods for the calculation of accurate absolute or relative pK a ,s [14][15][16][17].
In this paper, a theoretical study carried out on the pK a of xylenol orange, in water, by ab initio and density functional theory (DFT) methods. Hartree-Fock (HF), ab initio and density functional geometry optimizations were performed with the Gaussian 09 program. The results were reoptimized at the B3LYP (the Becke's three-parameter exchange functional and the Lee Parr correlation functional) type of DFT by using the basis set 6-31+G(d). The ab initio geometries were employed for calculating the solvation free energies at the self-consistent reaction filed (SCRF) level [18]. ∆G 0 was calculated and employed for determination of p ) is one of the properties and has received considerable attention for understanding many chemical and biochemical processes. It depends on proton transfer and interprets the K a data also important for understanding reaction mechanisms that do not involve proton transfer. data, are used to determine the hydricities and e critical data can be coupled electron transfer [5]. For these reasons, there is a strong interest for the development of reliable everal experimental methods, like capillary electrophoresis [6] potentiometric 11], for studying and semiempirical levels of theory have been extensively employed to the study of acidities and the results have been compared with the experimental values. Therefore, there are some studies olutions and gas phases [12,13]. Computational chemistry can be valuable tool for evaluating the right sequence of deprotonation. This explains the many attempts to develop reliable methods for the calculation of xylenol orange, in water, by ab Fock (HF), ab initio and density 09 program. The results parameter exchange functional and the Lee-31+G(d). The ab initio consistent was calculated and employed for determination of pK a by 09 system in the framework of density functional theory utilizing different combinations of functional and basis sets. By the semiempirical PM3 method includes in the program Hyper Chem version 7.0, the initial f the different conformers of neutral xylenol orange, its anions and cations were modeled. Hartree-Fock ab initio and density functional geometry optimizations were performed with the Gaussian 09 program. The optimizations were done using HF/6-31+G(d) method. The results were reoptimized at the B3LYP type of Density Functional Theory by using the basis set 6-31+G(d). The ab initio geometries were employed in calculating the solvation free energies at the mentioned basis set (Table 1).

RESULTS AND DISCUSSION
Xylenol orange is a triphenylmethane dye. It is well-known that the xylenol orange, in water, loses three protons and generates H 9 L 3+ . The H 9 L 3+ form has tendency to lose nine acidic hydrogens. For H 9 L 3+ , a proton can be lost from four different groups to give different ionized species. These groups are including the carboxyl group, ammonium group, hydroxyl group and sulfonate (SO 3 H) group. The proton losing from the sulfonate group is more probable than the other groups. The chemical interpretation of the changes is not straightforward. It is predicted that the proton of sulfonyl has the most acidic property. The calculations of microscopic constants indicate that the first and second pK a ,s correspond to remove the proton of sulfonyl and hydroxyl groups, respectively. The third, fourth, fifth and sixth pK a, s correspond to remove the protons of the four carboxyl groups. The seventh pK a belongs to remove of the next hydroxyl group and finally the eighth and ninth pK a ,s correspond to remove the protons of the two ammonium groups. It can be exactly approved by NMR spectroscopy [3].
The different models of molecules (zwitterions and unzwitterions) were investigated by the G09 program and different reactions including cationic, neutral, and anionic species were tested. But some of these reactions were not further considered because the estimated error in its acidic dissociation constants was unacceptable. Suitable models finally were chosen for the studied systems and the calculated values of the acidic dissociation constants for species are listed in Table 2.  The acidic dissociation constants of xylenol orange have been determined using the potentiometric technique. The method of determining acidic dissociation constants was previously described, and its values were used in this work. These values are listed in Table 2 together with the calculated values using B3LYP type of Density Functional Theory by using the basis set 6-31+G(d) [3].

Solvent-solute interactions
Ionic product of water. It is well-known that all aqueous solutions contain hydrogen (H + ) and hydroxyl (OH -) ions. In pure water, these ions are derived completely from the ionization of the water molecules as shown in the following equation: The H + ion is hydrated by water molecules and appears as H 3 O + . Therefore, the autoprotolysis of water molecules is better represented by the bellow reaction: Taking into account that water is only slightly dissociated, and also to simplify the discussion, we shall make the approximations of replacing the activities in acidity constants by the numerical values of the molar concentrations. Consequently: At T = 298.15 K, K w = 1.008×10 -14 . It shows that only a few of the water molecules are ionized [19]. Equations 2 and 3 are more used in studies of acid-base equilibria in aqueous media. On the other hand, the solvation of anions is effective in protic solvents where hydrogen bonds may be formed between the proton of the solvent and the lone pairs of electrons of the anion [20,21]. The total energies of the single and solvated OHions have been calculated in water at the B3LYP/6-31+ G(d) level of theory, using Tomasi's model. Considering these facts and to provide a more satisfactory representation of the protolysis of water, the reaction has been shown as follows: The above reaction shows that both H + and OHions are hydrated with one water molecule. Moreover, indicating with K N the equilibrium constant of the reaction of equation 5 and taking into account equations 2 and 3, it is inferred that [11]: Where, [H 2 O] is the molar concentration of water at 298.15K. The total energies of xylenol orange species (cationic, neutral, and anionic) were calculated in water at the B3LYP/6-31+G(d) level of the theory. Table 1 summarizes the variations of the total energy (kJ·mol -1 ) of the species.

First ionization constant of xylenol orange (XO)
As it has been mentioned, the first proton has lost from the sulphonyl group in XO and it suffers a reaction of partial neutralization as follows: In this reaction, H 9 L 3+ and H 8 L 2+ are the cation forms of xylenol orange. This reaction is characterized by an equilibrium constant, K c1 , which theoretically were determined. By combining equations 6 and 4, we obtained the reaction of equation 7 which defines the first ionization constant of xylenol orange (K a1 ) and which considers the solvation of the H 9 L 3+ : It is evident that: The above equations were used to theoretically determine the value of the first ionization constant of xylenol orange in water.
The formation of H 8 L 2+ implies that the electronic density of the O 72 atom (q = -0.673) decreases, in absolute value, compared with the O 72 atom of the H 9 L 3+ (q = -0.780). It shows the first deprotonation of XO.

Second ionization constant of xylenol orange
In second stage of ionization of xylenol orange, the H 8 L 2+ losses proton from the hydroxyl agent and changes to H 7 L + by a total neutralization as follows: In the above equation, H 8 L 2+ and H 7 L + represent the xylenol orange cations with two and one positive charges, respectively. The reaction of eq. 9 is characterized by another equilibrium constant, K C2 , which was also theoretically determined. By combining equations 2 and 9, the second ionization constant of xylenol orange were obtained as the bellow: The equilibrium constant K a2 that characterizes the above reaction, are: Equation 11 was used to obtain the value of the second ionization constant of xylenol orange in water. The formation of the H 7 L + implies that the electronic density of the O 32 atom (q = -0.583) decreases, in absolute value, compared with the O 32 atom of the H 8 L 2+ (q = -0.614). It is evidence for the second deprotonation of XO.

Third ionization constant of xylenol orange
In the above reaction, H 7 L + represents the xylenol orange with one positive charge and H 6 L represents the natural xylenol orange molecule. The reaction of equation 12 is characterized by another equilibrium constant, K C3 , which was also theoretically determined. By combining equations 2 and 12, the third ionization constant of xylenol orange were obtained as the bellow: The equilibrium constant, K a3, that characterizes the above reaction, are: Equation 14 was used to obtain the value of the third ionization constant of xylenol orange in water. At this step, the proton is lost from O 60 of carboxyl group. The formation of the H 6 L implies that the electronic density of the O 60 atom (q = -0.557) increases notably (in absolute value) compared with the O 60 atom of the H 7 L + (q = -0.0177). It shows the third deprotonation of XO.

Fourth ionization constant of xylenol orange
There is selected that the H 6 L suffers total neutralization as the bellow: In the above reaction, H 6 L represents the natural xylenol orange molecule and H 5 Lrepresents xylenol orange anion with one negative charge. The reaction of equation 15 is characterized by another equilibrium constant, K C4 , which was also theoretically determined. By combining equations 2 and 15, the forth ionization constant of xylenol orange, in water, was obtained: The equilibrium constant, K a4 , that characterizes the above reaction, are: Also the pK a4 value of xylenol orange was theoretically calculated (pK a4 = 1.12) ( Table 2). It can be seen that the theoretical pK a4 value is relatively comparable with the experimentally determined pK a4 (pK a4 = 1.15) [3].

Fifth ionization constant of xylenol orange
The fifth pK a value of XO in aqueous solution can be calculated using the following protontransfer reaction: In this reaction, H 5 Land H 4 L 2are the xylenol orange anions with one and two negative charges, respectively. This reaction is characterized by an equilibrium constant, K c5 , which were theoretically determined. By combining equations 18 and 5, we obtained the reaction of equation 19 which defines the fifth ionization constant of xylenol orange, K a5 : It is evident that: The above equations were used to theoretically determine the value of the fifth ionization constant of xylenol orange in water. At this step, proton is lost from O 43 atom of another carboxyl group, obviously. The formation of the H 4 L 2implies that the electronic density of the O 43 atom (q = -0.665) increases notably (in absolute value) compared with the O 43 atom of the H 5 L -(q = -0.0450). It shows the fifth deprotonation of XO.
The pK a5 value of xylenol orange was theoretically obtained (pK a5 = 2.53). Table 2 shows that the theoretically obtained pK a5 value of xylenol orange is relatively comparable with the experimental pK a5 value (pK a5 = 2.58) [3].

Sixth ionization constant of xylenol orange
There is selected that the H 4 L 2suffers total neutralization as the bellow: In the above reaction, H 4 L 2and H 3 L 3represent the xylenol orange anions with two and three negative charges, respectively. The reaction which was described in equation 21 is characterized by another equilibrium constant, K C6 , which was also theoretically determined. Combining equations 2 and 21 results the sixth ionization constant of xylenol orange, in water: The equilibrium constant, K a6 , that characterizes the above reaction, are: Equation 23 was used to obtain the value of the sixth ionization constant of xylenol orange in water. At this step proton is lost from O 58 atom of the latest carboxyl group. The formation of the H 3 L 3implies that the electronic density of the O 58 atom (q = -0.706) increases notably (in absolute value) compared with the O 58 atom of the H 4 L 2-(q = -0.615). It is evidence for sixth deprotonation of XO.
At this step, proton is lost from N 35 atom. The formation of the HL 5implies that the electronic density of the N 35 atom (q = 0.146) increases, in absolute value, compared with the N 35 atom of the H 2 L 4-(q = -0.391). It is evidence for eighth deprotonation of XO. The pK a8 value of xylenol orange was theoretically obtained (pK a8 = 10.7). Table 2 shows that the pK a8 value of xylenol orange is relatively comparable with the experimental pK a8 value (pK a8 = 10.5) [3].

Ninth ionization constant of xylenol orange
Finally the latest proton is transferred according to the equation 30: In this reaction, HL 5and L 6are the xylenol orange anions with five and six negative charges, respectively. This reaction is characterized by equilibrium constants, K c9 , which was theoretically determined. By combining equations 30 and 5, we obtained the reaction of equation 31 which defines the ninth ionization constant of xylenol orange, K a9 . It shows the solvation of the HL 5-: It is evident that: Equation 32 was used to theoretically determine the value of the ninth ionization constant of xylenol orange in water. At this step, proton is lost from N 53 atom. The formation of the L 6implies that the electronic density of the N 53 (q = 0.152) atom increases notably (in absolute value) compared with the N 53 atom of the HL 5-(q = -0.318). It shows the ninth deprotonation of XO.

CONCLUSION
In this study, the pK a values of xylenol (XO), in water, have theoretically determined at 298.15 K using the ab initio and DFT methods. For XO, we compared the theoretical values of pK a with the experimental ones and found that there is a good agreement between them. This agreement along with the electronic density (q) and structural properties are useful in nano calculation and nanotechnology for building nano sensors.