218 6. INTERACTIONS OF INHIBITORS WITH ENZYMES 



polarization P ^ will be the important quantity for our present purpose. 

 The dipole induced in a molecule by the field of an ion will always lead to 

 attraction between the ion and the molecule and thus will contribute to 

 the energy of interaction in favor of stability. 



The induced dipole moment will be proportional to the field strength: 



/', = ocoF (6-23) 



and oriented with the field; in the field of an ion the dipole will be aligned 

 radially to the ion. The proportionality constant a^ is called the polar- 

 izability of the molecule; in conformity with previous usage, the total 

 polarizability, including the orientation of a permanent dipole, will be 

 designated by a. Since the potential energy of a dijwle in an electrical 

 field is given by 9? = — /.iF cos and here — 0°: 



(f- = - ttoi^" (6-24) 



However, it requires energy to induce the dipole and this is a^F^j^. Thus 

 the potential energy of the dipole in the ion field is: 



cp = — -— - UoF- = — (6-25) 



The field of an ion is given by i^ = qjd^D, where q = ze, so that: 



^ = - ^ = " ^''^ 1^^ ^o^\ln^ole (6-26) 



where the energy is given in kcal/mole if a^ is in units of 10"-* ml/molecule 

 and d is in A. The potential energy of a water molecule (c^q ~ 1.444) in 

 the field of a univalent ion at a distance of 5 A in vacuum, due only to 

 inductive effects, is thus — 0.384 kcal/mole. This contribution would be 

 small compared to the interaction of the ion with the permanent dijiole of 

 the water molecule, which would be around — 5 kcal/mole. The potential 

 energy due to an induced dipole is dominant only in interactions between 

 ions and nonpolar molecules. 



The values of the polarizability a^ are determined l)y measurements of 

 the optical refraction since the latter depends upon the electronic and atom- 

 ic distortions induced by the alternating electrical field of the radiation. 

 The refraction varies with the wavelength of the light used; by determi- 

 nations at two or more wavelengths it is possible to calculate the refrac- 

 tion at zero frequency where the effect of a constant field is obtained. 

 The molar refraction at zero frequency is related to the polarizability: 



R. = '-^ (6-27) 



