38 YOS, BADE AND JEHLE 



of the interaction may be lost if the representative oscillators are anhormonic 

 (Jehle, 1950; Yos, 1956), or for other reasons have permanent dipole mo- 

 ments. 



If the term "identical" is used to mean that I-I and II-II, properly oriented, 

 are both pairs of actually identical molecules (or both pairs of mirror image 

 molecules), then the results of the preceding section on the dipole-dipole inter- 

 action of systems of coupled harmonic oscillators can be summarized in the 

 Specificity Theorem : 



If all of the interactions occur at the same separation 7?, and if the inter- 

 actions of "identical" pairs of I-I or II-II occur in the mutual orientations of 

 lowest free energy, then, to terms in 7?~^, 



A4.4i II = A/li I + A.4ii II - 2A.4i „ < (10b) 



Molecular Polarizabilities 



In an oscillator model, the static polarizabilities and the dynamic polariza- 

 bility tensor are defined by 



ai 



= u'Imim , a(co) = ^ a/U/U//[l — {</ / Cii')\ (13) 



with the dyadic product U/U/ . The <i/ are the normal mode frequencies of the 

 isolated molecules; that is, the eigenvalues of Foo are h-ibi/WT^. Equations (8), 

 (12), and (13) give 



,-3 ^ «' 



Ulx UlxUly \/2 UlxUi, 



^"^si = —R 2^ , 2,2^2 iiiytiix uiy -y/luiyUu (14) 



h'ccr \y/2ui,uu s/luiaiiy 2uu 



It is seen that Ws i is, apart from the tensorial factors containing the orienta- 

 tion vectors ui the dynamic polarizability analytically continued into the 

 purely imaginary argument co = islirkT/h. Insofar as the oscillator model 

 corresponds with reality, one can infer from the experimental dispersion curves 

 and absorption spectra ai , cbi , U; , because the partial fraction expansion (13) 

 is unique. W^i is then determined from these quantities, (la) and (Ic) are readily 

 evaluated from (7), (9) and (14) (cf below). 



In studying changes in the rearrangement energy (10a) due to changing the 

 structures of the molecules, a natural idea is to study the effects of small 

 changes in ai , cof , and U; . This approach can be carried out most readily on 

 the basis of (14). Earlier work along this line has been reported by one of us 

 (Bade, 1954) and integrated with the present work (Yos). One may call this the 

 "detuning approach." 



