Singlet Fission - Department of Chemistry

B Chemical Reviews, XXXX, Vol. xxx, No. xx Smith and Michl
Millicent Smith received her B.A. in chemistry in 2002 from Tufts University.
In 2007 she earned her Ph.D. in physical chemistry from Columbia
University under the supervision of Professor Louis Brus. Her graduate
work included the synthesis and characterization of nanocrystalline barium
titanate. She is currently a postdoctoral fellow in the group of Professor
Josef Michl at the University of Colorado at Boulder. Her current research
focuses on the photophysics of singlet fission chromophores.
A somewhat similar process, involving the successive
emission of two longer-wavelength photons after excitation
by absorption of a single higher-energy photon, is known
for inorganic chromophores, especially rare earth ions, under
the name quantum cutting. 3-5
The multiple exciton generation process known in quantum
dots of inorganic semiconductors and reviewed elsewhere
in this thematic issue 6 may also have a related physical origin
even though it occurs within a single but much larger
“chromophore” in which singlet and triplet excitations have
nearly identical energies and are not readily differentiated.
This is particularly true in the presence of heavy elements
and strong spin-orbit coupling, where the spin quantum
number is not even approximately meaningful. In spite of
the obvious differences between singlet fission in organic
materials and multiple exciton generation in quantum dots,
certain features of the theoretical treatment of the former
given in section 2 are related to one of the theories proposed
for the latter. 7 Unlike singlet fission, multiple exciton
generation in quantum dots inevitably faces stiff competition
with conversion of electronic energy into vibrational energy
followed by vibrational cooling.
We review only the literature dealing with organic
chromophores (singlet fission), from the time of the initial
discovery of the phenomenon to the present day. An
extensive review of the subject appeared in 1973, 1 and the
most recent update we are aware of is found in a 1999 book
chapter. 2
1.1. Singlet Fission
Singlet fission is spin-allowed in the sense that the two
resulting triplet excitations produced from an excited singlet
Figure 1. Singlet fission: (1) The chromophore on the left
undergoes an initial excitation to S1. (2) The excited chromophore
shares its energy with the chromophore on the right, creating a T1
state on each.
are born coupled into a pure singlet state. Singlet fission can
therefore be viewed as a special case of internal conversion
(radiationless transition between two electronic states of equal
multiplicity). Like many other internal conversion processes,
it can be very fast, particularly in molecular crystals. There,
when it is isoergic or slightly exoergic and the coupling is
favorable, the transformation occurs on a ps or even sub-ps
time scale, competing with vibrational relaxation and easily
outcompeting prompt fluorescence. Only excimer formation
and separation into positive and negative charge carriers
appear to have the potential to be even faster under favorable
circumstances.
In the absence of any interaction between the two
triplets, the singlet 1 (TT), triplet 3 (TT), and quintet 5 (TT)
states that result from the nine substates originating in
the three sublevels of each triplet would have the same
energy. In reality, there will be some interaction and the
1 (TT), 3 (TT), and 5 (TT) states will not be exactly degenerate.
As long as they are at least approximately degenerate,
they will be mixed significantly by small spin-dependent
terms in the Hamiltonian, familiar from electron paramagnetic
resonance spectroscopy (EPR). In organic molecules
that do not contain heavy atoms, these terms are
primarily the spin dipole-dipole interaction, responsible
for the EPR zero-field splitting, and the Zeeman interaction
if an outside magnetic field is present. Hyperfine interaction
with nuclear magnetic moments, responsible for the
fine structure in EPR spectra, is also present but is weaker.
In molecular crystals, where triplet excitons are mobile,
its effect averages to zero if exciton hopping is fast on
the EPR time scale. Spin-orbit coupling is present as well,
but in molecules without heavy atoms it is weak and is
normally negligible relative to the spin dipole-dipole and
Zeeman interactions.
The nine eigenstates of the spin Hamiltonian are not of
pure spin multiplicity. The wave function of the initially
formed pure singlet state 1 (TT) is a coherent superposition
of the wave functions of these nine sublevels, and their
ultimate population will reflect the amplitude of the singlet
1 (TT) wave function in each one. As long as the states
resulting from singlet fission are of mixed multiplicity, the
overall process can also be viewed as a special case of
intersystem crossing (radiationless transition between two
electronic states of different multiplicities).
There is an interesting difference between intersystem
crossing induced by singlet fission, primarily as a result
of the existence of spin dipole-dipole interaction, and
the much more common intersystem crossing induced by
spin-orbit coupling. Unlike the spin-orbit coupling
operator, which connects singlets only with triplets, the
spin dipole-dipole interaction is a tensor operator of rank
two, and it has nonvanishing matrix elements between
singlets and triplets, as well as between singlets and
quintets. Therefore, singlet fission has the potential for
converting singlets into both triplets and quintets efficiently,
thus expanding the Jablonski diagram as shown
in red in Figure 2. Excited quintet states of organic
chromophores with a closed-shell ground state have never
been observed to our knowledge. In the singlet fission
literature they are usually dismissed as too high in energy,
but this need not be always justified.
Why is it, then, that singlet fission has remained relatively
obscure, and all textbooks and monographs dealing with
organic molecular photophysics show a version of the