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Herein, we demonstrate that first-principles calculations can be used formapping electronic properties of two-dimensional (2d) materials with respect tonon-uniform strain. By investigating four representative single-layer 2dcompounds with different symmetries and bonding characters, namely2d-${MoS_2}$, phosphorene, ${\alpha}$-Te, and ${\beta}$-Te, we reveal that sucha mapping can be an effective guidance for advanced strain engineering anddevelopment of strain-tunable nanoelectronics devices, including transistors,sensors, and photodetectors. Thus, we show that ${\alpha}$-Te and ${\beta}$-Teare considerably more elastic compared to the 2d compounds with strong chemicalbonding. In case of ${\beta}$-Te, the mapping uncovers an existence of curiousregimes where non-uniform deformations allow to achieve unique localization ofband edges in momentum space that cannot be realized under either uniform oruniaxial deformations. For all other systems, the strain mapping is shown toprovide deeper insight into the known trends of band gap modulation anddirect-indirect transitions under strain. Hence, we prove that the standard wayof analyzing selected strain directions is insufficient for some 2d systems,and a more general mapping strategy should be employed instead.

First-Principles Mapping of the Electronic Properties of Two-Dimensional Materials for Strain-Tunable Nanoelectronics