  In our theoretical study in which we combine a nonequilibrium Green's
function (NEGF) approach with density functional theory (DFT) we investigate
branched compounds containing Ru or Os metal complexes in two branches, which
due to their identical or different metal centers are symmetric or asymmetric.
In these compounds the metal atoms are connected to pyridyl anchor groups via
acetylenic and phenyl spacer groups in a meta-connection. We find there is no
destructive quantum interference (DQI) feature in the transmission function
near the Fermi level for the investigated molecules regardless of their
symmetry, neither in their neutral states nor in their charged states. We map
the structural characteristics of the range of molecules onto a simplified
tight-binding model in order to identify the main differences between the
molecules in this study and previously investigated ferrocene compounds in
order to clarify the structural sources for DQI, which we found for the latter
but not for the former. We also find that local charging on one of the branches
only changes the conductance by about one order of magnitude which we explain
in terms of the spatial distributions and charge-induced energy shifts of the
relevant molecular orbitals for the branched compounds.
