A R T I C L E S
Kang et al.
and reduction potentials (vs SCE) of benzene (E1/20/+ ) 2.30 V;
-/0
E1/2 ) -3.35 V)45,46 differ significantly from those deter-
-/0
mined for nucleobases [e.g., E1/20/+(guanine) ) 1.24 V; E1/2
(cytosine) ) -2.42 V],47 the comparatively soft decay of CS
and CR rate constants in the (1-3)a-Zn series (Figure 4) with
increasing D-A distance, relative to that observed for D-Sp-A
assemblies based upon oligonucleotide scaffolds, is exceptional
in light of the McConnell relation,48 as the tunneling energy
lies several electronvolts from the medium frontier orbitals.49
(3) Reaction energetics50,51 suggest that these CS and CR
reactions are near barrierless only for 2a-Zn.52,53 This fact,
coupled with the expected distance dependence of λS,54-57
suggests that the pure electronic â values should be further
diminished with respect to the phenomenological âCS and
â
CR values extracted from the data shown in Figure 4. (4) The
Figure 4. Distance dependence of the CS and CR rate constants for
(1-3)a-Zn in methylene chloride at 23 ( 1 °C. Slopes of the straight
line plots shown give âCR ) 0.35 ( 0.16 Å-1 (CR) and âCS ) 0.43 Å-1
(CS) [R0 ) 2.97 Å; k0 ) 1.1 × 1012 s-1 (CR); k0 ) 8.5 × 1013 s-1 (CS)].
Given the adiabatic nature of CS in 1a-Zn, âCS was computed using the
relevant data points for 2a-Zn and 3a-Zn only. Error bars for each
experimental rate constant are shown. Note that the lower limit of the
error bar for the CS rate constant of 1a-Zn corresponds to the fastest rate
constant that we can resolve (5 × 1013 s-1); the width of this error bar is
arbitrary. The error reported in âCR was determined via standard linear
regression analysis.
magnitude of kCS/kCR is unusual (>60) for 1a-Zn, given
that the driving forces for CS and CR are predicted to be
approximately isoergic.52
(41) Sachs, S. B.; Dudek, S. P.; Hsung, R. P.; Sita, L. R.; Smalley, J. F.; Newton,
M. D.; Feldberg, S. W.; Chidsey, C. E. D. J. Am. Chem. Soc. 1997, 119,
10563-10564.
(42) Davis, W. B.; Svec, W. A.; Ratner, M. A.; Wasielewski, M. R. Nature
1998, 396, 60-63.
(43) Helms, A.; Heiler, D.; McLendon, G. J. Am. Chem. Soc. 1992, 114, 6227-
6238.
(44) Osuka, A.; Maruyama, K.; Mataga, N.; Asahi, T.; Yamazaki, I.; Tamai, N.
J. Am. Chem. Soc. 1990, 112, 4958-4959.
expression that reflects the expected rapid decay of electronic
coupling with increasing donor (D)-acceptor (A) distance.2,6,13,14
Figure 4 highlights the distance dependence of the CS and CR
rate constants for the 1a-Zn, 2a-Zn, and 3a-Zn ET systems,
analyzed in terms of a simplified Marcus-Levich-Jortner
equation (eq 1).35-38 Here, the ET rate constant (kET) is assumed
(45) Osa, T.; Yildiz, A.; Kuwana, T. J. Am. Chem. Soc. 1969, 91, 3994-3995.
(46) Meerholz, K.; Heinze, J. J. Am. Chem. Soc. 1989, 111, 2325-2326.
(47) Seidel, C. A. M.; Schulz, A.; Sauer, M. H. M. J. Phys. Chem. 1996, 100,
5541-5553.
(48) McConnell, H. M. J. Chem. Phys. 1961, 35, 508-515. The McConnell
relation predicts that â (1/R) ln(∆E/T), where R is the nearest-neighbor
spacing, ∆E is the tunneling energy gap, and T is the nearest-neighbor
electronic interaction.
(49) Lee, M.; Shephard, M. J.; Risser, S. M.; Priyadarshy, S.; Paddon-Row, M.
N.; Beratan, D. N. J. Phys. Chem. A 2000, 104, 7593-7599.
(50) Marcus, R. A. J. Chem. Phys. 1965, 43, 679-701.
(51) Weller, A. Z. Phys. Chem. N. F. 1982, 133, 93-98.
(52) The Gibbs energies for charge separation (∆GCS) and charge recombination
(∆GCR) were estimated using the following equations,
kET ) k0 exp[-â(RDA - R0)]
(1)
to be dependent upon the magnitude of the maximal rate
constant at D-A contact (k0), an exponential decay parameter
(â), and the difference between the D-A separation distance
(RDA) and the smallest possible reactant separation (R0), which
for these systems is taken as 2.97 Å.26 Note that because the
magnitude of the ET rate constant for CS in 1a-Zn greatly
exceeds that of the fastest component of solvent relaxation
(∼1013 s-1),39 it was considered adiabatic and thus was not
factored into our determination of âCS (Figure 4).
-(∆GCS) ) E(0,0)(MP) - E1/2(MP/MP+) + E1/2(A-/A) - ∆G(ꢀ) (i)
∆G(ꢀ) ) (e2/4πꢀ0)[(1/ꢀS){1/(2RD) + 1/(2RA) - 1/RDA} -
(1/ꢀT){1/(2RD) + 1/2RA)}] (ii)
-(∆GCR) ) E(0,0) + ∆GCS
(iii)
where E(0,0) is the energy of the lowest excited singlet state [(1a-3a)-Zn )
1.88, 2.05, and 2.05 eV, respectively],
1/2(MP/MP+) is the one-
E
electron oxidation potential of the PZn unit [(1a-3a)-Zn ) 0.83, 0.84, and
0.82 V, respectively], E1/2(A-/A) is the Q one-electron reduction potential
[(1a-3a)-Zn ) -0.60, -0.58, and -0.56 V, respectively], and ꢀT is
the static dielectric constant for the high-dielectric solvent in which
the potentiometric measurements were obtained. The estimated energetics
for these CS and CR reactions are thus ∆GCS(1a-Zn) ) -0.90 eV,
∆GCR(1a-Zn) ) -0.98 eV; ∆GCS(2a-Zn) ) -0.87 eV, ∆GCR(2a-Zn) )
-1.18 eV; ∆GCS(3a-Zn) ) -0.82 eV, ∆GCR(3a-Zn) ) -1.23 eV.
(53) The solvent reorganization energy (λS) and the total reorganization energy
(λT) were calculated using
A number of aspects of these data deserve comment. (1)
Taking the extensive data set of distance- and driving force-
dependent ET rate data compiled by Lewis and Wasielewski
as benchmarks,6-10 it is clear that the magnitude of the
phenomenological ET distance dependence (â) for both the
CS and CR reactions in these systems (âCS ) 0.43 Å-1
;
âCR ) 0.35 ( 0.16 Å-1) is approximately a factor of 2
smaller than that determined in D/A-modified DNA hairpin
structures (âCS ) 0.7 Å-1; âCR ) 0.9 Å-1);10 interestingly, the
magnitude of these decay parameters is reminiscent of those
determined for several classes of highly conjugated organic
structures.40-44 (2) Considering that the one-electron oxidation
λS ) (e2/4πꢀ0)({1/(2RD) + 1/(2RA) - 1/RDA})[(1/ꢀOP) - (1/ꢀS)] (iv)
λT ) λS + λi
(v)
where RD is the PZn radius (5.5 Å), RA is the Q radius (3.2 Å), RDA is the
porphyrin plane-to-quinonyl centroid distance (1a-Zn ) 3.3 Å; 2a-Zn )
6.8 Å; 3a-Zn ) 10.5 Å), and ꢀOP and ꢀS are the optical and static dielectric
constants. This analysis estimates λS values for 1a-Zn, 2a-Zn, and 3a-Zn
as 0.24, 0.96, and 1.24 eV, respectively). The total inner-sphere reorganiza-
tion energy (λi) for (1a-3a)-Zn was estimated to be 0.4 eV using standard
methods (see, for example: Rubtsov, I. V.; Shirota, H.; Yoshihara, K. J.
Phys. Chem. A 1999, 103, 1801-1808).
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M. J. Phys. Chem. 1996, 100, 10337-10354.
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9
8278 J. AM. CHEM. SOC. VOL. 124, NO. 28, 2002