SPECIFICITY or LONDON-EISENSCHITZ-WANG FORCE 47 



and of (14), i.e. 



A'l A' I _ 



(Wo i).. = -2R'' E "''«' = -2^~' Z uiW/Ki (19a) 



;=i z=i 



(W. i).3 = -2/?-' i; {h'i,?/^k'T')ulai/[s\'' + (/i^ci,V4)fe'r^)] (19b) 

 z=i 



where the force constants Ki = (hfnii have been introduced; the polarizabilities 

 (13) are ai = tf/Ki . This shows that 2 tr (WoiWon) is independent of h (and 

 of the masses, given the force constants). This part 5 = of the series (7), i.e 

 (for one-dimensional single oscillator molecules ui, = 1) 



A.4i „ = -^okT tr (WoiWoii) = -2kTR~'aiau (20) 



represents the classical part of the interaction free energy and is the one- 

 dimensional equivalent of (la). In the quantum limit case of the same type of 

 simplified molecule model one can replace the sum over s by an integral. Si , 5ii 

 are used as in (14a). 



/+<x> 

 tr (W.iWsii) ds 



/+C0 

 [1 + (^Ai)-]-^[l + (s/suY]-'ds (21) 

 ■X 



= ->2^7^(Woi)..(Wnii)..-7r5i5„/(5i -f Sn) 



= —R~^aiau h (biCOii/(wi + Wn), 

 the one-dimensional equivalent of (Ic). 



Summary of the Scope and Results of the Calculations 



The London-Eisenschitz-Wang (van der Waals) force between two molecules 

 is due to the net effect of the electrical interaction of the fluctuating electric 

 dipole moments in one molecule with those of the other. The simplest model of a 

 molecule as regards its London-van der Waals interaction is to represent it by a 

 set of harmonic oscillators. Would only their lowest quantum state come into 

 the picture, one would not need to calculate the free energy and the inter- 

 action force could be completely characterized by the dependence of the energy 

 (of interaction of these fluctuating dipoles) as a function of the distance R 

 between the two molecules. Actually there are, however, many excited quantum 

 states (energy levels) which are in thermal reach, and the proper assessment of 

 their influence on the present problem is necessary, and it is handled by sta- 

 tistical mechanics, i.e. by calculating partition function Z and free energy .4 

 as a function of the separation R. The kinds of macromolecules considered 

 here are of the roughly globular type. If those molecules can actually come into 

 contact with each other, bond formation and steric complementarity will be 



