Semilocal density functionals up to the generalized gradient approximation (GGA) level cannot accurately describe band gaps of bulk solids. Meta-GGA density functionals with a dependence on the kinetic energy density ingredient (τ) can potentially give wider band gaps compared with GGAs. The recently developed TASK meta-GGA functional yields excellent band gaps of bulk solids. The accuracy of the TASK functional for band gaps of bulk solids cannot be straightforwardly transferred to low-dimensional materials due to reduced screening in low-dimensional materials. We have developed mTASK from TASK by changing (a) the tight upper-bound for one or two-electron systems (h0X) from 1.174 to 1.29 and (b) the limit of the interpolation function fX(α → ∞) of the TASK functional that interpolates the exchange enhancement factor FX(s,α) from α = 0 to 1, so that mTASK has the screening appropriate for low-dimensional materials. These two conditions guarantee the increased nonlocality within the generalized Kohn-Sham scheme in the mTASK functional and yield a better description of band gaps of low-dimensional materials. We computed the band gaps of bulk solids from mTASK having a wide range of gaps such as Ge, CdO, ZnS, MgO, NiF, Ar. The improvement in the band gaps from mTASK is more consistent than TASK for the large-gaps crystals. We have studied the band structures in two forms of transition metal dichalcogenide (TMD) monolayers, i.e., monolayer hexagonal (1H) and monolayer trigonal (1T) and their nanoribbons. The mTASK functional systematically improves the band gaps and is in close agreement with the experiments or the hybrid level HSE06 density functional for 2D single-layer and nanoribbon systems. In the second part of this assessment, we explore the large tunability of band gaps and optical absorption of phosphorene nanoribbons under mechanical bending from first-principles. Bending can induce an unoccupied edge state in armchair phosphorene nanoribbons. The electronic and optical properties of nanoribbons drastically change because of this edge state. GW-Bethe–Salpeter equation calculations for armchair phosphorene nanoribbons at different bending curvatures show that the absorption peaks generally shift toward the high energy direction with increasing curvature. Our study suggests that bright excitons can also be formed from the transition from the valence bands to the edge state when the edge state completely separates out from the continuum conduction bands. We systematically study the role of the edge state to form bound excitons at large curvatures. Our analysis suggests that the optical absorption peaks of zigzag phosphorene nanoribbons shift toward the low-energy region, and the height of the absorption peaks increases while increasingthe bending curvature. In the third part of this assessment, we extend our study of phosphorene nanoribbons to MoS2 nanoribbons under bending from GW and Bethe-Salpeter equation approaches. We find three critical bending curvatures for armchair MoS2 nanoribbons, and the edge and non-edge band gaps show a non-monotonic trend with bending. The edge band gap shows an oscillating feature with ribbon width n, with a period of ∆n=3. The binding energy and the lowest exciton energy decrease with the curvature. The large tunability of optical properties of bent MoS2 nanoribbon is applicable in tunable optoelectronic nanodevices. / Physics