Calculation of Electron Transfer Rate Constants from Emission Spectra in Re(I) Chromophore−Quencher Complexes

Abstract

The photophysical properties of the chromophore−quencher complexes, fac-[(4,4‘-R2bpy)ReI(CO)3(LA)] n + (4,4‘-R2bpy = 4,4‘-R2-2,2‘-bipyridine, R = Me or t Bu, and LA = the quinone acceptor ligands, benz[g]isoquinoline-5,10-dione (BIQD), 2-oxy-1,4-naphthoquinone anion (ONQ-), 1/2 2,6-dihydroxyanthraquinone dianion (AFA2-), or the pyridinium acceptor, 1-methyl-6-oxyquinoline (OQD)) in 1,2-dichloroethane are described. Following ReI → 4,4‘-R2bpy metal-to-ligand charge transfer (MLCT) excitation, intramolecular electron transfer leads to the transients, fac-[(4,4‘-R2bpy)ReII(CO)3(LA•-)] n+. They have been characterized by emission spectral fitting and transient absorption measurements and, for LA = OQD, by transient infrared measurements. As shown by analysis of excited-state emission, there is weak-to-moderate electronic coupling between the electron donor and acceptor sites in the transients with H DA varying from 153 cm-1 for the BIQD complex to 3.9 cm-1 for the OQD complex. The transients are redox-separated (RS) states with the electronic configurations dπ5πLA* for BIQD or σ(Re−O)1πLA*1 for ONQ-, AFA -, and OQD. They are weak emitters and return to the ground state largely by nonradiative decay which occurs by back electron transfer (k ET). Reasonable agreement has been reached between k ET and values calculated from kinetic parameters derived by emission spectral fitting and excited-state decay. The RS states for the AFA2- and OQD complexes are remarkably long-lived (τ = 4 μs for LA = AFA2- in DCE at 296 K and 16 μs for LA = OQD in DCE at 296 K) due to orbital and spin restrictions on back electron transfer.

The Golden Rule. Application for fun and profit in electron transfer, energy transfer, and excited-state decay

“…Intramolecular electron transfer (dp Re 5 p* bpy 1dp Re gives the corresponding Redox Separated (RS) states, [Re II (4,4 0 -R 2 bpy)(CO) 3 (LA À )] + . 69,103,104 In these assemblies the RS states lie deeply in the inverted region with energy-coordinate curves that are embedded in the energy-coordinate curves of the ground state. They share this property with excited states but the two differ in significant ways.…”

“…Application of the Golden Rule to nonradiative decay leads to eqn (69) with V k the vibrationally induced electronic coupling matrix element and FC the usual Franck-Condon density of states.…”

“…In this approximation l includes both solvent (l o ) and low-frequency modes treated classically, l L , with l = l o + l L . [61][62][63][64][65][66][67][68][69][70][71] IðñÞ ¼…”

“…33,35,50,[87][88][89][90][91][92][93][94][95][96] With one coupled medium-or high-frequency mode (or averaged mode), only the v i = 0 vibrational level is appreciably populated at room temperature ( ho c k B T), and k ET is given by eqn (29). 30,35,69,80,84,97,98 In these equations, the pre-exponential square root term is the classical density of states defining the number of classical reaction channels available for electron transfer to occur with energy conservation.…”

“…40,50,90 However, these bands are not experimentally observable because of their low oscillator strengths and were calculated instead from radiative decay rate constants, k r , by use of eqn (38). 69 In eqn (38), E abs in cm À1 , is the absorption band energy, d is the electron transfer distance, and h n À3 i is defined in eqn (39). I(ñ) is the emission intensity at frequency ñ.…”