The main purpose of this paper is to report results of quantum mechanical calculation of the H-2 system using the q-Integral method with correlation corrections to the SCF (Self Consistent Field) wave functions included through the Moller-Plesset second-order perturbation (MP2) and Coupled-Cluster (CC) theory. Using the q-Integral method, we evaluated potential energy curves, rovibrational spectroscopy constants, rovibrational spectra, interatomic equilibrium distance and longitudinal static hyper(polarizability). All calculations were carried out through the STO-3G, STO-6G, and double-zeta (DZV) atomic basis set. The q-Integral method was implemented in the Source code of the general ab initio quantum chemistry package GAMESS.