Nonadiabatic factors w<<1 are expected for intersystems
crossings between singlet and triplet states, which are formally
spin-forbidden processes. The extent of the prohibition depends
significantly on the spin–orbit coupling, and this in turn is related
to the atomic spin–orbit coupling constantzavailable from the
atomic spectra. The magnitude of the spin–orbit coupling
increases rapidly with the atomic number, and its effect on the
intersystems crossing rate is usually calledheavy-atom effect.
The heavy-atom effect of substituents introduced in a porphyrin
will depend on the substitution pattern and may be different for
S 1 !T 1 and T 1 !S 0 transitions. Thus, it should be possible to con-
trol the electronic factor to increase the triplet quantum yield
without compromising its lifetime. This hypothesis was
investigated in detail using variousmeso- andbeta-substituted
free-base and Mg, Zn, or Cd metalloporphyrins( 53 ). It was consid-
ered that the spin–orbit coupling of atoms in identical substitution
patterns gives additive contributions to the nonadiabatic factor
w¼w 0Xni¼ 11 þciz^2 i
(13)Appropriate consideration of the Franck–Condon factors using
Eq. (12) allowed for the fitting the intersystems crossing rates
of many diverse systems just by changing the coefficient affecting
the heavy-atom effect. It was possible to characterize each sub-
stitution patterns by a single value ofc, as shown in Table II.
Analysis of Table II shows that only closed-shell
metalloporphyrins or meso-TPPs with halogens in the ortho-
positions of the phenyl rings have stronger heavy-atom effects in
the rate of the S 1 !T 1 transition than in the rate of the T 1 !S 0
transition. Thus, these porphyrins can have long-lived triplet
states formed with nearly unit quantum yields. This is a much
desired property of PDT sensitizers because only triplet states
with tens of microseconds lifetimes in solution can quantitatively
react with molecular oxygen and produce ROS. These reactions
will be discussed in detail below, but the relevance of long-lived
excited states is obvious using simple kinetic arguments. Bimolec-
ular reaction rates of electronically excited porphyrins are limited
by diffusion and have to compete with their decay. Diffusion-con-
trolled rate constants of porphyrins approach 3 1010 M^1 s^1 in
water ( 54 ). The most ubiquitous quencher of electronically excited
states is molecular oxygen (^3
P
g
O
2 ), and its concentration in
air-equilibrated water is 2.9 10 ^4 M at 20C( 55 ). Thus, the reac-
tivity of porphyrins in their singlet states toward molecular oxy-
gen can be characterized by a first-order rate of 8.7 106 s^1.
DESIGN OF PORPHYRIN-BASED PHOTOSENSITIZERS 207