C. Spectroscopy and Fluorescence of Pigments* 

 (Addenda to Chapters 21-24) 



1. Theory of Chlorophyll Spectrum 

 (Addendum to Chapter 21, Section A4) 



In Vol. II, Part 1 (pp. 619-635), a purely empirical discussion of regular- 

 ities in the spectra of porphin derivatives was given. Since then, several 

 papers have appeared dealing with the theoretical analysis of the spectra of 

 large conjugated bond systems in general, and of porphin and its deriva- 

 tives in particular. 



Simpson (1949), Kuhn (1949), and Nakajima and Kon (1952) used the 

 free-electron model; Piatt (1950'''-) and Longuet-Higgins, Rector and Piatt 

 (1950), the one-electron LCAO model (LCAO = linear combination of 

 atomic orbitals). They arrived, in general, at similar results concerning 

 the sequence of low excited states of porphin and tetrahydroporphin. 

 (These two molecules were treated, in preference to dihydroporphin, be- 

 cause of their simpler symmetry — D4h in porphin and Doi, in tetrahydro- 

 porphin.) 



The basis of all theoretical considerations in this field is the well-founded 

 postulate that ring systems such as porphin, containing a closed sequence 

 of conjugated double bonds, are, similarly to benzene, naphthalene, etc., 

 rigid planar structures. Their chromophoric properties are due to the 

 excitation of the so called " x-electrons" in the conjugated ring system — 

 electrons which can be considered as belonging to this system as a whole, 

 rather than to an individual atom. In the more nearly circular porphin 

 structure (fig. 37C.1A), the electric dipole oscillations corresponding to the 

 combination of the ground state with the low excited states, while confined 

 to the plane of the ring system, are not further restricted ("polarized") in 

 respect to any special direction in this plane. An electron in a round 

 potential box therefore provides an appropriate first approximation for 

 the analysis of the term system of porphin and its derivatives, such as proto- 

 chlorophyll — although the side chains, particularly such containing double 

 bonds conjugated with the main ring system, may strongly affect the close- 

 ness of the approximation. In the more elongated tetrahydroporphin 



* Bibliography, page 1882. 



1793 



