## 3 Results and Discussions
### Ultraviolet-Visible Spectroscopy and Ab Initio Calculations  
The optical study of the \(\alpha\)-MnO\({}_{2}\) nanowires was conducted by employing UV-Vis spectroscopy to record diffuse reflectance spectra in the 300 nm \(\div\) 800 nm range. The formation of the two types of \(\alpha\)-MnO\({}_{2}\), black and brown, are validated by a lower reflectance curve for the black \(\alpha\)-MnO\({}_{2}\) when compared to the brown \(\alpha\)-MnO\({}_{2}\), knowing that the black materials absorb more light in the visible spectrum range than materials with lighter colors, including brown. According to the theory of [PERSON]. [PERSON] and [PERSON], presented in 1931, the measured reflectance spectra can be transformed into the corresponding absorption spectra by applying the Kubelka-Munk function [46]. Figure 4a shows the reflectance and calculated absorbance spectrum of black (a) and brown (b) \(\alpha\)-MnO\({}_{2}\) nanowires transformed according to [PERSON] et al. [46] and plotted against the wavelength. For both samples, broad absorption bands extending from 400 to 550 nm with a peak location of 400 nm were detected. The absorption in the visible light range is caused by the d2d transitions of Mn ions in \(\alpha\) -MnO\({}_{2}\) nanowires. In the ligand field of MnO\({}_{6}\) octahedra, the Mn 3d energy level separates into lower (t2\({}_{g}\)) and higher (eg) energy levels, and the energy difference  
Figure 3: Raman spectra of black (**a**) and brown \(\alpha\)-MnO\({}_{2}\) (**b**). between the eg and t2g states is responsible for the optical bandgap energy [47]. The Tauc plot gives an estimate of the bandgap energy. Band-to-band transition in oxide depends on the absorption coefficient \(\alpha\) and photon energy by the following relation--(Equation (3)):  
\[(\alpha\text{h}\
u)^{\text{n}}=\text{A}\left(\text{h}\
u-\text{Eg}\right) \tag{3}\]  
where A is the constant, hv is the photon energy, and \(\alpha\) is the absorption coefficient, while n = 2 for direct and n = 1/2 for indirect transition, depending on whether they are allowed or forbidden, respectively. The experimental curve was fitted to obtain the band gap semiconductor absorption function with n = 1/2 for direct band gap energy values and n = 2 for indirect band gap energy values. The calculated values of the direct energy band gap from Figure 4b lie in the range of 1.70-2.05 eV. The values obtained for the indirect energy band gap lie within 0.60-1.0 eV. The value Eg is calculated by plotting \((\alpha\text{h}\
u)^{2}\) vs. \((\text{h}\
u)\). The graph \((\alpha\text{h}\
u)^{2}\) versus the photon energy has a linear region, which can be extrapolated to the abscissa to yield the bandgap energy. The region showing a steep, linear increase in light absorption with increasing energy characteristic of semiconductor materials. Figure 4b shows the Tauc [48] relation, \((\alpha\text{h}\
u)^{2}\) vs. photon energy (hv) for the determination of optical band gap (Eg) related to the allowed direct transition of black and brown \(\alpha\text{-MnO}_{2}\) associated with \((\alpha\text{h}\
u)^{1/2}\) vs. photon energy (hv) for the determination of the optical band gap (Eg) related to the allowed indirect transition of black and brown \(\alpha\text{-MnO}_{2}\). The calculated values for direct transitions are near 2.0 eV for both materials, which indicates wide bandgap energy, suggesting that the activation of the obtained \(\alpha\text{-MnO}_{2}\) toward photocatalytic and semiconductor properties is given by light absorption in the visible range. The bandgap calculated for indirect transitions for brown and black \(\alpha\text{-MnO}_{2}\) are in 0.6-1.0 eV range. Notable variations in the bandgap energies of \(\alpha\text{-MnO}_{2}\) were previously observed. For example, [PERSON] et al. noticed a bandgap of 3.82 eV in \(\alpha\text{-MnO}_{2}\) thin films [49]. The shift in the bandgap to higher energies can be attributed to the carrier confinement in the small semiconductor particles.