The density matrix variational theory (DMVT) algorithm developed previously [J. Chem. Phys. 114, 8282 (2001)] was utilized for calculations of the potential energy surfaces of molecules, H-4, H2O, NH3, BH3, CO, N-2, C-2, and Be-2. The DMVT(PQG), using the P, Q, and G conditions as subsidiary condition, reproduced the full-CI curves very accurately even up to the dissociation limit. The method described well the quasidegenerate states and the strongly correlated systems. On the other hand, the DMVT(PQ) was not satisfactory especially in the dissociation limit and its potential curves were always repulsive. The size consistency of the method was discussed and the G condition was found to be essential for the correct behavior of the potential curve. Further, we also examined the Weinhold-Wilson inequalities for the resultant 2-RDM of DMVT(PQG) calculations. Two linear inequalities were violated when the results were less accurate, suggesting that this inequality may provide a useful N-representability condition for the DMVT.