27 : 4/ Quantum Mechanical Basis of Molecular Spectra 517 



some of their numerical values are specified by letters rather than 

 numbers. A large number of letters is summarized in Table IV in the 

 next subsection. Not only are many letters used but several have more 

 than one meaning. These letters are the language of quantum mechanics 

 and spectroscopy. If one wishes to discuss the nature of absorption 

 bands, it is customary to describe them in terms of these letters. 



Although the atomic electronic wave functions are simpler than the 

 molecular ones, they are by no means as simple as those describing mole- 

 cular rotations and vibrations. In order to designate an electron 

 within an atom completely, there are two sets of five numbers, either set 

 of which may be specified. Both include a total quantum number n, 

 an orbital quantum number /, and a spin quantum number s. There 

 are two possible choices for the other two numbers. One may specify 

 the projection of / and s on a given axis by the quantum numbers m t 

 and m s , or one may specify the total angular momentum by the quan- 

 tum number j and its projection on a given axis by m ; . 



These quantum numbers are restricted for an electron so that 



l-Ul 



•J-1,J 



The total quantum number n appears in the energy and in the eigen- 

 function. The others are all related to angular momenta in the same 

 fashion as J is to the rotational angular momentum of a molecule. For 

 example, if p s is the intrinsic momentum, then 



p s = shl2n 

 and 



p 2 = s(s+\)h 2 j47T 2 



Again, for the projection of the total angular momentum on the z axis 

 p 2 , one may write 



p z = mjh/27r and p 2 = m^Trij+l)^/^ 2 



Just as in the case of rotational and vibrational spectra, there are 

 selection rules for absorption and radiations involving electrical dipoles. 

 For a single electron change, these selection rules are 



M = ±1 



A^ = 



Aj = ±1,0 



