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) bX"porphyrines, (c) by polyenes. Recently it was shown tnat 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 ".-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 ".-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 AI= (8mc/h) (L2/[N+IJ),