Electron density, exchange-correlation density, and bond characterization from the perspective of the valence-bond theory. I. Two simple analytical cases

In this work, using a valence-bond wave function we obtain analytical expressions for the first- and second-order reduced density matrices of two simple, but quite representative, cases of diatomic molecular systems, namely, H2 and LiH. A detailed study of their exchange-correlation density is performed for both equilibrium and nonequilibrium internuclear distances, discriminating the parallel- and antiparallel-spin contributions. The results show that the behavior of the exchange-correlation density clearly changes with the character of the bond, making it possible to obtain a good deal of information regarding the type of the bond interaction.