Organic-inorganic hybrid semiconductor $\mathrm{Zn}\mathrm{Se}{({\mathrm{C}}_{2}{\mathrm{H}}_{8}{\mathrm{N}}_{2})}_{1∕2}$ under hydrostatic pressure is studied using a first-principles pseudopotential method with mixed-basis set, aimed at understanding its structural, mechanical, and electronic properties. The bulk modulus of the hybrid is determined to be $35.3\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, which is considerably smaller than that of bulk ZnSe and, in fact, smaller than most known tetrahedral bulk semiconductors. We find that, when the hybrid is exposed to pressure, the chemical bonds of the inorganic constituent, not those of the organic constituent, are significantly compressed. This is important and allows the band-edge electronic properties of hybrid chalcogenides to be effectively tuned by applying pressure, since these properties can be substantially modified only by changing the inorganic $\mathrm{Zn}\text{\ensuremath{-}}\mathrm{Se}$ bonds. Our calculations further demonstrate that the pressure dependence of the band gap in hybrid semiconductor shows an unusual nonlinearity, with a bowing coefficient that is more than one order of magnitude larger than in bulk ZnSe. Moreover, our results reveal that the in-plane electron mobility mass is notably small $({m}_{e}^{*}\ensuremath{\sim}0.27)$ and remains unchanged over a wide range of pressure. The hybrids will thus continue to maintain a fast electron mobility when they are under mechanical loading. However, and interestingly, the in-plane hole mass along the $x$ and $y$ direction is predicted to undergo at $2.14\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ a dramatic change from 0.35 to 2.2 and from 2.0 to 0.24, respectively. A pressure-induced isostructural phase transition is found to be responsible for this behavior of hole mass.
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