SURFACES OF MOLECULES 221 



The quantum theory teaches that each electron in an atom is charac- 

 terized by four quantum numbers, which are integers. Not all quantum 

 numbers are possible; there are, for example, certain conditions (selection 

 rules) which they must satisfy. The normal atom or molecule, with which 

 the chemist is concerned, is one in which the electrons are so arranged 

 that the total energy is a minimum, subject to the quantum rules that must 

 be fulfilled. 



It seems that the factor of greatest importance to the clicniist is that 

 which is known as the Pauli principle, which states that no two electrons 

 in an atom can have the same combination of four quantum numbers. It is 

 this principle which underlies the Periodic Table of the elements, and in 

 a similar manner determines the arrangement of electrons in a molecule. 

 It is through the development of methods of this kind that our greatest 

 hope lies in obtaining a better understanding of the nature of repulsive 

 forces. 



For most practical purposes it is best for the chemist to regard mole- 

 cules of organic substances as having shapes suggested by chemical struc- 

 tural formulas, and as having surfaces which are rather rigid so that 

 strong repulsive forces are called into play for only moderate deforma- 

 tions. For many purposes it is still useful to look upon the surfaces as 

 completely rigid. 



ATTRACTIVE FORCES BETWEEN MOLECULES ^ 



Whereas the quantum theory seems essential in an understanding of the 

 repulsive forces, the classical laws, such as the Coulomb law, are largely 

 sufficient for dealing with the attractive forces between molecules. For 

 example, the Debye-Hiickel theory of electrolytes (8) is based on the 

 Coulomb law, the Poisson equation, and the Boltzmann equation — all laws 

 of classical mechanics. 



In discussing forces between molecules, Debye has classified molecules 

 in three groups: "(i) ionic, (2) polar and (3) non-polar." The ionic type 

 is represented by electrolytic ions, such as K\ NO3", etc., and gaseous 

 ions. In these molecules the number of electrons is unequal to the number 

 of positive charges of the nuclei of atoms, so that the molecule as a whole 

 has an electric charge which is some multiple of e, the charge of an electron. 

 The polar type is represented by molecules which have a dipole moment — 

 that is, uncharged molecules in which the center of gravity of the negative 

 charges does not coincide with that of the positive. Non-polar molecules 

 thus include all molecules which are uncharged and in which the centers 



* The term "molecule" is to be used in its broad sense, which includes atoms and 

 ions. 



