586 



TABLE 625.— MOLECULAR CONSTANTS OF DIATOMIC MOLECULES* 



The energy, E, of a molecule is the sum of three contributions, the electronic energy, 

 E„ the vibrational energy, E v , and the rotational energy, E r , i.e., 



E = E e + E v + Er (1) 



The electronic energy, E e , gives the largest contribution and is entirely similar to the 

 energy of atoms. Similar to S, P, D states of atoms, one distinguishes 2, n, A, . . . 

 states of diatomic molecules depending on whether the electronic orbital angular momentum 

 about the intei nuclear axis is 0, 1, 2 ... in units of h/2ir. Just as for atoms the resultant 

 electron spin 6 determines the multiplicity (2S + 1) of the electronic state which is added 

 to the term symbol as a left superscript. 2 states are designated 2 + or 2" depending 

 on whether their eigenfunctions remain unchanged or change sign upon reflection at a 

 plane through the internuclear axis. For molecules with identical nuclei (such as N», H 2 , 

 O2, . . .) a subscript g or u indicates whether the eigenf unction upon reflection at the 

 center remains unchanged or changes sign (e.g. 1 2„ + , * S u + , 1 n„, . . .). 



In each electronic state the molecule may have various amounts of vibrational energy. 

 Quantum mechanics shows that for diatomic molecules the vibrational energy is given by 



|^ = G (v) = w e (v + i) - «. x e (v + i) 2 + . . . (2) 



where v is the vibrational quantum number which can assume the values 0, 1, 2, . . . and 

 where w e is the (classical) vibrational frequency (in cm" 1 ) for infinitesimal amplitudes. 

 The constant w e x e is small compared to w e and is due to the anharmonicity of the vibration. 



If the vibrational energy is increased more and more, a point is reached at which the 

 two atoms fly apart, that is, the molecule is dissociated. The dissociation energy, Do, 

 corresponds to the maximum of the function G (v) and can in many cases be determined 

 from the spectrum. 



In each vibrational level the molecule may have various amounts of rotational energy. 

 For diatomic molecules, in the simplest case ('2 state), the rotational energy is given by 



jf c = F(J) = B v J(J + l)-. . . (3) 



where / is the rotational quantum number which may take the values 0, 1, 2, . . . and 

 where B v is the so-called rotational constant which is slightly different for different 

 vibrational levels of a given electronic state : one has 



B v = B. - a. (v + i) + . . . (4) 



Here a„ is small compared to the rotational constant B e which refers to the equilibrium 

 position. For Be one finds 



Be = 5—5 5 (5) 



Sir 2 c fir e 



Here m = ■ is the reduced mass of the molecule with wji and m 3 the masses of 



Wi -f- tn 2 



the two atoms, and r e is the internuclear distance in the equilibrium position. The product 

 v-r? is the moment of inertia of the molecule ; in other words, Be, apart from universal 

 constants, is the reciprocal moment of inertia. 



Each electronic state of a diatomic molecule is characterized by a certain set of values for 

 the vibrational and rotational constants o> e , u e x e , . . . , Do, r„ Be, a,, . . . . These con- 

 stants have been determined for a large number of diatomic molecules in various electronic 

 states from the analysis of band spectra. A comprehensive and up-to-date table may be 

 found in "Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules," 

 by G. Herzberg (Van Nostrand. New York, 1950). The following table is an excerpt 

 from the compilation just mentioned, but brought up to date, 1953. Here only the constants 

 <»e, D °, and r e for the ground states are listed and the type of the ground state is given. 

 From r e the rotational constant B e can be obtained according to the formula (5) given 

 above. D ° corresponds to dissociation into normal atoms. The values are given in ev 

 (electron-volts) where 1 ev corresponds to 8068.3 cm" 1 . The numbers on the element sym- 

 bols give the mass numbers of the isotopic species to which the constants refer.' When no 

 mass number is given the data refer to the ordinary isotopic mixture. With the exception 

 of the hydrogen molecule in each case only the data for one isotopic species are listed. 



More detailed explanation of the underlying theory, the methods of determination of 

 these constants and references for each individual molecule may be found in the book 

 already quoted. 



* Prepared by G. Herzberg, National Research Council of Canada. 



SMITHSONIAN PHYSICAL TABLES 



