  Luminescence lifetimes of Ruthenium (II) polypyridine compounds is thought to
be controlled by the barrier to conversion of triplet metal-ligand charge
transfer ($^{3}$MLCT) state to a non-luminescent triplet metal-centered
($^{3}$MC) state. This work builds on earlier work [J. Photochem. Photobiol. A
276, 8 (2014)] and [J. Photochem. Photobiol. A 348, 305 (2017)] that derived
several orbital-based luminescence indices of which the third (LI3) was based
upon frontier-molecular-orbital-like ideas and correlated linearly with values
of $E_{ave}$. $E_{ave}$ is a large underestimate of the true
$^3$MLCT$\rightarrow$ $^3$MC TS barrier height in the case of the tris
bipyridine ruthenium(II) cation {[Ru(bpy)$_3]^{2+}$}, but accurate TS barrier
heights are difficult to obtain experimentally, it was judged useful to verify
the ideas used to derive the LI3 index by calculating the energetics of the
gas-phase $^{3}$MLCT $\rightarrow$ $^{3}$MC reaction for four complexes
$\{$[Ru(N$^\wedge$N)$_3$]$^{2+}$ with N$^\wedge$N = bpy ({6}), 4,4'-dm-bpy
({70}), 4,4'-dph-bpy ({73}), and 4,4'-DTB-bpy ({74}) $\}$ using the same
density functional and basis sets used in calculating LI3. We examine the trans
dissociation mechanism in detail at the B3LYP/6-31G+LANLDZ(Ru) level and
uncover a two-part mechanism. In the first part, the electron is transferred to
a single ligand rather than symmetrically to all three ligands. It is the two
Ru-N bonds to this ligand which are equally elongated in the transition state.
The intrinsic reaction coordinate then continues down a ridge in hyperspace and
bifurcates into one of two symmetry-equivalent $^3$MC structures with elongated
trans bonds. Interestingly, no significant difference is found for the TS
barriers for the four complexes treated here. Instead, LI3 is linearly
correlated with the energy difference $\Delta$ E = E($^{3}$MLCT) - E($^{3}$MC).
