THE QUANTUM PHYSICS OF SOLIDS 669 



in the Is state. When the atoms have come together the Is states 

 have spHt into two energies with two states for each energy — one 

 with each spin. In the H2 molecule, the two electrons will both 

 go into the lower Is states, which both have the wave function of 

 Fig. 8b. Bringing the atoms closer together decreases the energy 

 of the electrons and results in the binding together of the atoms. 

 This tendency of the electrons to reduce their energies by drawing 

 the atoms together is opposed by the electrostatic repulsion between 

 the nuclei. The repulsion between the nuclei is inoperative when 

 the atoms are sensibly separated because then each nucleus is shielded 

 from the nucleus of the other atom by the electron of that atom. 

 When the atoms are closer together, however, the electrons no longer 

 perform this shielding perfectly and the nuclear repulsions are impor- 

 tant. Hence with decreasing interatomic spacing the electronic energy 

 decreases and the energy of repulsion of the nuclei increases, and the 

 equilibrium internuclear distance is the one which makes the total 

 energy of the molecule a minimum. 



The situation is quite different for two helium atoms. There being 

 two electrons in each, for them all four of the " \s molecular orbitals," 

 as the states of Fig. 9 are called, are occupied. When all the molecu- 

 lar orbitals are occupied, there is no decrease in energy when the two 

 atoms are brought together: in this case the decrease of energy for the 

 electrons in the two lowest states is compensated by the increase for the 

 electrons in the upper states — more than compensated, as a matter of 

 fact, because the upper states rise slightly more rapidly than the lower 

 ones fall. This effect results in a repulsion between two helium atoms. 

 This repulsion is a consequence of the closed shell nature of the helium 

 atom and always occurs between such closed shells even if the atoms 

 are different, as, for example, a neon and an argon atom. We shall 

 refer to this closed shell repulsion, which occurs when the wave func- 

 tions of the two closed shells encroach upon each other, as an "en- 

 croachment energy." The encroachment energy, as we have said, 

 always corresponds to a repulsive force between the closed shells. We 

 shall find that it plays a very important role both in ionic crystals 

 and in metals. 



The encroachment energy occurs not only between rare gas atoms 

 but also between ions of elements which as neutral atoms have partly 

 filled shells but in the ionic form have closed shells. Consider, for 

 example, an alkali halide molecule such as LiF. For this case the 

 2s valence electron of lithium is transferred to the vacant 2p level of 

 fluorine (see Fig. 4), thus leaving two ions with closed shell configura- 

 tions, the Li+ being He-like, the F~ being Ne-like. These two oppo- 



