512 Table 622 



MOLECULAR CONSTANTS OF DIATOMIC MOLECULES 



(From manuscript by E. D. McAlister, 1932.) 



Energy levels for molecules can be evaluated from their spectra, just as for atoms. 

 Widely spaced levels in molecules correspond roughly to those known for atoms, are 

 similarly designated (see " Notation for Spectra of Diatomic Molecules," R. S. Mulliken, 

 Phys. Rev., 36, 611, 1930) and are said to be related to the electronic configuration. A 

 system of bands arise from transitions from one (often multiple) electronic configuration 

 to another. 



Diatomic molecules have two other sets of levels in addition to the electronic. One is 

 due to the energy of mutual vibration of the two nuclei and the other to the energy of 

 rotation of the molecule as a whole. A distinct set of vibrational levels is associated with 

 each electronic state. The energy difference corresponding to each level of such a set from 

 that of the associated electronic state is obtained (approximately) by giving successive 

 positive integral values to n in the expression n(w — io X " + • • ■) ; x a positive constant. 

 The frequency of vibration (a>) is obtained by differentiating this with respect to n; 

 u=w (i — 2x11 +...). At the lowest level where the amplitude and energy of vibration 

 are vanishingly small, n = and w = w . A transition from one vibrational level to 

 another gives rise to a single band. 



A distinct set of rotational levels is associated with each vibrational level. The presence 



of large numbers of these closely spaced rotational levels gives rise to the many individual 



lines of the band. The rotational energy, relative to the associated vibrational level is 



2B 

 given (approximately) by B m 2 (1 — m 2 u 2 -\- ...); where u = and m is a parameter 



Wo 



which is zero for zero rotation. Usually BI = h/Sir 2 c — 27.70 X io~ 40 g. cm, where 

 / = moment of inertia of the molecule about an axis through its center of mass and per- 

 pendicular to the line joining its nuclei. For multiple levels this relation is not accurately 

 true. / varies with the vibrational energy, and becomes h when it is zero; the correspond- 

 ing nuclear separation is 70= VI /n where n= -. — — - — 2 —r- . j«o = mass of an atom of 



(Wli -f- VI2) 



unit atomic weight = 1.650 X io~ 24 g. mi, mi are the atomic weights of the two atoms 

 composing the molecule. 



f M ° 

 The heat of dissociation is D v = \ udn, where n is the value of n for w = 0. If the 



J 

 bands can be experimentally followed to a = 0, D v can be determined from spectroscopic 

 data. Usually this cannot be done but Birge and Sponer (Phys. Rev., 28, 259, 1926) have 

 found that, for the normal state of certain types of molecules, fairly trustworthy values 

 of D v can be obtained by assuming w = w (i — 2 X it) throughout the range n=o to 

 n = n ; then D = w 2 /4«o.v. In the accompanying table D is D v plus the electronic 

 energy for the particular state in question. Each horizontal line in the table is for one 

 electronic state. The second column labelled energy (volts) is the electronic energy above 

 the normal level which is assumed to have zero electronic energy. The heat of dissociation 

 is tabulated in the same units which is the number of volts potential change an electron 

 must undergo in order to acquire the corresponding energy. One electron volt per mole- 

 cule = 2.306 X io 4 g — cal.15 per g-mole = 8ioo cm" 1 per molecule. The data in the table 

 are taken from compilations by Birge, Nat. Res. Council Bull. 57, " Molecular Spectra 

 in Gases " and Mulliken, Phys. Rev., 32, 206, 1928, and ibid., 33, 73%, I9 2 9. an d are calcu- 

 lated with the " old mechanics " formulae. 



Smithsonian Tables 



