Dichalcogenides of transition metals are attractive material due to its unique properties.In this work,it has been investigated the electronic band structure, phonon spectrum and heat capacity of MoS2 under the applied tensile and compressive strain using the density functional theory. The Molybdenum disulfide under compressive (tensile) strain upto 6% (10%) has stable atomic structure without any negative frequencies in the phonon dispersion curves. The tensile strain reduces the energy gap in the electronic band structure and the optical-acoustic gap in phonon dispersion curves. The tensile strain also increases the specific heat capacity.On the other hand , the compressive strain in this material increases phonon gap and reduces the heat capacity and the electronic band gap.The phonon softening/hardening is reported for biaxial tensile/compressive strain in MoS2.We reportphonon hardening for out of plane ZA mode in the presence of both tensile and compressive strains.Resultsshow thatthe linear variation of specific heat with strain (CV ) and square dependency of specific heat with the temperature (CV T2)forlow temperature regime.The results demonstrate that the applied strain tunes the electronic energy gap and modifies the phonon spectrum of MoS2.

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