Degradation of Indigo Dye Using Quantum Mechanical Calculations

: The semiempirical (PM3) and DFT quantum mechanical methods were used to investigate the theoretical degradation of Indigo dye. The chemical reactivity of the Indigo dye was evaluated by comparing the potential energy stability of the mean bonds. Seven transition states were suggested and studied to estimate the actually starting step of the degradation reaction. The bond length and bond angle calculations indicate that the best active site in the Indigo dye molecule is at C10=C11. The most possible transition states are examined for all suggested paths of Indigo dye degradation predicated on zero-point energy and imaginary frequency. The first starting step of the reaction mechanism is proposed. The change in enthalpy, Gibbs free energy and change in entropy of the overall reaction are equal to -548268.223 kcal/mol, 30831.951 kcal/mol and 48.552 cal/mol . deg, respectively. The activation energy is 46176.405 kcal/mol. The reaction rate is equal to 22.867 × 10 11 s −1 .


Introduction:
One of the main environmental problems in the world is wastewater. The contamination of water sources such as rivers and lakes occurs when untreated wastewater is released into these sources. Plants and species living in or around the aquatic system can be harmed by polluted water. It can also cause harm to those who consume it, including humans, plants, and animals 1 . Pathogens, inorganic substances, organic material, and macroscopic pollutants are the four basic types of water pollution. Dye is one of the most significant of these pollutants, and it is becoming a major environmental and public health hazard. Dyes in water cause issues for instance lowering the levels of oxygen in the water, interfering with sunlight diffusion through waters, slowing photosynthesis as well as interfering with the solubility of gases in water bodies 2 .
Indigo is a natural dye prepared from Indigofera tinctoria and Isatis tintoria plants. Due to a scarcity of natural blue dyes, indigo has played a key part in the economics of many countries since its inception, mostly for textile dyeing and printing, and it is still utilized in the fabric business today 3 .
Chemical oxidation 4 , adsorption 5 , biodegradation 6 , and photolysis 7 are some of the current technologies utilized to treat wastewater. Chemical oxidation technology employs a sequence of oxidants and catalysts to remove organic molecules from wastewater. Oxidants are used in chemical oxidation processes to destroy contaminants and transform them into less hazardous by-products or end products (e.g., carbon dioxide, water). Ozone, oxygen, peroxide, permanganate, and other oxidants are widely applied 8 . Researchers have been applying computation methods to descript the molecular structure and reactivity of compounds in recent years. Chemical reaction simulations require optimal geometry of chemical compounds and transition states. When computing the potential energy surface, they are found the key to chemical reactivity 9 . For minimum transitions, the first-order saddle point must be carefully considered to order to land on the most possible states. The reaction mechanisms begin with the first cleavage step, which is usually the slowest deciding step compared to the faster later steps 10,11 .
In this paper, the mechanisms of the first cleavage step for the degradation of indigo dye with superoxide anion radical have been studied using quantum chemical calculations.

Material and methods:
In this article, depending on molecular orbital theory different theoretical calculations were performed using the semiemperial PM3 method in the Hyperchem package 8.02 12 . All reactants, suggested transition states and products have been optimized by DFT, 6-31G / B3LYP by Gaussian 09 program. The bond stability of main bonds in indigo dye molecule was studied using the PM3 method. Vibrational frequencies of suggested transition state structures were calculated. The parameters of thermodynamics (ΔG, ΔH and ΔS) have been estimated at DFT, 6-31G / B3LYP by Gaussian 09 program 13 .

Results and Discussion: Optimizing the structure of Indigo dye
Electronic properties of Indigo dye were studied at the PM3 level shown in Fig. 1. The atomic charge orientation and electrostatic potential of the Indigo dye molecule were used to estimate the possible active site that reacts toward O2radicals 14 .

Atomic ball view
Atomic symbol The density of charge Electrostatic potential Charge of atoms (coulomb) Numbering atoms and 0.992 Aº respectively. Due to these results, the C10=C11 bond is more active to react 15 . Bond strength was measured for the main important bonds as shown in Table 1. Fig. 2 illustrates the stability of bonds C10=C11, C7-O9 and N8-H24 calculated by the PM3 method. The results indicate that the C10=C11 is the best active site due to the lowest bond dissociation energy 16 .  The bond angles of the O9=C7-C10, C7-C10=C11, N8-C10=C11 and C10-N8-H24 are equal to 127.142 ͦ , 128.06 ͦ , 124.062 ͦ and 117.886 ͦ , respectively. These bond angles are higher than the other angles. That is, the O9=C7-C10 and C7-C10=C11 bonds are more likely to be attacked by the superoxide anion radical than the other bonds 17 . Fig. 3 shows the potential energy stability of bonds in indigo. Different seven transition states have been suggested for indigo dye degradation. As indicated in Fig. 4, all transition states were investigated to determine the most likely transition state to give the product. Table 2 shows the Energetic values for suggested transition states. The first transition state is the most likely to give up reaction products than other states since it has the highest value of zeropoint energy and the lowest heat of formation 18 .  Figure 4. Proposed transition states for indigo degradation by superoxide anion free radical using semiempirical PM3.
The initial broken step of the Indigo dye by the reaction with superoxide anion radical was proposed from the first transition state to produce Isatin. The proposed reaction mechanism for the initiating step of the reaction is shown in Scheme 1. The energy barrier value of the forwarding reaction is -548436.731 kcal mol -1 , while the backward reaction is -89.039 kcal mol -1 . These results indicate the reaction goes to the product Isatin 19 . The energetic properties of reactant and transition state and product are listed in table 3.
Schem1. The suggested mechanism for the first broken step of indigo dye with .− .  The change in enthalpy, Gibbs free energy and change in entropy of the overall reaction are equal to -548268.223 kcal/mol, 30831.951 kcal/mol and 48.552 cal/mol.deg, respectively. These results indicate that the reaction is exothermic 20 and nonspontaneous 21 at 298.15 K. The activation energy is 46176.405 kcal/mol. The reaction rate is equal to 22.867 × 10 11 s −1 .

Conclusion:
The chemical reactivity of indigo dye optimized structure has been examined utilizing computational methods towards superoxide anion radical. The active site in the dye molecule was determined using the bond strength and bond angles calculations. The first transition state is the most probable and the reaction mechanism is the first cleavage step at the C10-C11 bond due to the lowest energy value.