Fluorescence Lifetime of Fluorescent Proteins - Fluorescent Proteins: From Understanding to Design - page 74

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