Density matrix variational theory: Application to the potential energy surfaces and strongly correlated systems

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, $H4,$ $H2O,$ $NH3,$ $BH3,$ CO, $N2,$ $C2,$ and $Be2.$ 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.