Theoretical study on ionization of boric acid in aqueous solution by ab initio and DFT methods at T = 298.15 K

INTRODUCTION: Boric acid has antifungal and antiviral properties. It is used in various prescription pharmaceutical products. In this research work, we theoretically calculated the pKa value of boric acid in aqueous solution by ab initio and DFT methods at T = 298.15 K. To explain the determined acidic dissociation constant, the various molecular conformations and solute-solvent interactions of the species of boric acid were considered. The basis set at the B3LYP/6-31+G (d) level of theory was selected for DFT calculations. We analyzed the formation of intermolecular hydrogen bonds between several species of boric acid and water molecules through Tomasʼs method. The result shows that there is a comparable agreement between the experimentally and theoretically determined pKa values for boric acid.
METHODS: Initially, the structure of species of boric acid was optimized by semi empirical PM3 method in program Hyper Chem (CS Chem 3D version 5.0). All calculations about geometries of the initial and solvated molecules in water were done using Gaussian 09 program package. DFT calculations were carried out using the hybrid exchange – correlation functional of Becke, Lee, Yang, and Parr (B3LYP) and the Gaussian 6-31G (d) basis set was used [16].
To analyze the solvent effects on all species involved in the selected ionization reaction, the polarized continuum model (PCM) of Tomasi et al. was used. In this method, the solvent is represented as a structure less polarizable medium characterized by its dielectric constant [17].
Finally, we selected the solvation of the species by means of intermolecular hydrogen bonds (IHBS) that involve one molecule of the mentioned species and some molecules of water.

RESULTS: The trend of a molecule to lose its H+ is quantified as pKa. Boric acid is a weak acid and it has three acid groups. A proton can separate from hydroxyl group to give ionized specie (Fig. 1). This concept of microscopic ionization constant is shown in the Eq. 1:

(1)

The total energies of the single and solvated species of boric acid, in water, were calculated at the B3LYP/6¬-31+G (d) level of the theory, using Tomasiʼs method at T = 298.15 K and the results were showed in Table 1.
It can be found from Table 1 that the total free energy for various species of boric acid increases by increasing the number of water molecules. It shows that the solvation of the boric acid is an endothermic process.
Various reactions including the neutral and anion species of boric acid were considered in an excel program and some of these reactions were not further considered because their equilibrium constants are not comparable with experimental ones. The selected equation for deprotonation process of boric acid as well as the experimentally determined and theoretically calculated pKa have been shown in Table 2.

Ionization constant of boric acid:
In aqueous solutions, the molecule of boric acid can involve in below reaction:
H3L(H2O)4 + OH- ⇌ H2L-(H2O)3 + 2H2O Kc (2)
In the above reaction, H3L(H2O)4 (Fig. 2A) is the neutral specie of boric acid solvated with four molecules of water and H2L-(H2O)3 (Fig. 2B) represents the anion specie of boric acid solvated with three water molecules.
During reaction of Eq. 2, the autopyrolysis of two water molecules, in pure water, can occur as the below:
2H2O ⇌ OH– + H3O+ Kw = 1.008×10-14 (3)
The very low amount of Kw shows that a few water molecules are ionized in pure liquid water.
The reaction of Eq. 4 can be obtained by combining Eqs. 2 and 3:
H3L(H2O)4 ⇌ H2L-(H2O)3 + H3O+ Ka (4)
It is clear that the value of Ka can be calculated using Kc and Kw as the below:
Ka = Kc × Kw (5)
Eq. 5 was applied to calculate the values of the ionization constant of boric acid, Ka, in water at T = 298.15 K. The theoretically calculated value of pKa for boric acid at T = 298.15 K is shown in Table 2. As it can be seen in this table, there is a good agreement between experimentally determined and theoretically calculated pKa values of boric acid at this temperature.
Table 3 shows the optimized values of structural properties for the anion and neutral species of boric acid, in water, obtained at the B3LYP/6-31+G (d) level of theory with Tomasiʼs method at T = 298.15 K.
As it can be seen in Table 3, for boric acid, the values of qO4 for HL-(H2O)3 and H2L(H2O)4 are -1.104481 and -0.907847, respectively. It shows that the absolute value of electrical charge around O4 atom in HL-(H2O)3, compared to that of in H2L(H2O)4, increases and it can imply to separate H+ form O4 atom during deprotonation process of boric acid in water.

Study on H-bonding between selected species of boric acid and water
The structural properties of specie, solved in water, can help us to understand the interaction between this specie and water (H-bonding). One of the most important of these structural properties is the bond length between the indicated atoms form solute and solvent (water) molecules (in Å). These data, for neutral and cation species of boric acid, are listed in Table 3. The power of hydrogen bonds can be classified as strong (bond length is between 1.2 Å to 2.2 Å and the angle is between 175° to 180°), moderate (bond length is between 1.5 Å to 2.2 Å and the angle is between 130° to 180°), and weak (bond length is between 2.2 Å to 3.2 Å and the angle is between 90° to 150°) [18]. As it can be seen in Table 3, for H2L(H2O)4, the bond length between atom H6, from boric acid, and O9, from water, is 2.124582 (dH6O9 = 2.124582). In addition, for H2L-(H2O)3, the bond length between atom O2, from boric acid, and H19, from water, is 2.098563 (dH19O2 = 2.098563). These data shows that for boric acid, the power of H-bonding between H2L(H2O)4 and water and also, between H2L-(H2O)3 and water are classified as moderate. It must be noted that IHBs data can be used in the design of benefit and help us to predict Nano drug [19].


DISCUSSION AND CONCLUSION: In this research work, we showed the feasibility of a theoretical method, DFT and ab ignition, to calculate the ionization constants of boric acid at T = 298.15 K. As a result, we selected various acid-base reaction that include the solvation of the hydrogen, hydroxyl ions, and other anions or neutral molecules in protic solvents such as water, which process a high hydrogen-bond-donor capability. The calculations performed at the B3LYP/6-31+G(d) levels of theory using Tomasi s method allowed us to prove that neutral molecules and anions form IHBs with some molecules of water. In addition, the comparison between experimentally determined and theoretically calculated pKa,s, for boric acid, shows that there is a good agreement between them at 298.15 K.