Effects of Self-Assembled Aggregation on Excited States - Carotenoids: Physical, Chemical, and Biological Functions and Properties - page 143

φ 1 = 90º, φ 2 = 90º, κ = 1 φ 1 = 180º, φ 2 = 0º, κ = -2

FIGURE 8.4 Orientation factor for the card-pack and head-to-tail dimers.

where is the angle between the two interacting dipoles (van Amerongen et al. 2000). The specii c

cases of the card-pack and head-to-tail aggregates are shown in Figure 8.4. Although

θ

θ = 0° for

, gives different values of V 12 for the
two mutual orientations of the transition dipoles. Thus, although in both cases it is the E 1 exciton
component that gains the dipole strength according to Equation 8.8, for the card-pack aggregates,
E 1 is the upper exciton component ( V 12 positive), whereas for the head-to-tail aggregates, the E 1 level
is the lower exciton component ( V 12 negative), explaining the difference in absorption spectra of
H- and J-aggregates shown in Figure 8.5.

both arrangements, the analysis of the orientation factor, κ

8.3.1.3 Limitations
The dipole-dipole approximation as described above is valid only under certain conditions that
must be carefully considered when applying it to carotenoid aggregates. First, the approximation
is reasonable only when the distance R between the interacting molecules is larger than the size
of the charge distributions of individual molecules. This represents a signii cant problem in inter-
preting spectra of carotenoid aggregates, because distances between carotenoid molecules in the
aggregate are usually less than 10 Å (Zsila et al. 2001b, Billsten et al. 2005), whereas the length of
the conjugated backbone, which limits the distribution of -electrons, for most carotenoids, exceeds

this value. Consequently, although the dipole-dipole approximation is a useful tool to explain the
aggregation-induced changes in absorption spectra qualitatively, to obtain quantitative agreement

π

Energy (cm -1 )

40,000 35,000 30,000 25, 0 00 20, 0 00 15,000

1:4

H-b an d

3:2

1

EtOH

J-band

0

300 400 500 600 700

Wavelength (nm)

FIGURE 8.5 Absorption spectra of zeaxanthin: dissolved in pure ethanol (solid line), in ethanol/water
mixture with 1:4 ratio (dotted line), and in 3:2 ethanol/water mixture. Minor bands of the H-aggregate are
denoted by *.