INTERMOLECULAR FORCES AND INTERACTION ENERGY 



213 



Head-to-tail: 



d -I 



d +1 



(6-17) 



Taking different ratios of d to I leads to the following values of the poten- 

 tial energy (see tabulation below). As d becomes much larger than I the 

 potential energies, of course, approach (Pa^ — //g/Zj/^^^ and 9?j = — 2/i^iLiJd^. 

 However, when djl becomes less than 5 the usual expressions for dipolar 

 interaction are progressively more inaccurate. When the dipoles are paral- 

 lel, the potential energy upon close approach becomes less than expected 

 on the basis of Eq. 6-15 (i.e., less absolute potential energy), while when the 

 dipoles are head-to-tail the interaction energy becomes greater than ex- 



pected. These deviations may be of considerable importance in enzyme 

 interactions. 



Equations of the type (p = K/u^juJd^D, such as 6-15 to 6-17, can be writ- 

 ten in the following convenient form: 



14.4 A "J* kcal/mole 



(6-18) 



when the //'s are in debyes and d in A. The energy involved in such dipole 

 pairs is usually not very large: two dipoles of // = 2 debyes at a distance 

 of 5 A in orientation for maximal interaction possess a potential energy of 

 approximately 1 kcal/mole in a vacuum, much less than for ionic interactions 

 over the same distance. 



The problem of freely rotating dipoles must now be considered. There 

 are two possible situations of interest. The first is where dipole A is fixed 

 and dipole B is free, as might occur in the interaction of a small molecule 

 in solution with a dipole on the enzyme surface, in which case the poten- 

 tial energy is given by: 



SkTd'D 



(1 + Scos^e) 



(6-19) 



where 6 is the angle the line of centers makes with the axis of dipole A. 

 The second is where both dipoles are free and their interaction is due to 



