The comparison between single-point energy scanning (SPES) and geometry optimization (OPT) in determining the equilibrium geometry of the a3∑u+ state for 7Li2 is made at numerous basis sets such as 6-311++G(2df), cc-PVTZ,6-311++G(2df, p), 6-311G(3df,3pd), 6-311++G(2df,2pd), D95(3df, 3pd), 6-311++G, DGDZVP, 6-311++G(3df,2pd),6-311G(2df,2pd), D95V++, CEP-121G, 6-311++G(d,p), 6-311++G(2df, pd) and 6-311++G(3df,3pd) in full active space using a symmetry-adapted-cluster/ symmetry-adapted-cluster configuration-interaction (SAC/SAC-CI) method presented in Gaussian03 program package. The difference of the equilibrium geometries obtained by SPES and by OPT is reported. Analyses show that the results obtained by SPES are more reasonable than those obtained by OPT. We have calculated the complete potential energy curves at these sets over a wide inteuclear distance range from about 3.0a0to 37.0a0, and the conclusion is that the basis set cc-PVTZ is the most suitable one. With the potential obtained at cc-PVTZ, the spectroscopic data (Te, De, Do, ωe, ωeχe, αe and Be) are computed and they are 1.006 eV, 338.71 cm-1,307.12 cm-1, 64.88 cm-1, 3.41 cm-1, 0.0187 cm-1 and 0.279 cm-1, respectively, which are in good agreement with recent measurements. The total 11 vibrational states are found at J=0. Their corresponding vibrational levels and classical tuing points are computed and compared with available RKR data, and good agreement is found. One inertial rotation constant (By) and six centrifugal distortion constants (Dy Hv, Lv, My, Nv and Ov) are calculated.The scattering length is calculated to be -27.138a0, which is in good accord with the experimental data.