TABLE 1
HOMO, LUMO ESP of A1, A2, A3, B1, B2 form and transition states were given in Figure 3. HOMO is the outermost orbit filled with electrons; it can be thought of as a valance band as it is represented by the ionization potential of a molecule and acts as an electron donor. LUMO, on the other hand, represents the innermost orbital that is not filled by electrons and is directly related to electron affinity and it acts as an electron acceptor.
FIGURE 3
The main orbitals involved in the chemical reaction are the highest-occupied molecular orbital (HOMO) and the lowest-occupied molecular orbital (LUMO) since they act as electron acceptors.[22]
MEP map of the molecule is calculated in optimized geometries in estimating reactive regions for electrophilic and nucleophilic attack. In most MEPs, the maximum negative region is indicated in red for electrophilic attack indications and the maximum positive region in blue for nucleophilic attack symptoms. In terms of colour grading, it shows molecular size, shape, positive, negative and neutral electrostatic potential regions simultaneously and MEP is very useful in the investigation of molecular structure with its physicochemical property relationship.
The highest occupied molecular orbital (HOMO) and the lowest empty molecular orbital (LUMO) are called boundary orbitals, and these orbitals are key parameters in determining molecular properties and molecular electrical transport properties, the eigenvalues of HOMO (transmitter) and LUMO (receiver). Moreover, the energy difference between them determines the chemical activity of molecules. The Frontier molecular orbital energies have been calculated with B3LYP/6–311G (d,p) level. Results obtained from solvent (ethanol, DMF, DMSO and water) and gas-phase for of A1, A2, A3, B1, B2 form and transition states are listed in Table-2 with the parameters obtained from frontier molecular orbital.
TABLE 2
Band gap, electronegativity (χ), global hardness (η), chemical potential (µ),, global electrophilic index (ω), spherical softness (σ), Nucleofugality ΔEn and electrofugality ΔEe and electronic charge (∆Nmax) can be calculated using the followng equations.[23-25]
\(E_{\text{gap}}=E_{\text{LUMO}}-E_{\text{HOMO}}\) (1)
\begin{equation} \eta\cong-\left(\frac{E_{\text{HOMO}}-E_{\text{LUMO}}}{2}\right)\nonumber \\ \end{equation}\begin{equation} \mu=-\chi\cong\left(\frac{E_{\text{HOMO}}+E_{\text{LUMO}}}{2}\right)\text{\ \ }\nonumber \\ \end{equation}\begin{equation} \sigma=\frac{1}{\eta}\cong-\left(\frac{2}{E_{\text{HOMO}}-E_{\text{LUMO}}}\right)\text{\ \ \ \ \ \ \ \ \ }\nonumber \\ \end{equation}\begin{equation} \omega=-\frac{\mu^{2}}{2\eta}\text{\ \ \ \ }\nonumber \\ \end{equation}\begin{equation} E_{n}=-A+\ \omega=\frac{\left(\mu+\eta\right)^{2}}{2\eta}\nonumber \\ \end{equation}\begin{equation} E_{e}=I+\ \omega=\frac{\left(\mu-\eta\right)^{2}}{2\eta}\nonumber \\ \end{equation}\begin{equation} {N}_{\max}=-\mu/\eta\nonumber \\ \end{equation}
The electrophilic index, chemical hardness, the chemical potential is a global reactivity index. ΔNmax refers to the maximum charge transfer to the electrophile. ΔNmax was evaluated as showing the ability of the system to obtain additional electronic charge from the medium that defines the charge capacity of the molecule. This index measures energy stabilization when the system receives an additional electronic charge (ΔNmax) from the environment. With the electronic chemical potential of the molecule, the direction of charge transfer is completely determined. Since an electrophile is a chemical type that can accept electrons from the environment, after accepting the electronic charge, its energy should decrease and the electronic chemical potential should be negative.[26-29]
The global hardness index has changed as A3 <B1 < A1 < A2 < B2 for gas phase and studied solvent phase. It seems the structure A3has the less hardness index and more reactive than the others Table 2 represents the solvent effect of the ΔNmax for A1, TS1, A2, TS2, A3, TS2, B1, and B2 in different solvents. The max charge transfer index (ΔNmax) of A1, T1, A2, A3, TS3, B1 decreases as follow: gas > ethanol > DMF > DMSO > water. ΔNmax of favipiravir forms increases in following order: B2 < A2 < A1 < B1 < A3 in gas phase, however in solvent phese (ethanol, DMF, DMSO, water) increase in following order: B2 < A1 < A2 < B1 < A3. According to these results, it can be easily estimated that B2 and A3 structures have the largest ΔNmax value in the gas phase and also in the solvent phase. Increase in the max charge transfer values of B2, A2, A1, B1, A3 in gas phase are 2.21 %, 3.09 %, 13.79 %, and 1.55 %.
The Energy Gaps (ΔE) for the favipiravir form studied increase in the following order: A3 < B1 < A1 < A2 <B2 for gas phase and the other solvent phases at B3LYP/6311G(d,p). Also, the energy gap of favipiravir form has depended on the solvent media. The most significant difference of energy gap for water and gas phases is 0.05 eV, 0.12 eV, 0.13 eV respectively for A1, A2, and B2 forms, however, energy gap in water is smaller than gas phase only 0.01 eV for A3 and 0.04 for B1.
Dipol moment, which is a measurement of the asymmetry in the charge distribution, indicates the degree of separation of the charge in a molecule. The number of atoms in tautomers is constant, and it is stated that only the movement of the H atom between N and O atomic regions can bring important properties in tautomeric structures in which it is evaluated. The trends can be seen much better with the values of dipole moments (DM), where different values of the DM can detect different directions of the electronic directions.
The dipole moments of Favipiravir’s A1, A2, A3, B1, B2 forms and transition states (TS1, TS2, and TS3) between A1 and A2, A2 and A3 and B1 and A3 were calculated in the gas and solvent phases and are given in Figure 4.
The values of the dipole moments in Figure 4 show that the presence of the solvent generally increases in the dipole moment of the A1, A2, A3, B1, B2 form of favipiravir and transition states relative to the gas phase. The dipole moments increase by changing the gas phase to the solution as well as by increasing the solvent polarity. In more polar solvents, Polar solvents have higher dipole moment values than non-polar solvents, so delocalization of loads is higher in polar solvents.[30-32] The gaseous A1, A2, A3, B1 and B2 forms  have a dipole moment value of 1.28, 0.93, 2.03, 2.33 and 2.24 D in the gas phase. A2 tautomer has smaller dipole moments than the other forms, and B1 form has an enormous dipole moment.
FIGURE 4
The polarity of organic materials is usually due to the contributions of the components of the system (atoms, molecules) due to the molecules’ Van der Waals, dipole-dipole interactions, hydrogen bond interactions. The nonlinear optical properties of molecular systems depend on the polarization of electrons in their bonding orbitals. The mean polarization and anisotropy of the polarization (αa and Δα) were calculated as follows using the polarization components:
\(\alpha=\frac{1}{3}(\alpha_{\text{xx}}+\alpha_{\text{yy}}+\alpha_{\text{zz}})\)
\begin{equation} \alpha=\left[\frac{{(\alpha_{\text{xx}}-\alpha_{\text{yy}})}^{2}+{(\alpha_{\text{yy}}-\alpha_{\text{zz}})}^{2}+\left(\alpha_{\text{zz}}-\alpha_{\text{xx}}\right)^{2}+6(\alpha_{\text{xz}}^{2}+\alpha_{\text{xy}}^{2}+\alpha_{\text{yz}}^{2})}{2}\right]^{\frac{1}{2}}\nonumber \\ \end{equation}
The results of the static polarizability of A1, A2, A3, B1, B2 forms and TS1, TS2 and TS3 transition states of favipiravir calculated in the gas phase and different solvents are shown in Figure 5. The highest <α> value was found as 15.63 for A3 in water phases. Furthermore, the dipole moment difference between gas and water phase is the biggest; this difference is 3.53 esu, 3.48 esu, 3.76 esu, 3.75 esu, 3.46 esu, respectively for the forms A1, A2, A3, B1 and B2.
FIGURE 5
Static values of polarizability evolve in the following order B2<B1< in gas phase and different media, and static values of polarizability evolve in the following order A3<A2<A1 in gas phase, but A3<A2=A1.
The high polarity of a molecule means that the molecule has a small frontier orbital gap. [33-36] Form A3 has the smallest frontier orbital gap energy in the gas phase and the largest polarization of the favipiravir forms examined, so this is associated with a high chemical reactivity, low kinetic stability and is also termed as a soft molecule.
Frontier orbital gap energy of A3 form in the solvent phase is smaller than the gas phase so, it could be concluded that A3 form in the solvent phase is a higher chemical reactivity than the gas phase. Figure 5 shows that polar solvents increase the polarisability of all studied favipiravir tautomers in compare to the gas phase.
Results of polarization anisotropy calculated in the gas phase and different solvents of the forms of Favipiravir molecule A1, A2, A3, B1, B2 and their transition states are shown in Figure 6.
FIGURE 6
For these forms, the anisotropy of polarizability is found as 9.95, 9.76, 10.18, 10.57, 9.78 in the gas phase, and as 13.42, 13.16, 14.31, 14.64, 13.17 in the water phase. The most significant difference in polarization anisotropy value was found between the water and gas phases, which are 3.48 esu, 3.39 esu, 4.14 esu, 4.07 esu, 3.39 esu for A1, A2, A3, B1 and B2 forms, respectively.
The total hyperpolarizabilities in atomic units (a.u.) are related to the electrostatic units (esu) by the relation: 1 a.u. = 8.6393X10-33 esu. The first hyperpolarizability is a third-degree tensor that can be defined by a 3 x 3 x 3 matrix. Due to the Kleinman symmetry, 27 components of the 3-D matrix can be reduced to 10 components. The output of Gaussian 09 provides ten components of this matrix as βxxx, βxxy, βxyy, βyyy, βxxz, βxyz, βyyz, βxzz, βyzz, βzzz, respectively. The values of the first hyperpolarized tensors calculated in atomic units were converted to electrostatic units using 1au =0.0086393x10-30 esu. The calculated first static hyperpolarizability value for A1 is equal to 1.31x10-30, 2.09x10-30, 2.10x10-30, 2.11x10-30, and 2.12x10-30 calculated DFT level of theory in gas, ethanol, DMSO, DMF, and water respectively.
Thermodynamic parameters such as heat capacity (\(C_{p,m}^{o}\)), entropy (\(S_{p,m}^{o}\)) and enthalpy (\(H_{p,m}^{o}\)Hm◦), changes Gibbs Free energy changes (\(G_{p,m}^{o}\)) were calculated for the A3 favipiravir form at temperatures ranging from 200 K to 1000 K, under 1 atm pressure and vacuum. Based on vibration analysis, these static thermodynamic functions were obtained from theoretical harmonic frequencies and their correlation graphs are shown in Figure 7.
FIGURE 7
It can be observed from Figure 7 that heat capacity, entropy, and enthalpy of favipiravir increase with temperatures ranging from 200 to 1000 K due to increased molecular vibration intensities with temperature and Gibbs free energy of For A3 favipiravir form decreases. It means that with increase of temperature, the stability of A3 favipiravir form increases. [37] Correlation equations between heat capacity, entropy, enthalpy, Gibbs Free energy changes and temperatures were placed by quadratic formulas as in the equation below
\(C_{p,m}^{o}={-6x10}^{-5}T^{2}+0.1194T+4.9341\)
\begin{equation} S_{p,m}^{o}={-4x10}^{-5}T^{2}+0.1491T-56.726\nonumber \\ \end{equation}\begin{equation} H_{p,m}^{o}={2x10}^{-5}T^{2}+0.0264T-3.3117\nonumber \\ \end{equation}\begin{equation} G_{p,m}^{o}={-5x10}^{-5}T^{2}+0.0707T+2.8816\nonumber \\ \end{equation}
with the corresponding fit factors (R2) for these thermodynamic properties are 0.9983, 0.9999 and 0.9997, 1.000 respectively.
All thermodynamics data can provide useful information for further study about 4Cl3NT and can be used to predict directions of chemical reactions according to the relationship of thermodynamic functions, other thermodynamic energies and the second law of thermodynamics in the thermochemical field.
4 . SUMMARY
In this research, we have tried to explain quantum chemical parameters of the A1, A2, A3, B1, B2 form of favipiravir and transition states TS1 between A1 and A2 forms, TS2, A2 and A3 forms and TS3 A3 and B1 forms in gas and studied solvent phase at B3LYPP/6-311G(d, p) to show the computed parameters strongly depend on the solvent media. The dipole moments, polarisability of all forms are affected by the solvent. With the increase of the polarity of solvents, the dipole moments of all tautomers were increased.
CONFLICT OF INTERES
The authors declare no competing financial interests.
ORCID https://orcid.org/ 0000-0001- 6097-2184