We calculate the c (b) over bar mass spectrum, the splitting values and some other properties in the framework of the semirelativistic equation by applying the shifted large-N expansion technique. We use seven different central potentials together with an improved QCD-motivated interquark potentials calculated to two loops in the modified minimal-subtraction ((MS) over bar) scheme. The parameters of these potentials are fitted to generate the semirelativistic bound states of c (b) over bar quarkonium system in close conformity with the experimental and the present available calculated center-of-gravity (c.o.g.) data. Calculations of the energy bound states are carried out up to third order. Our results axe in excellent fit with the results of the other works.