Singlet Fission - Department of Chemistry

X Chemical Reviews, XXXX, Vol. xxx, No. xx Smith and Michl
Table 4. Diffusion Coefficients in the ab Plane (Dab) and in the c
Direction (Dc) and In-Plane (Ψin) and Out-of-Plane (Ψout)
Hopping Rates
compd. ref Dab/cm 2 s -1 Dc/cm 2 s -1 Ψin/s -1 Ψout/s -1
2 85 b 4 × 10 -3 10 -6 6 × 10 12 6 × 10 7
2 85 b 4 × 10 -4 2 × 10 -6 7 × 10 11 10 8
2 85 b 6 × 10 -5 10 -7 10 11 10 7
2 101 5.3 × 10 -5 1.31 × 10 10 6 × 10 6
2 143 a 4.8 × 10 -2
2 146 2 × 10 -3
2 161 c 4 × 10 -3
2 162 3.3 × 10 -3
a Value for Dab was extrapolated to infinite temperature. b Several
sets of parameters were tried. c This value was calculated for the b
direction and may be viewed as a lower limit for Dab. We suspect that
it is the most reliable of the results reported.
In perusing the old literature on singlet fission in 2, the
reader needs to be aware of two potential pitfalls. The first
is minor, in that different authors favor different units for
first-order rate constants. Some use s -1 whereas others use
cm 3 s -1 , and the two are related by the density of molecules
of 2 in its crystal, 3.37 × 10 21 cm -3 . 155 We have converted
all results to s -1 . The second complication is more serious,
in that most of the published rate constants have been derived
using the approximate Johnson-Merrifield theory 17 and their
absolute values need to be taken with a large grain of salt
(section 2.1). Strictly speaking, the rate constants k-1 and k2
defined in eq 2 do not have separate significance and only
their ratio ε ) k2/k-1 is meaningful. The inadequacy of the
Johnson-Merrifield model for a quantitative description is
perhaps best illustrated by noting 90 that it permits a fit of
the dependence of fluorescence intensity of 2 on the
orientation of a static magnetic field both in the presence
and in the absence of microwave radiation, but the resulting
rate constants k-1 differ by an order of magnitude. Even
fitting to the more accurate Suna model 18 requires assumptions
that lead to considerable uncertainties. The widely
varying published values of singlet fission rate constants
(Table 3) clearly represent no more than order-of-magnitude
estimates. The most recent directly measured S1 lifetimes
favor the higher values among the previously reported rates.
The spread in the values of the diffusion coefficients
of triplet exciton determined for 2 by various methods is
huge (Table 4). Even though the numerical values of
parameters derived from fitting to approximate models are
of limited utility, it seemed worthwhile to summarize the
results because there is no reason to question the underlying
experimental data.
Thermally Activated Singlet Fission. An activation
barrier to fission is expected, since the process is slightly
endoergic. The best determination of the endoergicity probably
is the observation of the 0-0 transition of S0 f T1
excitation at 1.25 eV and that of S1 f S0 emission at 2.32
eV, yielding 0.18 eV for the activation energy. 103 Other
determinations of the 2E(T1) - E(S1) energy that appear
reliable range from 0.15 to 0.24 eV 14,78,85,103,104,152,162 (additional
old values of activation energy for fluorescence
quenching are 0.02 156 and 0.10 157 eV). Above 160 K, this
energy barrier can be overcome thermally fast enough for
fission to compete successfully with fluorescence, and at
room temperature, fission is believed to be the fate of nearly
all singlet excitons. This accounts for the low roomtemperature
fluorescence quantum yield of crystalline 2
(0.002) 158 compared with 1 (0.95). 131 A much higher value
of room-temperature fluorescence quantum yield (0.15) was
reported more recently by one set of authors, 153 possibly
because they were investigating another crystal form, but
the results may be unreliable since one of the authors was
subsequently shown to have falsified a large amount of other
experimental data. 159
Fluorescence. The fluorescence of single crystals of 2 has
been investigated by many authors. With ps pulsed laser
excitation, a fluorescence rise time of 12 ps and decay time
of 145 ps were found. 143 From the fluorescence decay time,
the fission rate constant was calculated to be 5.7 × 10 9 s -1
at 300 K and 1.7 × 10 13 s -1 at infinite temperature. From
the latter, the hopping rate in the ab plane is 10 13 s -1 , and
the diffusion coefficient for the ab plane (Dab, “in-plane”) is
4.8 × 10 -2 cm 2 s -1 , ∼100 times larger than for the c direction
(Dc, “out-of-plane”). The diffusion of triplet excitons is
known to be highly anisotropic, and Dab has been variously
reported to be 100-4000 times larger than Dc. 35,85,143 These
rates are important for the description of singlet fission by
the Suna model. 18
Using less intense synchrotron radiation, biexponential decay
was observed. 160 The fast component was fitted to a lifetime
of 0.2 ns and is consistent with other measurements. 143-145
The slow component had a lifetime of 1.7 ns and was later 37
attributed to a slow decay of triplet exciton pairs. The
authors 160 argued convincingly that a previously reported
even slower component of fluorescence with a 10-14 ns
lifetime observed at 77 K 144 and 100-300 K 145 was an
artifact due to nonlinear effects caused by high laser
excitation intensity (the original attribution was to emission
from a second level separated by 0.05 eV, 145 perhaps due to
a different crystalline form at grain boundaries, or a
monomer-like and a dimer-like form within the crystal). The
fast fluorescence decay obtained with synchrotron radiation 160
was later fitted 37 to the Suna diffusion model, 18 taking into
account the possibility of fusion of triplet exciton pairs into
a singlet exciton. The fit yielded an in-plane hopping rate
(Ψin) of2× 10 11 s -1 , an out-of-plane hopping rate (Ψout) of
2.8 × 10 9 s -1 , and a fission rate constant of 6.7 × 10 9 s -1 .
A later study of fluorescence decay in 2 using a series of
excitation densities separated the effects due to singlet exciton
annihilation. 146 The singlet exciton lifetime was 300 ps at
293 K. No slow component was observable in single crystals
of 2 (