EXCITATION OF POLYENES AND PORPHYRINS 



73 



This is followed by two or three distinct transitions of various intensities 

 at shorter wave lengths. Empirically and theoretically, the first few 

 strong transitions in such a spectrum have the same general properties 

 with respect to their electron distributions, polarizations, intensities, 

 change of intensities with cis-trans isomerism, and so on, regardless of 



.THEORETICAL f-g 



2000 



I 1 r 



3000 4000 



WAVE LENGTH, A 



5000 



6000 



Fig. 2-2. Spectra of symmetrical amidinium ions I, II, III: 



[N— C— (C=C)„— N]+ with N = 2/j + 3 = 5, 7, 9 



{from Si»ipson, 1948, and Koniy and Regner, 1930); corrected 500 A to violet to allow 

 for tetramethyl substitution. Michler's Hydro! Blue. (Brooker and Sprague, 1941.) 



whether the conjugated chain is a polyene, a phenyl or diphenyl polyene 

 (or naphthyl polyene if the chain is long enough), or a cyanine dye. We 

 may therefore use the same general theory to account for the long-wave- 

 length spectra of all these molecular types. 



THE FREE-ELECTRON MODEL 



The main features of the spectra are accounted for if we assume that 

 the 7r-electrons are simply confined to a line running the length of the 

 conjugated system — whether straight 

 or zigzag does not much matter. 

 If the atomic nuclei are equally 

 spaced along this line, the potential 

 field in which the electrons move 

 will look something like the lower 

 line in Fig. 2-3, with deep holes 

 near every nucleus. For simplicity, 

 we may approximate this potential 

 by the one-dimensional "square 

 well" shown by the straight line, 



with the potential constant and \^d^ 



equal to zero along the line and Fig. 2-3. Free-electron orbitals, ener- 

 rising to infinity at the ends. g^^^' ^^^ transitions for hexatriene. 



In such a potential well the permissible wave functions ^ are sine 

 functions, vanishing at the ends of the trough: 



(^ 



/ tVEN 



EVEN 



, /2 . nirx 



n = 1,2, 3, 



(2-1) 



