Light Absorption in Ordered Structures

Abstract

The probability of absorption of a photon by a molecule (at a given wavelength) can be represented as the ratio of two areas [6, 58, 59]:

$$ P = \delta /X $$

(2.1)

where δ is the absorption cross-section, i. e. “the area impermeable for a photon” [6], and X is the cross-sectional area of the molecule; δ does not exceed X. δ(Ų) should be converted to the molecular extinction coefficient E(Ų) The conversion from δ to E requires to multiply E by 2.3, i.e., δ=2.3E. The value 2.3 arises from replacing natural logarithms by decimal ones [58, 59]. E(Ų) can be converted directly to the molar extinction coefficient ε (M^−lcm⁻¹). There is a direct conversion of the dimension Ų into M^−lcm⁻¹, for instance, 1 Ų=6×10⁷ cm³/6×10²³ cm = 6×10⁴ litre/mol cm = 60000 M^−lcm⁻¹. To take into account the dependence of absorbing ability of the chromophore on its orientation [6, 60–62], the orientation factor (q) should be included in the equation. Finally, instead of the ambiguous parameter X, which is not strictly defined [6], it is necessary to use the more exact parameter — area of density of the electrons which is responsible for optical transition, i. e. the cross-section of the valence electrons (S). Now we can rewrite (2.1) as follows [63]:

$$ P = 2.3Eq/S $$

(2.2)

S is described as the projection of maximum cross-section of electron density responsible for a given optical transition. S can be predicted by quantum-chemical methods [64] or obtained from low-temperature x-ray analysis [65]. The typical values of the area for single bonds between carbon, hydrogen, oxygen or nitrogen atoms and for lone electron pairs on oxygen or nitrogen atoms are 0.32–0.91 Ų [64]. For double and conjugate bonds between carbon atoms, S is about 0.9–1.5 Ų per bond. A value of S for a molecule is obtained by summing all the elementary electron cross-sectional areas (cross-sections of electron density) participating in the absorption of a photon by the chromophore.