INTERMOLECULAR FORCES AND INTERACTION ENERGY 



219 



and thus the expression for the potential energy may be rewritten as: 

 3RoZ-e^ „^ ^ RoZ 



S7i^d*D' 



= - 65.8 



d'D' 



kcal/mole 



(6-28) 



The potential energy is given in kcal/mole when R^ is in ml/mole and d 

 in A. The molar refraction of a substance is approximately equal to the 

 sum of the atomic refractions of the constituent atoms, as proposed by 

 Landolt in 1862. The usually accepted values for atomic refractions are 

 given in the tabulation below. 



A somewhat more accurate approach is to consider the molar refraction as 

 the sum of bond refractions, inasmuch as the polarizability is mainly due 

 to the bonding electrons. Bond refractions and polarizabilities are presented 

 in Table 6-2. Double bond conjugation leads to refractions greater than 

 expected on the basis of the atomic or bond refractions; this is called 

 exaltation and values for certain conjugated systems are shown in Table 

 6-3. Some approximate ionic and group refractions are given in Tables 6-4 

 and 6-5. The molar refractions of compounds may also be calculated from 

 the indices of refraction by the Lorentz-Lorenz equation (indices of re- 

 fraction for many compounds are given in the International Critical Tables, 

 1930, Vol. 7. and in Timmermans' " Physico-Chemical Constants of Pure 

 Organic Compounds " 1950). The induced polarization involves principally 

 the electrons in the outer shell of an atom or ion, including those in bonding 

 orbitals, and the contribution from atomic polarization is only 1-5% of 

 the electronic contribution. 



The polarizability a^ is a spherical average but actually most bonds 

 and molecules are asymmetric with respect to their polarizability. Bonds 

 generally exhibit a much greater polarizability along the bond axis than 

 transversely, and the polarizability of benzene is about twice as great in 

 the plane of the ring as perpendicular to it. This refraction anisotropy may 



