Calculation of Electron-Transfer Rate Constants in the Inverted Region from Absorption Spectra

Abstract

Nanosecond transient absorption spectroscopy was used to measure back-electron-transfer rate constants kb in the series [(4,4'-(X)2bpy'-)Re1(CO)3(py-PTZ'+)]+ with X = C02Et, C(O)NEt2, H, Me, MeO, NH2 and also the 2,2'-bipyrazine (bpz) and 3,4,7,&tetramethyl-1,lO-phenanthroline (Medphen) complexes in propylene carbonate (PC). These states are formed following Re' -(4,4'-(X)zbpy) excitation and -PTZ -Re" electron transfer. The reactions occur in the Marcus inverted region and In kb varies linearly with AGO as predicted by the energy gap law. In the complexes with X = Me, MeO, and Me4phen, weak, ground-state absorption bands corresponding to ligand-to-ligand charge transfer (LLCT) transitions between py-PTZ and 4,4'-(X)2bpy or Me4phen were detected. These bands are not present in the spectra of the corresponding 4-ethylpyridine model complexes. From the Hush analysis of the ground state absorption bands, the electron-transfer matrix elements Hat, are 44 cm-l (X = Me), 51 cm-l (X = MeO), and 61 cm-l (Me4phen) with A,-,' = 0.4 eV in PC.XO' is the sum of the solvent reorganizational energy and the coupled low frequency vibrations treated classically. By combining Hab, A,-,' , and kinetic parameters obtained in the kinetic study, it is possible to calculate kb from a form of the energy gap law. The calculated values for kb are within a factor of 10 of the experimental values, e.g., kb = 3.1 X lo's-l, kb(ca1c) = 3.0 X lo8 s-l for x = Me. These results point to the feasibility of using absorption band measurements routinely to calculate electron-transfer rate constants in the inverted region.Hush has shown1 that in mixed-valence complexes and, more generally, for donor-acceptor pairs, quantitative relationships exist between optical and thermal electron transfer. In the classical limit with weak electronic coupling, the free energy of activation (AG*) is related to the absorption band energy ea^), thereorganizational energy (A), and the freeenergychange (AGO) bylJ The delocalization energy (Hab) from electronic coupling between donor and acceptor is related to the integrated absorption band intensity. For a Gaussian band, this relationship is given by' where e, , , is the molar absorptivity coefficient, ; , , , is the absorption maximum in cm-1, A i 1 p is the full width at halfheight in cm-I, and r is the distance separating the redox sites in angstroms. In principle, these relationships allow simple absorption band measurements to be used to calculate rate constants for electron transfer. This has been tested experimentally3 in a few cases in the normal region by comparing absorption band measurements with direct observation of electron transfer rate constants. Gould et al.3e have used emission spectra and quantitative measurement of radiative decay to calculate back electron transfer rate constants following photoexcitation of donor-acceptor pairs. We report here an application of the Hush approach to electron transfer in the inverted region in a molecular assembly.In earlier papers4 the role of driving force, solvent,...

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

“…Application of the Hush analysis gave V DA B44 cm À1 for [Re I (4,4 0 -Me 2 bpy)(CO) 3 (py-PTZ)] + and 51 cm À1 for [Re I (4,4 0 -(MeO) 2 bpy)(CO) 3 (py-PTZ)] + . 116 Parameters for calculating k BET were evaluated by a combination of spectral analysis, Raman spectroscopy, and electrochemical measurements with application of eqn (36). Once again, agreement between observed and calculated rate constants was remarkable.…”

“…(33), ln k BET was found to vary linearly with DG 0 ET (and E 0 ) over a range of DG 0 ET values from 1.5-2.2 eV. 116 In highly concentrated solutions, weak py-PTZ -4,4 0 -X 2 bpy, Ligand-to-Ligand Charge Transfer (LLCT), absorption bands are observed in the visible. As shown in Scheme 2, these transitions lead directly to the ligand-based RS states.…”

Long-range photoinduced electron transfer dynamics in rigid media

“…Back electron transfer occurs deeply in the inverted region with |DG BET | c l. In this region the driving force dependence assumes an energy gap law form with ln k varying linearly with the driving force. 44,104,105 An additional factor that may contribute or even dominate back electron transfer is hole (oxidative equivalent) migration by site-to-site hopping, D + + D -D + D + , followed by rapid re-oxidation of [Ru(bpy) 3 ] + .…”

Flash Photolysis and Chemistry of Transients and Excited States

“…Experimental results and theoretical expectations have been found to be in good agreement. 91,92 It must be noted that optical transitions to LLCT and MLCT excited states are not always being observed in the spectrum of a complex. It has been stated that direct optical transfer between the donor and the acceptor has a low probability; that is, the transition will have a small oscillator strength, when there is negligible overlap between the orbitals involved in the transition.…”

“…It has been stated that direct optical transfer between the donor and the acceptor has a low probability; that is, the transition will have a small oscillator strength, when there is negligible overlap between the orbitals involved in the transition. 92,93 A further property associated with the radial displacement of charge associated with CT electronic transitions is a change in the dipolar moment of the molecule. If the electronic transition causes, for example, an increase in the dipolar moment, the energy of the CT excited state will decrease (other factors aside) with the polarity of the solvent.…”