210 6. INTEKACTIONS OF INHIBITORS WITH ENZYMES 



between them is 2 A, // = 2.4xl0-i« X 2x10-8 = 4.8xl0-i8 esii. The 

 moments of most bonds and small molecules are of the order of magnitude 

 of 10-^8 esu and this has been called a debye. In the case above, the dipole 

 moment would be 4.8 debyes. The potential energy will be given in ergs/ 

 molecule when q and // are in electrostatic units and d is in centimeters. 

 Thus a dipole of 1 debye at a distance of 10 A from a univalent ion at 37.5° 

 would give a potential energy due to orientation polarization in the ion 

 field of: 



(4.8x10-10)^10-")^ , .„ ,^ , , , 



- 1.87 X 10-" ergs/molecule 



(3) (1.38x10-1") (310.7) (10-')* 



which is equivalent to — 0.269 kcal/mole. Since at 37.5° the thermal energy 

 is 4.29 X 10"^^ ergs/molecule or 0.617 kcal/mole and over twice the magni- 

 tude of the interaction energy, it is evident that the dipole will not be fixed 

 but rotating with preferential orientation towards the ion. It is interesting 

 to note that a rigidly fixed dipole in the position of maximal attraction to 

 the ion would give a potential energy of — 0.691 kcal/mole; the electro- 

 static interaction when the dipole is free is thus about 40% of that when 

 the dipole is fixed. Equations 6-9 and 6-11 may be rewritten as: 



(p = 69.1 -^ cos 6 kcal/mole (6-12) 



(p = - 2693 ^^ kcal/mole (6-13) 



where z is the valence of the ion, ju is in debyes, and d is in A. 



The dipole moment of a molecule in solution may be different from that 

 in the gas phase as pointed out by Kirkwood (1939). Let us represent the 

 classic moment of the isolated molecule in the gas phase by jl/q. When this 

 molecule is surrounded by water molecules, its moment may be altered by 

 the electrostatic displacement effects of the water dipoles. The moment 

 of the molecule in solution, designated by //, is usually somewhat larger 

 than jUq. Finally, this dipole will exert a slight orienting effect on the sur- 

 rounding water molecviles and partially restrict their rotation. The electric 

 field at some distance from this molecule will depend not only on its in- 

 trinsic moment is solution, //, but on the vector sum of the moments of 

 all the water molecules influenced by the central molecule; this moment of 

 the molecule with its solvent cluster may be designated //. The relationship 

 between these may be wi'itten: 



^/V = jii-Ti (6-14) 



where g is a correlation parameter. In Kirkwood's theory of polar liquids, 



