Carbyne material with sp-hybridized atoms has been considered as a one dimensional structure with unique properties which has been widely used in nanotechnology. In the presented work the effect of electron overlap energy in the form of electron interaction with in the unit cell and nearest neighbors is explored. In addition, the band structure variation under proposed interaction in one dimensional carbyne is investigated. The effect of overlap energy variation inside and outside the unit cell on the band gap is intended. Under proposed structure the effective mass and density of states parameters are explored. It is demonstrated that by increasing the interaction between s and p orbitals in the unit cell, the band gap increases. However, the band gap is decreased by increasing the interaction between s and p orbitals out the unit cell which can be sued as a sensing mechanism.