86 JOSEPH O, HIRSCHFELDER 



charge on B so that Ra+,b- is smaller than the other three charge-charge 

 distances in Eq. (1), the energy of interaction becomes 



E = -eACB/RA+.B- (2) 



This energy of interaction may be orders of magnitude larger than the ideal 

 dipole-dipole interaction energy which one would calculate on the basis of the 

 dipole moments of A and of B. The usual ideal dipole concept only applies when 

 the distance between the centers of the two molecules is much greater than 

 the distance between the charge centers in both molecules, i.e. Rab > Ra+,a- 

 and Rab > Rb+ ,b- • Thus in treating biological molecules it is usually wise to 

 forego any considerations of dipole moments but rather think of each of the 

 positive and negative charge centers in the system as interacting in a simple 

 coulombic fashion. Thus the first step in determining the intermolecular forces 

 is to locate the position of each of the electrical charge centers within the mole- 

 cules and determine how much charge is concentrated at each center. 



Hydrogen bonds provide a good example of the strong interactions possible 

 with unshielded dipoles. Consider an interaction, • • • -O — H 0^- ■ • • , between 

 an OH group in one molecule with an 0^ on another molecule. Due to electron 

 affinities, the H atom becomes positively charged and the oxygen atoms nega- 

 tive. Thus this interaction resembles the situation shown in Fig. 1 with the 

 H atom serving as the center A-f and the 0= serving as the B— . The special 

 feature of the hydrogen bond is that the collision diameter of the hydrogen 

 atom is so very small that the 0= can come very close to the center of the H 

 atom making Ra+,b- small and hence by Eq. (1) the energy of interaction can 

 be very large. 



In addition to the electrostatic interactions of the "permanent" charge dis- 

 tributions which we have just considered we should consider the effects of 

 polarization. The word "permanent" is used to denote the charge distribution 

 of the separated molecules. However, as the molecules come together they 

 polarize each other. That is, the charge distributions on the two molecules 

 become readjusted in such a way as to make the energy of the two molecule 

 system as low as possible. This polarization results in producmg much larger 

 energy of interaction than would be possible otherwise. In conjugate double 

 bond systems and many other molecular structures of interest in biology, very 

 little effort is required to make even large changes in the electrical charge dis- 

 tribution. Thus polarization forces are very important. Resonance forces, which 

 we shall discuss subsequently, are special examples of polarization forces. 



There is a third type of force which has no classical analogy. It is the London 

 dispersion force. This involves the "transition dipole moment" for the electrons 

 in the interacting molecules jumping to excited states. If i/'a(o) is the wave 

 function for the initial or ground state of molecule A and \1/aO^) is the wave 

 function for some excited state k and if ri is the instantaneous position of one 



