SPECIFICITY OF LONDON-EISENSCHITZ-WANG FORCE 37 



If both molecules I and II are referred lo the same axes (x, y, 2), where the 

 2-axis is the line connecting the centers of the molecules, then from (4) 



^ki = {h:^/WT-y^mtr'-ejmr''R~%tkxtijx + UkyUjy - 2z<a,m>J (11) 



where the e's are charges, the w's are masses and the u/'s, are orientation vectors 

 of the oscillators. The orientation of the oscillators can be described with 

 reference to fixed axes in the molecules, e.g. those determined by the static 

 electric moments. The interaction matrix III 'Uii~ has the value (11) if one sets 



h _3 / —1 _i /- 



111 = :=rr^ R ' ti^i 'Hix , eiWi hliy , 1 V2 eimi 'Uh 



Zkl 



I = \, 2 ■ ■ ■ Xi , and similarly for Tin . This matrix is, however, neither purely 

 real nor purely imaginary. 



If the two molecules are referred to coordinate systems {xi , yi , Zi) and 

 (-Vii , yii y 2ii) respectively, two right-handed systems whose z-axes are parallel 

 and whose x- and y-axes are antiparallel, then the interaction matrix 'Ui'Uii~ 

 has the value (11) if one sets 



Iti = {h/2kT)R-' I iermi "uix , ietmi "uiy , iy/letmi "ui, , , . 



and similarly for lln . In this notation, 11i'Tli~ denotes the interaction matrix 

 of a molecule I located at the origin of the coordinate system I with a molecule 

 II at origin II whose dipole distribution relative to {xu , yu , Zn) is exactly 

 the same as the dipole distribution of I with respect to (xi , yj , Zi). This mole- 

 cule II is identical with I except for 180° rotation around thez-axis; this is the 

 mutual orientation of lowest free energy for two identical molecules. With such 

 a definition of pairs of identical molecules I-I and II-II, the matrices W,- 1 

 and Ws II are Hermitean and accordingly the quadruplet inequality (10b) 

 holds. 



If the two molecules are referred to two mirror image coordinate systems 

 whose s-axes are antiparallel and whose .v- and y-axes are parallel, the interac- 

 tion matrix Tii'Uii~ = 11 again has the value (11) if Tlj is given by — ?' times (12), 

 and similarly for lin . In this case, IIiHli represents the interaction of one 

 molecule with another which is the mirror image of the first one with respect 

 to a plane perpendicular to their line of centers; this is the mutual orientation 

 of lowest free energy for two mirror image molecules. The inequality (10b) 

 holds in this case also. In this case of mirror molecules, however, the specificity 



