Optimized solution procedure of the G-particle-hole hypervirial equation for multiplets: application to doublet and triplet states.

Highly accurate descriptions of the correlated electronic structure of atoms and molecules in singlet states have recently been directly obtained within the framework of the G-particle-hole hypervirial (GHV) equation method, without any reference to the wave function [Int. J. Quantum Chem. 2009, 109, 3170; ibid. 2011, 111, 245]. Here, the GHV method is optimized and applied to the direct study of doublet and triplet atomic and molecular states. A new set of spin-representability conditions for triplet states has been derived and is also reported here. The results obtained with this optimized version of the GHV method are compared with those yielded by several standard wave function methods. This analysis shows that the GHV energies are more accurate than those obtained with a single-double excitation configuration interaction as well as with a coupled-cluster singles and doubles treatment. Moreover, the resulting 2-body matrices closely satisfy a set of stringent N- and spin-representability conditions.