A Quantum-Mechanical Theory of Light Absorption of Organic Dyes and Similar Compounds

The most important organic compounds which absorb visible light can be classified into three groups typified: (a) by symmetrical polymethines, (b) by porphyrines, (c) by polyenes. Recently it was shown that the position of the absorption maxima of symmetrical polymethines and related compounds (symmetrical cyanine and oxanole dyes; Michler's hydrol blue and derivatives; malachite green and other triphenyl methane dyes; etc.) can be calculated by adopting a model of the dye molecule which is analogous to the free-electron gas model used in particular by Sommerfeld to describe the condition of metals. The π-electrons of the polymethine chain are considered as a one-dimensional free-electron gas which extends itself along the length of the chain. In the normal state the stablest energy states of the electron gas each contain two electrons in accordance with Pauli's exclusion principle. The remaining states are empty. The existence of the first absorption band is a consequence of the jump of a π-electron from the highest energy level occupied in the normal state to the lowest empty level. For the wave-length of the maximum of the first absorption band of this group of dyes, the relationship obtains that λ1=(8mc/h)(L2/N+1),where L is the length of the polymethine zig-zag chain, N, the number of π-electrons, m, the mass of the electron, c, the velocity of light, h, Planck's universal constant. Good agreement with experimental results for λ1 is obtained by the use of this equation. The problem of porphyrine and phthalocyanine compounds can also be dealt with on the basis of a free-electron gas model. We treat the π-electrons of the porphyrine ring as electrons which are confined to move in a closed ring-shaped path in a field of constant potential energy. In the case of polyenes and related compounds (Carotenes, unsymmetrical cyanines and oxanoles, merocyanines, azo- and stilbene dyes, etc.) a description by means of a free-electron gas model is no longer permissible. The electron gas in this case suffers a disturbance from its condition in the case of the first and second groups of dyes, and, to allow for this, the π-electrons are considered placed in a one-dimensional potential having a sine curve periodicity. The wave-length λ1 is expressed by λ1=V0hc(1−1N)+h8mcN+1L2−1,where V0 is the amplitude of the sine-shaped potential along the chain. This relation is confirmed by the experimental data. It also gives an explanation for the markedly different manner (compared with the symmetrical polymethines) in which the position of the absorption bands of polyenes and related compounds depends on the chain length. The results of the classical color theory of Witt are capable of a simple explanation when considered in the light of the electron gas model.