CHAPTER 2 



Electronic Structure and Excitation of Polyenes 



and Porphyrins 



John R. Platt 



University of Chicago 



Polyenes: The free-electron model — Emission of light — Photoisomerism — Effect of 

 substitution — Ring-chain syste7ns. Porphyrins: Porphin — Structure of the visible bands 

 — Effect of substitutions — Light emission — Electron density and excitation. References. 



This chapter might be entitled: "Why grass is green, butter yellow, 

 and blood red." It will deal with polyenes and porphyrins, the com- 

 pounds responsible for these colors. These are probably the two most 

 important classes of biological pigments. 



To understand the colors requires knowledge of the electronic structure 

 of each compound and its connection with the absorption of light in the 

 visible and near-ultraviolet regions of the spectrum. Three principal 

 theoretical methods of investigation have been applied to this problem: 



1. The valence bond or resonance method (Pauling, 1945; Wheland, 

 1944) ; 



2. The LCAO ("Linear Combination of Atomic Orbitals") molecular- 

 orbital method (Mulliken, 1939; Roothaan, 1951); and 



3. The free-electron molecular-orbital method (Bayliss, 1948, 1949a, b, 

 1950, 1952; Kuhn, 1948a,b, 1949a,b, 1950; Simpson, 1948, 1949; Platt, 

 1949, 1953b; Ruedenberg and Scherr, 1953; Scherr, 1953). 



The last of these methods is the most recent, the least known, and in 

 many respects the simplest of the three. It will be the basis of the theo- 

 retical treatment in the present discussion. A review of this method is 

 given by Bayliss (1952), and a later bibliography is given by Ruedenberg 

 and Scherr (1953). 



The exact general correspondence between the first two methods was 

 recently shown by Longuet-Higgins (1950a) and Dewar and Longuet- 

 Higgins (1952). Ruedenberg and Scherr (1953) have shown an even 

 more detailed correspondence between the last two methods. Conse- 

 quently results obtained by one method are expected to be valid for all, 

 except for numerical details. 



An exhaustive bibhography of the free-electron method would run to 



71 



