A. Nitzan, Tel Aviv University ELECTRON TRANSFER AND TRANSMISSION IN MOLECULES AND MOLECULAR JUNCTIONS AEC, Grenoble, Sept 2005. Lecture 2. Grenoble Sept 2005. (1) Relaxation and reactions in condensed molecular systems Kinetic models Transition state theory
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Coming March 2006
WIDE BAND APPROXIMATION
Born solvation energy
tD=10 ps tL=125 fs
(1) Increase in the kinetic energy (localization) – seems NOT to affect dynamics
(2) Non-adiabatic solvation (several electronic states involved)
Diffusion controlled rates
Low friction limit
High friction limit
Transition State theory
(1) Equilibrium in the well
(2) Every trajectory on the barrier that goes out makes it
THIS IS AN UPPER BOUND ON THE ACTUAL RATE!
Quantum barrier crossing:
Coming March 2006
Electron transition takes place in unstable nuclear configurations obtained via thermal fluctuations
Solvent polarization coordinate
Alternatively – solvent control
Adiabatic and non-adiabatic ET processes
(For diabatic surfaces (1/2)KR2)
Correlation between the fluorescence lifetime and the longitudinal dielectric relaxation time, of 6-N-(4-methylphenylamino-2-naphthalene-sulfon-N,N-dimethylamide) (TNSDMA) and 4-N,N-dimethylaminobenzonitrile (DMAB) in linear alcohol solvents. The fluorescence signal is used to monitor an electron transfer process that precedes it. The line is drawn with a slope of 1. (From E. M. Kosower and D. Huppert, Ann. Rev. Phys. Chem. 37, 127 (1986))
We are interested in changes in solvent configuration that take place at constant solute charge distribution
They have the following characteristics:
(1) Pn fluctuates because of thermal motion of solvent nuclei.
(2) Pe , as a fast variable, satisfies the equilibrium relationship
(3) D= constant (depends on only)
Note that the relations E = D-4P; P=Pn + Pe are always satisfied per definition, however D sE. (the latter equality holds only at equilibrium).
Free energy associated with a nonequilibrium fluctuation of Pn
“reaction coordinate” that characterizes the nuclear polarization
Use q as a reaction coordinate. It defines the state of the medium that will be in equilibrium with the charge distribution rq. Marcus calculated the free energy (as function of q) of the solvent when it reaches this state in the systems q =0 and q=1.
Marcus papers 1955-6
Miller et al, JACS(1984)
Marcus Nobel Prize: 1992
0.2-0.6 for highly conjugated chains
0.9-1.2 for saturated hydrocarbons
~ 2 for vacuum
Charge recombination lifetimes in the compounds shown in the inset in dioxane solvent. (J. M. Warman et al, Adv. Chem. Phys. Vol 106, 1999). The process starts with a photoinduced electron transfer – a charge separation process. The lifetimes shown are for the back electron transfer (charge recombination) process.
The integrated elastic (dotted line) and activated (dashed line) components of the transmission, and the total transmission probability (full line) displayed as function of inverse temperature. Parameters are as in Fig. 3.
Michel - Beyerle et al