## 3 Results and Discussions
### Ultraviolet-Visible Spectroscopy and Ab Initio Calculations
We consider that the \(\alpha\text{-MnO}_{2}\) nanowires might have a similar effect because of their small feature sizes on diameters. Based on the above results, we can realize that MnO\({}_{2}\) nanowires can be potentially used for devices where the absorption of visible light such as solar cells and photocatalysts are required. First-principles density functional theory calculations were used to investigate \(\alpha\text{-MnO}_{2}\); the structure containing a framework of the corner- and edge-sharing MnO\({}_{6}\) octahedra with  
Figure 4: (**a**)—Diffuse reflectance and absorbance spectra vs. wavelength, recorded for the black (a) and the brown \(\alpha\text{-MnO}_{2}\) (b). (**b**)—Plot of \((\alpha\text{h}\
u)^{2}\) and \((\alpha\text{h}\
u)^{1/2}\) vs. (hv) for the black and brown \(\alpha\text{-MnO}_{2}\), with optical band gaps determination. tunnels in between with the view along the tetragonal axis is shown in Figure 5, showing the 2 \(\times\) 2 tunnels. The Mn-O bond distances in each octahedra are approximately four of 1.93 and two of 1.91 A. The antiferromagnetic order is shown by the different shading of the Mn O octahedra. We can see that the columns of edge-sharing octahedra have ferromagnetic coupling, but have antiferromagnetic coupling to the nearest corner sharing octahedra. This is the antiferromagnetic order found more stable in previous calculations [50]. We calculated the bandgap and density of states using ab initio calculations, using the generalized gradient approximation of Perdew, Burke, and Ernzerhof (PBE) [51], PBE + U with U = 4 eV for the Mn d electrons, and screened hybrid functional from Heyd, Scuseria and Ernzerhof HSE06 [52], using norm-conserving pseudopotentials [51; 53] with quantum espresso [54; 55]. PBE is a semi-local density functional that provides reasonable properties; however, it usually underestimates band gaps. The DFT + U considers an additional correction that can improve the description of correlated systems. We have used the Dudarev approach [56]. HSE06, which calculates exact exchange at short-range, generally improves upon PBE, and particularly the band gaps are much closer to the experiment, but at a higher computational cost. Experimental lattice parameters were used and the ionic forces were minimized to values less than 3.3 mRy/ au in the PBE approximation [57] with ferromagnetic spin polarization. The structure was left fixed for the other calculations, with both ferromagnetic and antiferromagnetic orders. The density of states is shown in Figure 6a. A bandgap of \(\sim\)2.4 eV can be seen for the FM case, with a slightly larger gap of 2.7 eV for the AFM case. The values are higher than the experimental gaps. While quantum confinement in small-diameter nanowires is expected to increase the bandgap concerning bulk samples, our periodic calculations overestimate it; the difference could be due to excitonic effects, which are known to be large in nanowires [58]. PBE and PBE + U result in bandgaps closer to our experimental values, and close to 0.9 eV for the FM state and 0.8 eV for the AFM state. The PBE + U results in the band gap of 1.3 eV, also close to our experimental indirect band gap for the black sample and in line with a different calculation [50] and a different measurement [39]. The PBE + U DOS is shown in Figure 6b, in this case also with projections of the main states contributing to the density of states, Mn3d and Op. O states have a more important contribution close to the top of the valence band, but otherwise both states contribute similarly in the energy range shown. Figure 5: MnO\({}_{2}\) plane view perpendicular to the tetragonal axis. The unit cell used in the calculation is shown by the black borders. The oxygen atoms are red, and the purple/blue shade represents Mn octahedra with up/down spins in the antiferromagnetic order.