Rates of electronic excitation hopping in anisotropic ionic crystals of [Ru(2,2'-bipyridine)3]X2 (X = ClO4-, PF6-, SbF6-); Monte Carlo simulation of single- and multi-exponential emission decays.

Emission decays of triplet metal-to-ligand charge transfer states in anisotropic crystals of [Ru 1 - x Os x (bpy) 3 ]X 2 (bpy = 2,2'-bipyridine, X = PF 6 - , ClO 4 - , SbF 6 - , and 0.115 > x > 0.001) at ∼300 K were measured by means of time-correlated single-photon counting. Rates of excitation hopping calculated on the basis of an interaction between transition dipoles of a donor cation and an acceptor cation are insufficient to simulate the single-exponential decays (x = 0.0099) and the multiexponential decays (x = 0.060 and 0.115) of the PF 6 - salt crystals. A limiting rate of excitation hopping to an imaginary cation at the van der Waals distance via a super-exchange interaction between d orbitals through the bpy ligands was determined to be 0.83 x 10 10 s -1 on average by means of a step-by-step Monte Carlo simulation, assuming an distance-attenuation factor, p, of the exchange interaction of 10 nm -1 . The total rate of excitation hopping via both a dipole-dipole mechanism and a super-exchange mechanism to the neighboring sites of the cation was calculated to be 5.4 × 10 9 s -1 for the PF 6 - crystal. Anisotropic diffusion constants estimated from the hopping rates and lengths in the PF 6 - crystal are 9.3 x 10 -6 , 9.1 × 10 -6 , and 1.4 × 10 -6 cm 2 s -1 along the a axis, the b axis, and the c axis, respectively, which are compared with an isotropic diffusion constant, 1.3 x 10 -6 cm 2 s -1 , estimated from the pseudo-bimolecular rate constant of excitation transfer to [Os-(bpy) 3 ] 2+ , using an isotropic Smoluchowski equation. A multiexponential emission decay of [Ru 0.885 Os 0.115 (bpy)3]-(PF 6 ) 2 was also simulated to determined the limiting rate of excitation transfer to [Os(bpy) 3 ] 2+ at the van der Waals distance (2.6 x 10 11 s -1 ). The magnitude of β determined is 6.5 and 11.5 nm -1 for the ClO 4 - and the SbF 6 - salt crystals, respectively, on reference to that of β (10 nm -1 ) for the PF 6 - salt crystal.