516 Quantum Mechanical Basis of Molecular Spectra /27 : 4 



relative amounts of a few similar compounds (for example, steroids) 

 present in a given fraction or sample. 



4. Electronic Levels of Atoms and Molecules 



Rotational and vibrational spectra involve the relative motion of atoms 

 or groups of atoms. It is also possible to change the energy levels of an 

 electron within a molecule without changing the location of the atoms. 

 In the most general case, a transition of the electronic-energy level is 

 accompanied by a change in vibrational and rotational levels. Sym- 

 bolically, the energy change may be represented as 



^E = AE r + AE V + A£ e (11) 



This predicts the existence of bands of bands of lines about any spectral 

 line representing an electronic change. In the liquid and solid states, 

 these bands of bands of lines are all smeared out into one continuous 

 absorption band for each electronic change. The absence of sharp lines 

 is due to interactions of the various parts of the same molecule and to 

 collisions with the solvent molecules or with the neighboring molecules. 

 These interactions and collisions may either add or subtract small 

 amounts AE t to the photon energy AE in Equation 1 1 , resulting 

 in a continuous absorption band. 



The details of the qualitative nature of electronic-energy levels of 

 molecular spectra are very similar to those of atomic spectra. Because 

 the atomic spectra are somewhat less complicated they are described 

 first. The same types of quantum numbers exist for the electronic- 

 energy levels of both atoms and molecules. However, only the atomic 

 wave functions can be computed exactly. 



A. Electronic Spectra of Atoms 



The electronic-energy levels of atoms can be found from a knowledge of 

 the numbers of electrons and the charge on the nucleus. The wave 

 functions for one-electron atoms such as H, D, T, He + , Li + + , Be + + + , 

 and so on, can be represented exactly in closed form. So can the electron 

 wave functions for two-electron atoms such as He, Li + , Be ++ , B + + + , 

 and so on. In all other cases, iterative approximation methods allow 

 one to come as close as desired to the eigenfunctions, energy levels, and 

 spectral lines. 



Atomic wave functions for isolated atoms can be used to derive very 

 exact expressions for the wavelengths of absorption and emission lines. 

 Five quantum numbers are used to specify the energy state of each 

 electron. These numbers are represented by certain letters. Also, 



