Theoretical calculations of the relative pKa values of some selected aromatic arsonic acids in water using density functional theory

Article history: Received July 21, 2015 Received in revised form August 29, 2015 Accepted 8 October 2015 Available online 8 October 2015 With the focus on calculating the equilibrium constant (Ka) of arsonic acids (RAsO(OH)2) in aqueous media, the behavior of both neutral and negatively charged species of some arsonic acids have been considered through the isodesmic reaction scheme with polarized continuum model of solvation. The relative pKa values of a number of arsonic acids were calculated using density functional theory (DFT), with methylarsonic acid (CH3AsO(OH)2) used as a reference molecule. Various basis sets such as (6-31G(d), 6-31+G(d), 6-311++G(d,p) and 6311++G(2d,2p)) in conjunction with B3LYP computational method were examined. Finally the latter one was found to give better results. The results of applied B3LYP 6-311++G(2d,2p) method for pKa values of 25 arsonic acids in aqueous media showed good agreement with corresponding experimental pKa values. In this level of theory the average error was less than 0.3 pKa units. The type of substituent affected the acid strength, with electron withdrawing substituents lowering the pKa and electron releasing groups increasing it. © 2016 Growing Science Ltd. All rights reserved.


Introduction
Arsonic acids have the general formula of RAs(O)(OH)2 in which R could be alkyl or aryl group.10] Organo arsenic compounds are very useful starting materials with important application in various fields of chemistry.] In addition some of the aryl arsonic acids have own application, for example 3-nitro-4-hydroxyphenyl arsonic acid (Roxarsone), 3-nitrophenyl arsonic acid (Nitarsone) and 4-aminophenyl arsonic acid (Arsanilic acid) are aryl arsonic acid derivatives which are produced commercially on a large scale.Roxarsone, Nitarsone and Arsanilic acid are growth promoter for poultry, and were used as a feed additive to increase weight gain and improve feed efficiency in poultry production. 13They also used as an animal drug in poultry.For example controlling of Histomoniasis is possible only by Nitarsone 14 and Arsanilic acid used to prevent or treat dysentery in poultry and swine. 13nally aryl arsonic acids can be used as an indicator for determining metal ions among other uses.For instance Miller 15 reports use of arsanilic acid for detection of cerium.Due to importance and wide range application of arsenic compounds it seems that we need for more research work about them.The goal of this work is determining of the pKa value as a criterion for acidity power of aryl arsonic acids.We hope that our reported results in this work could be helpful for other researchers who try to understand more about arsenic compounds behavior in biological systems and etc.
The pKa value for a compound, defined as the negative logarithm of the dissociation constant of the acid ( _ logKa), plays an important role in understanding a number of phenomena in different scientific domains including life sciences, chemistry and material sciences.7][18][19] The pKa value also indicates the ratio of neutral and anionic forms of a molecule at a given pH. 20The large number of papers describing computational research on the prediction of the acidity of various compounds in the recently published chemical literature indicates that the pKa is one of the important properties in many scientific domains such as chemistry and biology. 19,21 or example, determining the acidity of some ionizable groups could be helpful in understanding its role at the molecular level in some biologically active molecules. 22e experimental determination of pKa values in reaction intermediates, specific parts of large biological building blocks, and molecules with dissolution limitations is very difficult to obtain. 18,19,23 Iaddition, providing standard conditions for the experimental determination of pKa value is essential for allowing comparison of different results. However, to the best of our knowledge, there is no data on pKa calculations of arsonic acids by quantum chemical methods, and experimentally determined pKa values are limited to a small group of arsonic acid derivatives.Accordingly, we have calculated the relative pKa values of some of aryl arsonic acids using using the DFT/B3LYP approach in conjunction with some selected basis sets such as (6-31G(d), 6-31+G(d), 6-311++G(d,p) and 6-311++G(2d,2p)).Our results showed good agreement between theoretical values and experimental results, especially using the B3LYP/6-311++G(2d,2p) method for calculation; the average error was less than 0.8 when using B3LYP/6-311++G(d,p), and 0.3 when using B3LYP/6-311++G(2d,2p) level of theory.

Methods and theoretical calculations
First of all for choosing the best basis set with the minimum average of error we calculate pka values of three of arsonic acids (phenyl arsenic acid, 2-methoxyphenyl arsenic acid and 3-nitrophenyl arsenic acids ) using various selected basis sets.The results collected on Table 1.
As appears from the results of Table 1 the best basis set for our goal is the 6-311++G(2d,2p) which is resulted pKa values with lower difference from the experimental values.In the case of 6-31G(d) basis set in some cases we have approximately more than one unit (1.72) difference between experimental and calculated pKa values whereas with 6-311++G(2d,2p) basis set we can reduce this differences below 0.25 unit.Therefor the 6-311++G(2d,2p) basis set gives more accurate and reliable results than 6-31G(d) one.In continue we applied both of the B3LYP/6-311++G(d,p) and B3LYP/6-311++G(2d,2p) levels for pKa calculation.Initially the calculations for the arsonic acids and their conjugate anions were fully optimized at B3LYP/6-311++G(d,p) level of theory.Vibrational frequency calculations were done at the same level to verify that each stationary point was a real minimum.All calculations were performed using the GAMESS program package. 53he polarized continuum model (PCM) was used for acquiring data in the solution phase.The solution phase optimization of both neutral and anionic species was performed at the B3LYP/6-311++G(d,p) level on the structures obtained from gas phase optimizations.Natural bond orbital (NBO) analysis was also used to reveal the charge distribution in neutral and deprotonated structures.The calculation of the pKa value for an acid undergoing dissociation can be carried out using the change of Gibbs free energy for the dissociation reaction as shown below, where HA represents the arsonic acid.
Eq. ( 3) simply relates the equilibrium constant and changes of Gibbs free energy of dissociation process to each other.In this equation ∆G 0 is the standard change in the Gibbs free energy related to the dissociation process taking place at 298.15 K. ∆G 0 can be obtained by using a thermodynamic cycle which includes one isodesmic reaction (4) and one dissociation process (5).In this thermodynamic cycle methyl arsonic acid was used as a reference molecule 46 : In aqueous solution the Gibbs free energy of dissociation of acid HA , 0 G ∆ , can be written as a sum of Gibbs free energy changes of Eq. ( 4) and Eq. ( 5): [ ] [ ] [ ] [ ] Finally, using the above thermodynamic cycle and equations, the pKa values were calculated using Eq. ( 10):

Results and Discussion
The structure and nomenclature of the arsonic acids (1-25) selected for calculation are shown in Fig. 2.[56] In this study, we used the B3LYP method in combination with two different basis sets, 6-311++G(d,p)and 6-311++G(2d,2p).Gibbs free energy changes of acid dissociation in the gas phase and computed pKa values with both selected basis sets are summarized in Table 2. From these results it is concluded that the 6-311++G(2d,2p) basis set gives reliable pka values with less error than that of those obtained when 6-311++G(d,p) is used.Compound 4 (4-nitronaphthyl-1-arsonic acid) is the strongest acid among those studied.Compound 2 (benzylarsonic acid) shows the weakest acidity with pKa = 4.27 because it is a non aromatic arsonic acid.Electron withdrawing groups such as halogen and nitro on the aromatic ring, especially in the ortho position, increase the acidity of the arsonic acid.In contrast, electron releasing groups on the aromatic ring, such as methyl, decrease the acidity.

Atomic Charges
Charges on atoms in a molecule are not a quantum chemical observable property, but the atomic charge concept is a useful tool for the illustration of a variety of chemical phenomena.Determination of atomic charge in a molecule is accessible via several empirical and quantum mechanical methods.For each of the unionized arsonic acids, atomic polar tensor (APT) derived charges were calculated at B3LYP level of theory using 6-311++G(d,p) and 6-311++G(2d,2p) basis sets.For the acidic hydrogen (H) and the entire arsonic acid group (AsO(OH)2).Charges on the ionized oxygen (O -) and the charge on the whole corresponding conjugate anion, (AsO(OH)O -), were also determined and are shown in Table 3. 21,[57][58] Good correlation between calculated pKa and the APT charges can be observed.The results in Table 3 demonstrate that the delocalization of the negative charge of the deprotonated anion by the arsenic atom leads to an increase in the acidity of the corresponding arsonic acid.For example with the focus on data on Table 2 and Table 3 it could be concluded that as the delocalization of negative charge on (AsO(OH)O -) increased as a result an increase in acidity power observed.For example compounds 1, 2, 3 and 4 with respectively -0.599, -0.799, -0.656 and -0.525 negative charge on (AsO(OH)O -) and calculated pKa values of 3.34, 4.27, 2.85 and 1.74 verifies the direct relationship between acidity power and the amount of delocalization of negative charge on corresponding structure.Within four above mentioned structures, the more acidic compound 4 has the more delocalization value (lower negative charge on (AsO(OH)O -).It should be note that this relationship between delocalized charge and pKa value dose not completely linear in all cases, because the delocalization value is not the only factor which could be affect the pKa value.In this study, we also carried out quantitative analysis of the charge transfer from the O atom to the adjacent As atom using the NBO method.Fig. 4 shows the selected charges on selected arsonic acids.As shown in Fig. 4, in the neutral molecule the charge on the arsenic atom is more positive than that in the corresponding anion.For instance, the positive charge on the arsenic atom for the neutral molecules and (corresponding anions) of compounds 8 and 24 are 2.377 (2.356), and 2.380 (2.356), respectively.These data indicate that charge transfer occurs from the oxygen atom to arsenic during the deprotonation process.

Conclusions
This work reports the calculation of the pka value of 25 arsonic acids in aqueous media using two different levels of theory.The results show a good linear relationship between experimental pKa values and the calculations, the average error being less than 0.8 and 0.3 pKa units when the (B3LYP/6-311++G(d,p)) and (B3LYP/6-311++G(2d,2p)) levels were used for calculations, respectively.The results confirm that the acid strength depends on the type of the substituent.Electron withdrawing groups attached to the arsonic acid lead to greater acidity than electron releasing groups because of their anion stabilizing capability.We also showed that the relative pKa values of arsonic acids can be calculated using (B3LYP/6-311++G(2d,2p)) level of theory with an acceptable accuracy. 0

Fig. 4
Fig. 4 Natural Bond Orbital (NBO) charges on oxygen and arsenic in the neutral structures (8a and 24a) and corresponding deprotonated structures (8b and 24b).

Table 1 .
Results of pKa calculation using various basis sets.

Table 2 .
Changes in Gibbs free energy and pKa values of selected arsonic acids.

Table 3 .
Calculated APT charges for the studied arsonic acids.