30 PHYSICAL FORCES AND CHEMICAL BONDS 



to do the calculation properly, but the sharing idea has proved to be a 

 good one, in that excellent agreement of theory and experiment is ob- 

 tained for the binding energy of the hydrogen molecule. Since the elec- 

 trons involved are the valence electrons of the atoms and since they are 

 shared in a cooperative way, the shared electron bond has been given 

 the name covalent bond. 



For other molecular systems, an obvious extension of these notions has 

 proved useful. If the atoms share the electrons unequally — so that the 

 electrons spend somewhat more time with one atom than with another — 

 then there is a combination of sharing and ionic bonds. These situations 

 are usually spoken of as exhibiting some 'partial ionic bonding. To the 

 extent that the electrons are shared, we calculate the binding energy as 

 for a covalent bond. To the extent that electrons spend more time with 

 one atom than with another, the first is more negatively charged; this 

 requires that we calculate the electrical interaction as though each atom 

 had something less than a whole electron's worth of electric charge. 



In this fashion, then, the electric bond between atoms has been de- 

 composed into ionic bonds, covalent bonds, and intermediate cases of 

 covalent bonds with partial ionic character. Do these models permit us to 

 picture everything that takes place in the whirling clouds of electrons? 

 Unfortunately, the answer is no. There are still three other bonds which 

 are thought of as involving quite different electron configurations. And 

 there is a slight extension of the covalent bond that we present first. 



It is possible for electrons to be shared not just by pairs of atoms but 

 also by all the constituents of a piece of matter. Essentially, the elec- 

 trons, or rather, some of them, roam freely throughout the piece of 

 matter. This extreme case is that of metals; metals arc defined as sub- 

 stances in which electrons are completely free to move. We will not deal 

 further with this type of interaction. 



The next effect to be set forth involves the situation in which alterna- 

 tive electron configurations are possible. We return to the hydrogen 

 molecule already mentioned as being bonded by a sharing principle which 

 we did not elucidate at all. If we now look a little more at this case, 

 we can find a feature which Newtonian physics would consider irrelevant. 

 At any one time, the electron which belonged to one of the atoms might 

 be near that nucleus while the electron which arrived with the other atom 

 would be near its nucleus. But the electrons might also be with the 

 opposite nuclei. Now, it would seem to make no difference which electron 

 is with which nucleus, since in any event only one electron will be at one 

 place at one time. But (simplifying the physics enormously) the pro- 

 cedures of quantum physics force us to count both possibilities, even 

 though our intuition tells us this is counting things twice. The exchange 

 of electrons shouldn't make any difference in Newton's physics, but it 



