electron transfer determined by solvent reorganization
energy red
ox
Eact ∆G
reaction coordinate Freitag, 20. November 2009
Quantitative descritpion Taylor series
f ' (a ) f '' (a) f ''' ( a) 2 3 f ( x) = f (a ) + ( x − a) + (x − a) + (x − a) + ... 1! 2! 3! Harmonic oscillator approximation
1 2 2 Vi = Gi + mω ( q − qi ) 2
2 1 2 Vf = G f + mω ( q − q f ) 2
Energy of activation
E act =
( λ + ΔG)
2
4λ
Energy of solvent reorganization
2 1 2 λin = mω (q f − qi ) 2
Free energy of reaction:
ΔG = G f − Gi
Freitag, 20. November 2009
Energy surfaces for the two-dimensional model
red
energy
ox+e-
q2
saddle point of reaction hypersurface q1 N
Vi ( f ) Freitag, 20. November 2009
1 2 i( f ) 2 = Gi ( f ) + ∑ mkω k (qk − qk ) k =1 2
N=2
Rate constant
E act k = A exp − = kB T 2 (λ + ΔG) = A exp − 4 λ k T B
λ >> ΔG
ΔG < 0 λ /10 - 7
18
4.10 -6
20
The reduced force constant for the C0(NH3)36 +/2+ couple was used in calculating the inner-sphere reorganization energy for the Co(bpy)33+/2+ couple.
Freitag, 20. November 2009
24.0
I
I
+ A
"1~-'o v 20.0
i
4
c=
i
I
%
-20
_c
13 16.0
H
2
)7 -30 12.0 0.006
I
I
0.010
0.014
0.018
I 120, n r n - I
Fig. 6. Plot of the logarithm of the precursor-corrected exchange rate constants as a function of 1/2a. (1), Ru(NH3) 3+/2+; (2), R u ( N H 3 ) 5 ( p y ) 3 + / 2 + ; (3), Ru(NH3)4(bpy)3+/2+; (4), R u ( N H 3 ) 2 ( b p y ) ] + / 2 + ; (5) Ru(bpy)] +/2+ . From Ref. 96.