Energy spectra and the expectation values of diatomic molecules confined by the shifted Deng-Fan potential

The approximate bound state solutions of the Schrodinger equation with shifted Deng-Fan potential was obtained via proper quantization rule. The energy spectra for the homogenous diatomic molecules (H2, I2); the heterogeneous diatomic molecules (CO, HCl, LiH); the neutral transition metal hydrides (ScH, TiH, VH, CrH); the transition-metal lithide (CuLi); the transition-metal carbides (TiC, NiC); the transition- metal nitrite (ScN) and the transition-metal fluoride (ScF) were calculated. By applying Hellmann-Feynman theorem, the expression for the expectation values of the square of inverse of position, potential energy, kinetic energy and the square of momentum were derived and the numerical values for diatomic molecules were presented. The result is reliable and very consistent with the available ones in the literature.