Physical Chemistry , 1st ed.

and variation theory are two tools used in quantum mechanics to approxi-

mate the behavior and energy of multielectron systems. Application of either

approximation technique can in principle yield energy eigenvalues as close

to experiment as desired. Recall that this is the true test of a theory: how well

it reproduces and explains experiment (as with the discovery of antimatter,

predicted by Dirac’s relativistic quantum mechanics. Such agreement be-

tween theory and experiment fosters confidence in both). Depending on how

one approaches a system, one can devise a numerical understanding of elec-

tron behavior. We will also find in the next few chapters how quantum me-

chanics can be applied to behavior of not just electrons, but of molecules as

a whole.

414 CHAPTER 12 Atoms and Molecules

    1 s

*1s

    2 s

*2s

 2 px,  2 py

Li 2

    2 pz

*2px, *2py

*2pz

    1 s

*1s

    2 s

*2s

 2 px,  2 py

Be 2

    2 pz

*2px, *2py

*2pz

    1 s

*1s

    2 s

*2s

 2 px,  2 py

B 2

    2 pz

*2px, *2py

*2pz

    1 s

*1s

    2 s

*2s

 2 px,  2 py

C 2

    2 pz

*2px, *2py

*2pz

    1 s

*1s

    2 s

*2s

 2 px,  2 py

N 2

    2 pz

*2px, *2py

*2pz

    1 s

*1s

    2 s

*2s

    2 pz

O 2

 2 px,  2 py

*2px, *2py

*2pz

    1 s

*1s

    2 s

*2s

    2 pz

F 2

 2 px,  2 py

*2px, *2py

*2pz

    1 s

*1s

    2 s

*2s

    2 pz

Ne 2

 2 px,  2 py

*2px, *2py

*2pz

Figure 12.23 Molecular orbitals of Li 2 through F 2. The energy axis is not to scale, but this di-

agram should provide an idea of how the molecular orbitals are ordered and filled with electrons

for these homonuclear diatomic molecules.