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 approximately 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, beta, 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 x 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 x 10(-6), and 1.4 x 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 beta 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 beta (10 nm(-1)) for the PF(6)- salt crystal.