BioPHYSICAL chemistry

However, under high light conditions, the
excess light cannot be used to form the
charge separated state but could result in
photodamage. To avoid such harmful
reactions, plants use nonphotochemical
quenching, which involves the xantho-
phyll cycle to quench the excess energy
(Figure 10.7). The process is termed
nonphotochemical since it is distinct
from the normal light-induced reactions. The mechanism is debated as
the quenching can arise either from an energy transfer from excited
chlorophyll to another molecule that could safely dissipate the energy or
by electron transfer followed by recovery to the ground state.
How are energy and electron transfer related to the change in caro-
tenoids? In the particle-in-a-box model, the energy of the electron, E, is
inversely proportional to the square of the length, L, of the box:

(10.39)

When the epoxide groups of the carotenoid are removed to form zeax-
anthin, the conjugated πsystem is extended from nine to 10 and then
11 double bonds. This has the effect of lowering the energy levels of the
carotenoid, so allowing the new reactions to occur.
To investigate these different possible reactions, scientists have performed
many different spectroscopic measurements. Recently, scientists have made
picosecond measurements of these processes on mutants with different
quenching capabilities (Holt et al., 2005). The resulting spectra were
consistent with the formation of an oxidized carotenoid under quenched
conditions, and hence the mechanism may involve electron transfer.

Two-dimensional particle in a box

Although the problem of a one-dimensional particle in a box may be suit-
able for simple conjugated polyenes, most molecules are more complex.
Many biological complexes are composed of amino acid residues with con-
jugated rings, such as tyrosine, or even large cofactors such as chlorophylls.
Theoretical treatment of these molecules requires the additional dimen-
sions to be considered. The properties of particles confined to two- or three-
dimensional boxes can be solved following the approach used for the
one-dimensional case.
Consider a particle confined to a rectangular area where the potential
is zero, with the potential being infinite outside the box (Figure 10.8).
Schrödinger’s equation becomes:

E

L

∝

1

2

CHAPTER 10 PARTICLE IN A BOX AND TUNNELING 207



*

*

Chlbulk

664 nm

Chl-Zea Chl• Zea• Chl-Zea

Figure 10.7A

possible mechanism

of energy quenching

in the xanthophyll

cycle. Chl,

chlorophyll;

Zea, zeaxanthin.

Modified from

Holt et al. (2005).