Biology Reference

In-Depth Information

As we focus the discussion on the relaxation of
S
1
to
S
0
, ISC and also all

photochemical pathways are neglected, since, except from ESPT, the associated

rate constants are too small to distort the conclusions drawn in this chapter

for FPs.

Internal conversion is a generic term, which comprises different pathways, but

the mechanism is similar for all of these relaxation channels. In any case, the large

molecular excess energy, which corresponds to the energy difference

E
between

the ground and the excited state (between 160 and 300 kJ mol
1
in the visible range

of the electromagnetic spectrum) has to be released. Although energy dissipation to

the surrounding finally occurs by collisions, we will consider here only intramolec-

ular processes, which refer to the chromophore itself. It should be noted, however,

that the irreversibility of the transition
S
1
!

D

S
0
is ensured by the mentioned energy

dissipation. This is even true for ISC, which is, at first, an isoenergetic passage from

one electronic state to another followed by rapid IC, as depicted in Fig.
1
in a

simplified manner.

The most straightforward approach to IC is to consider a pair of potential

functions, each for one electronic state (see Fig.
3
). For the sake of simplicity, we

Fig. 3 Internal conversion and energy-gap law. The two singlet state
S
0
and
S
1
are described

by harmonic oscillators along most coordinates
q
i
, as done in (a) and (b), but separated by the

energy gap
D

E
.(a) The radiationless transition from
S
1
to
S
0
depends on the overlap between

the vibrational ground state wave function (
v

¼

0) of
S
1
(
light grey
) and the higher vibrational

state (
v

¼

7) of
S
0
. Upon decreasing

D

E
by lowering e.g. the energy of
S
1
, overlap with a lower

vibrational state (here
v

¼

5) is established. (b) The overlap, i.e., the product of the
S
1
wavefunc-

tion
v

7(
dark grey
), respectively, is

integrated over the whole coordinate yielding the Franck-Condon integral
f
FC
. Negative and

positive values of the product cancel to a large extent.
f
FC

¼

0 with the
S
0
wavefunctions
v

¼

5(
black
)or
v

¼

¼

0 if there is no geometrical change

upon excitation, i.e.,

D

q
i

¼

0, but increases with increasing

D

q
i
. Although both overlap functions

look similar, the integral for
v

7 in the depicted

example. The rate constant for internal conversion,
k
ic
, is proportional to the square of the

integrated overlap, i.e., the Franck-Condon factor
f
FC
is 100

¼

5 is ~10

larger than the integral for
v

¼

smaller for the larger change of

v
.(c) A reduction of

E
can also occur by one-bond rotations. As the stiffness of the protein

surrounding restricts the torsion to small movements - the
grey bars
symbolize the conformational

latitude -, only twisted structures (
light grey
) of chromophores can reach regions in the excited

state with smaller

D

D

E
. Chromophores locked in planar structures (
dark grey
) maintain large

energy gaps

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