The structures, electronic states, and point group symmetries of pure (ZnO)12, (ZnO)15, (ZnO)18, (ZnO)20, (ZnO)22, and (ZnO)24 NCs are optimized and represented in Fig. 1. The (ZnO)12 and (ZnO)18 NCs are found to be the potential energy surface (PES) of the 1AG state, the (ZnO)15 NC is the ground 1A´ singlet PES. The (ZnO)20, (ZnO)22, and (ZnO)24 NCs are found to be the PES of the 1A state. The point group symmetries of (ZnO)12, (ZnO)15, (ZnO)18, (ZnO)20, (ZnO)22, and (ZnO)24 NCs are Th, C3h, S6, C4h, C3 and S8, respectively. From the harmonic vibrational frequencies, the studied ZnO NC models corresponded to energetic a minimum which means the transition state at a saddle-point on the PES.
All possible interactions of the (ZnO)12, (ZnO)15, (ZnO)18, (ZnO)20, (ZnO)22, and (ZnO)24 NCs with favipiravir drug were carried out and among them, relaxed structures with the lowest energy are demonstrated in Fig. 2. The binding energy per atom \(\left({E}_{b}\right)\) of pure ZnO NCs and adsorption energy \(\left({E}_{ad}\right)\) of theoretically calculated geometries of the favipiravir adsorbed ZnO NCs are depicted in Fig. 3. The \({E}_{b}\) of the ZnO NCs shifts from 5.04 eV to 5.16 eV, depending on the increase in the size. These results indicate that an increase in the size of the NCs also enhances the stability. The \({E}_{ad}\) of the ZnO NCs are predicted in the range of -26.69 kcal/mol and − 34.27 kcal/mol where N – Zn and F – Zn atoms interact between the N and F atoms of favipiravir drug and Zn atoms of the ZnO NCs. The negative \({E}_{ad}\) means the adsorption of the favipiravir drug on ZnO NCs is exothermic and energetically favorable. The size of ZnO NC has a significant effect on the \({E}_{ad}\) between the favipiravir and ZnO NCs. It is important to note that the \({E}_{ad}\) (-34.27 kcal/mol) of between (ZnO)18 NC and the favipiravir is more desirable than the other interactions (ZnO)24 (-26.69 kcal/mol), (ZnO)20 (-27.14 kcal/mol), (ZnO)12 (-29.36 kcal/mol), (ZnO)15 (-29.50 kcal/mol), and (ZnO)22 (-31.04 kcal/mol) NCs with the favipiravir, which means that ZnO NCs can be used as drug delivery vehicle.
The HOMO and LUMO energy levels are an important parameter to understand perfectly the charge transfer interaction within interacting systems [35]. In this regard, the energy levels using the density of states (DOS) constructed by GaussSum [36] (see Fig. 4) and the energy gap \(\left({E}_{g}\right)\) which is obtained from HOMO and LUMO energy difference are performed to figure out the stability chemical reaction of the studied systems. The size of ZnO NCs causes changes over valence and conduction levels to shift to higher and lower energies both pure and interacting systems, leading to a shift in the studied systems. The value of the HOMO and LUMO energy levels are found to be about − 6.05 and − 3.28eV, respectively, and corresponding the \({E}_{g}\) is found as 2.77 eV for (ZnO)15 NC and the favipiravir interaction which is the smallest value among the studied models. Moreover, the HOMO and LUMO energy levels for (ZnO)12 NC and the favipiravir interaction are predicted as -6.19 and − 3.25 eV, respectively. The corresponding \({E}_{g}\)is found to be 2.94 eV, which is the greatest value than the other ZnO NC and the favipiravir interactions which change in the range of 2.85―3.94 eV. It is important to note that charge transfer can take place easier between HOMO and LUMO energy levels of (ZnO)15 NC which has the smallest \({E}_{g}\)value and the favipiravir interaction, which means a shift in the biological activity of the favipiravir and ZnO NC interaction shown in Fig. 5. That is, the change in the size of the ZnO NCs and the position of the favipiravir on the ZnO NCs cause a desirable shift in the HOMO and LUMO energy levels due to a decrease in the \({E}_{g}\), which further contributes to the charge-transfer process [37–39]. The percentage value \(\left(\varDelta {E}_{g}\right)\) of the difference in the \({E}_{g}\) energies for favipiravir adsorbed ZnO NCs also given in Fig. 5. When compared to pure ZnO NCs, the greatest change in the \(\varDelta {E}_{g}\) is predicted between (ZnO)12 NC and favipiravir (31.16%), whereas the lowest change in the \(\varDelta {E}_{g}\) is predicted between ZnO)22 NC and favipiravir (18.41%). The values show that the size of ZnO NCs has an important effect on the \({E}_{g}\) of interactions. The ZnO NCs are semi-conducting with the \({E}_{g}\) in the range of 2.77–2.97 eV.
The vertical ionization potential \(\left(VIP\right)\) and vertical electron affinity \(\left(VEA\right)\), which are defined in computational part, are carried out to explore the changes of the reactivity properties of pure ZnO NCs and ZnO NCs with favipiravir drug based on the size of ZnO NCs, as indicated in Fig. 6 (a, b). The greater \(VIP\) value of pure (ZnO)12 NC is 8.40 eV, which decreases to 7.84 eV for (ZnO)24 NC due to the increase in HOMO and LUMO energy levels in terms of the electron-donating ability of the favipiravir towards ZnO NCs. Similarly, the greater \(VIP\) value of (ZnO)18 NC with favipiravir drug is 7.53 eV, which decreases to 7.25 eV for (ZnO)22 and (ZnO)24 NCs with favipiravir drug as shown in Fig. 6a. It is important to note that pure (ZnO)12 NC and (ZnO)18 NC with favipiravir drug is more stable than that of the others so it is difficult to eject the electron from them. This result agrees also with the energy levels of HOMO and LUMO (see Table I). The VIP of the (ZnO)15, (ZnO)18 and (ZnO)20 NCs with favipiravir drug are predicted as 7.29, 7.53 and 7.31 eV. The value of \(VEA\) of pure (ZnO)20 is 2.01 eV, which decreases to 1.64 eV for pure (ZnO)20 as shown in Fig. 6b. Similarly, the greater \(VEA\) value of (ZnO)18 NC with favipiravir drug is 1.95 eV, which decreases to 1.57 eV for (ZnO)12 NC with favipiravir drug as shown in Fig. 6b. There is not a smooth change for the \(VEA\) with increase in the size of ZnO NC where the value of \(VEA\) increase for (ZnO)12, (ZnO)15 and (ZnO)18 with the favipiravir drug from 1.64 to 1.95 eV, and then fluctuations are observed from (ZnO)20 to (ZnO)24 with the favipiravir drug.
Ultraviolet-visible (UV–vis) absorption spectra of interacting pure and favipiravir adsorbed (ZnO)12, (ZnO)15, (ZnO)18, (ZnO)20, (ZnO)22 (ZnO)24 NCs are performed with TD-DFT, and the obtained results are piloted in Fig. 7. An excitation wavelength (electron-transfer wavelength) in the visible region is preferred because ultraviolet light is harmful to living organisms [40]. Our results show that the maximum UV–vis of ZnO NCs with different sizes and favipiravir interactions shows the peaks located wavelengths between 250 and 265 nm which corresponds to the near UV region and the closest visible light.
The bond order analysis of ZnO NCs with different sizes and favipiravir interactions was studied using Wiberg bond order (WBO), Mayer bond order (MBO) and Fuzzy bond order (FBO) methods. The values of WBI, FBO and MBO for the favipiravir on the (ZnO)22 NC were calculated about 0.432, 0.762, and 0.402, respectively, which are greater than other configurations (see Table 2, Fig. 8, and Fig. S1 in Supporting Information). WBI, FBO and MBO values also vary considerably based on the NC size and binding points of favipiravir molecule. Bond order values below 1.0 reflect the fact that bonds between O – Zn, N – Zn and F – Zn atoms exhibit dual covalent and ionic natures. Besides, the presence of metal ions bonded to oxygen atoms means that the O – Zn bonds are kind of polarized covalent bonds. The Mulliken charge distribution of the atoms in the ZnO NCs with different sizes and favipiravir interactions is also tabulated in Table 2 and shown in Fig. S1 (in Supporting Information). As can be seen from Table 2, the positive charge of the O – Zn interactions has been calculated between 0.304 and 0.360 |e| which are significantly bigger than the other positive charges of N – Zn and F – Zn interactions.
Table 1
The calculated binding energy per atom (Eb), adsorption energy (Ead), vertical ionization potential (VIP), vertical electron affinity (VEA), HOMO and LUMO energies, band gap energy (Eg) and reactivity parameters for pure and favipiravir adsorbed ZnO NCs. Ead in kcal/mol. Electronic properties are described in eV.
| (ZnO)12 | (ZnO)15 | (ZnO)18 | (ZnO)20 | (ZnO)22 | (ZnO)24 |
| Pure | Ads. | Pure | Ads. | Pure | Ads. | Pure | Ads. | Pure | Ads. | Pure | Ads. |
Eb | 5.04 | - | 5.08 | - | 5.11 | - | 5.13 | - | 5.15 | - | 5.16 | - |
Ead | - | -29.36 | - | -29.50 | - | -34.27 | - | -27.14 | - | -31.04 | - | -26.69 |
VIP | 8.40 | 7.46 | 8.13 | 7.29 | 8.03 | 7.53 | 7.99 | 7.31 | 7.80 | 7.25 | 7.84 | 7.25 |
VEA | 1.64 | 1.57 | 1.79 | 1.67 | 1.90 | 1.95 | 1.87 | 1.76 | 2.01 | 1.86 | 1.97 | 1.85 |
LUMO | -2.86 | -3.27 | -2.92 | -3.28 | -2.96 | -3.47 | -2.90 | -3.25 | -3.01 | -3.22 | -2.92 | -3.27 |
HOMO | -7.00 | -6.12 | -6.85 | -6.05 | -6.87 | -6.38 | -6.84 | -6.19 | -6.65 | -6.19 | -6.80 | -6.20 |
Eg | 4.14 | 2.85 | 3.93 | 2.77 | 3.91 | 2.91 | 3.94 | 2.94 | 3.64 | 2.97 | 3.88 | 2.93 |
ΔEg(%)* | - | 31.16 | - | 29.52 | - | 25.58 | - | 25.38 | - | 18.41 | - | 24.48 |
η | 2.07 | 1.43 | 1.97 | 1.39 | 1.96 | 1.46 | 1.97 | 1.47 | 1.82 | 1.49 | 1.94 | 1.47 |
ΔNtot | 2.38 | 3.29 | 2.49 | 3.37 | 2.51 | 3.38 | 2.47 | 3.21 | 2.65 | 3.17 | 2.51 | 3.23 |
*ΔEg(%) denotes the changes after adsorption. |
Table 2
Bond orders (Wiberg bond index; WBI, Fuzzy bond order; FBO, Mayer bond order; MBO) and Mulliken charges based on interactions between O – Zn, N – Zn and F – Zn atoms (The O, N, and F atoms indicate favipiravir, the Zn is the closest neighbors to these atoms; see Supporting Information Fig. S1 for detail).
Configurations | | Interactions | | WBI | | FBO | | MBO | | Charge |
Drug – (ZnO)12 | | 27O --- 19Zn | | 0.414 | | 0.732 | | 0.363 | | 0.321 |
| 35N --- 19Zn | | 0.189 | | 0.369 | | 0.115 | | 0.072 |
| 34F --- 6Zn | | 0.056 | | 0.105 | | 0.072 | | 0.064 |
Drug – (ZnO)15 | | 33O --- 30Zn | | 0.415 | | 0.732 | | 0.365 | | 0.325 |
| 41N --- 30Zn | | 0.195 | | 0.378 | | 0.117 | | 0.074 |
| 40F --- 7Zn | | 0.031 | | 0.041 | | 0.042 | | 0.039 |
Drug – (ZnO)18 | | 39O --- 25Zn | | 0.370 | | 0.675 | | 0.334 | | 0.304 |
| 47N --- 9Zn | | 0.373 | | 0.636 | | 0.259 | | 0.241 |
| 46F --- 9Zn | | 0.042 | | 0.079 | | 0.087 | | 0.085 |
Drug – (ZnO)20 | | 43O --- 19Zn | | 0.426 | | 0.750 | | 0.409 | | 0.358 |
| 51N --- 19Zn | | 0.089 | | 0.167 | | 0.061 | | 0.061 |
| 50F --- 16Zn | | 0.145 | | 0.312 | | 0.187 | | 0.169 |
Drug – (ZnO)22 | | 47O --- 33Zn | | 0.432 | | 0.762 | | 0.402 | | 0.360 |
| 55N --- 33Zn | | 0.067 | | 0.119 | | 0.029 | | 0.033 |
| 54F --- 25Zn | | 0.175 | | 0.371 | | 0.229 | | 0.199 |
Drug – (ZnO)24 | | 51O --- 16Zn | | 0.405 | | 0.725 | | 0.370 | | 0.338 |
| 59N --- 16Zn | | 0.172 | | 0.338 | | 0.092 | | 0.053 |
| 58F --- 22Zn | | 0.041 | | 0.060 | | 0.045 | | 0.040 |
To get an insight into the non-covalent interactions (NCI) within the studied systems, the NCI isosurfaces for favipiravir adsorbed (ZnO)12, (ZnO)15, (ZnO)18, (ZnO)20, (ZnO)22, (ZnO)24 NCs are investigated and plots for studied systems are shown in Fig. 9. As can be seen, disk-shaped blocks that indicate non-covalent interactions and the strongest H-bonds are observed near NH2 within the favipiravir molecule. Furthermore, the reduced density gradient (RDG) scatter plots for favipiravir adsorbed ZnO NCs were presented in Fig. 10. RDG scattered points indicate H-bonding interactions on the negative scale (blue color), indicating the dominance of the effect of strong attractive interactions. The green region in the range of ρ = 0.00 and ρ = −0.02 also shows the dominance of the effect of Van der Waals forces between binding atoms. Red areas indicate strong repulsive/steric interactions in a range of 0.01 and 0.05.