146 David L. Drabkin 



Notation. In the molecular interpretation of spectra, the frequency v (the 

 number of waves passing a fixed point in a unit time, as 1 sec) is of more 

 fundamental interest than the wavelength I. A term closely related to the 

 frequency is the wavenumber v (the number of waves in a unit of length, as 

 1 cm). The relationship between )' and v is given by v = v x c, where 

 c = 3 X 10^° cm/sec, the speed of light, and the relationship between v 

 in cm~^ and X in vnfx is given by r = (l/A) x 10^. Thus A500 vo-fx corresponds 

 Xov = 20,000 cm~^. It is convenient to use v X 10~^, and most of the graphs 

 are so plotted. Anotherterm, the fresnel,/, has been employed. /= v X 10~^^. 

 Hence, v x 10~^ =fl^- The absorption curves are plotted logically against v 

 in ascending order from left to right, which is in the descending order with 

 reference to A (cf. Drabkin, 1950). 



The Graphic Analysis of the Absorption Spectrum Curves. In their analysis 

 of the visible absorption spectrum of permanganate Hagenbach and Percy 

 (1922) made the assumption that the component bands (represented by 

 maxima in the spectrum) could be resolved into individual simple curves, all 

 of the same shape, but of different height. The shape of the curves was 

 determined by the curvature of the slope at the lowest frequency end of the 

 absorption curve. The summation of the resolved curves yielded the absorp- 

 tion spectrum curve. Erode (1928) used effectively a similar method of 

 analysis for the spectrum of CoClg. The spectra of these relatively simple 

 molecules could be regarded as possessing essentially one broad band in 

 which the multiple maxima represented a finer structure (Harrison, Lord and 

 Loofbourow, 1948). The general character of the absorption spectra of the 

 haemin chromoproteins is very different from that of KMn04 or CoCL, in 

 HCl (see Figs. 1 and 4), and the spectrum curves could not be shown to be 

 reproduced by a summation of component curves of the same shape, varying 

 only in height. 



A highly satisfactory resolution of the complex haemin-protein spectrum 

 curves has, however, been attained (Drabkin, 1937, 1938, 1940 and 1941a) 

 by assuming that the component elements (bands) did not have the shape of 

 simple curves but could be described by the 'bell-shaped' normal frequency 

 curves of the form 



;; = A: e ^ 2a== ; (1) 



or 



y = -tke:^ ^^^ 



q\ 2o^ ) 



The summation of unit curves of this type, each with different values for k 

 and a (Fig. 3), reproduced very accurately the original (determined) spectrum 

 curves. The families of curves in Fig. 3 are drawn for orientation to equation 

 (1). In such symmetrical curves the values of j and x on each side of the 



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