SPECIFICITY OF LONDON-EISENSCHITZ-WANG FORCE 39 



The inequality (10b) actually represents six inequalities for every | s |, one 

 inequality for each component iiu of the symmetric sum 



- A,A, u = }2 kT^^ l(V?s I - W. u)..}' (10c) 



Equation (10c) implies that A4.-I1 n = rigorously if and only if two molecules 

 have the same set of {'Ws)^^ values, i.e. according to the partial fractions ex- 

 pansion (14), if they have the same dynamic polarizability ellipsoids as function 

 of frequency. This defines what constitutes "identical" molecules in regard to 

 London interactions. 



It will turn out that, for the attainment of specificity, strong oscillator po- 

 larizabilities with a highly diversified frequency distribution in the quantum 

 region are imperative. The question might therefore be raised why the calcula- 

 tions in this paper deal with the entire partition function rather than with 

 the ground state alone. The answer is that the all-important question is the 

 evaluation of the degree of specificity which depends on the aforementioned 

 distribution of the total set of polarizable oscillators. Only the calculation 

 of the entire partition function will properly delimit the influence of oscillators 

 of low polarizability and of little diversified or low frequencies. Besides, the use 

 of the full partition function turns out to be surprisingly handsome because it 

 yields the rearrangement free energy as the square of a Euclidean distance (10c) 

 in a Ws space. The s was originally introduced into the calculations only to 

 provide for the series expansion (3). Now one realizes that the expression (10c) 

 for the rearrangement free energy is a very simple one, that it is a sum over s, 

 and not a sum over the normal modes /. This is most simply illustrated for 

 molecules whose oscillators are all oriented parallel to the s-axis, where 



r A'l 



- A^i.u = UtZ^R' 



Oil 



L^l -{-{2TkT/hy{syC:i') 



-Vi+.Vri n2 ^ •' 



_ Y^ ai 



z=4r+i 1 + {2wkT/hns'/ibi')_ 



if one has to do with one dimensional oscillators oriented in the z direction. 

 That represents an average situation insofar as one dimensional oscillators 

 in the xy plane would make for a smaller interaction, and three dimensional 

 oscillators would make for a larger interaction. 



Degree of Specificity 



The preceding sections have discussed particular quadruplet situations 

 arising from a given pair of molecule types I and II. The concept "specific inter- 

 actions" implies that a given molecule I is able to discriminate between mole- 

 cules identical with itself and a manifold of other molecules II. One may 



