9. Molecular Orbitals and      Molecular Structure   Previous PageNext Page
     Larger Diatomic Molecules

These are the molecular orbitals, or electron probability clouds, that a simple diatomic (two-atom) molecule can have. What can we say about their energies, other than that half of the MO's are bonding orbitals and half are antibonding? The energies all can be calculated from molecular orbital theory and given numerical values, but we can reach the same goal in our nonmathernatical treatment by recognizing the significance of nodes in the wave functions. Other things being equal, the greater the number of nodes in any wave, the higher the energy. We have seen this principle before, but have not recognized it explicitly. A high-frequency light wave has more nodes per unit length (the wave returns to zero more often) than a low-frequency one (see upper right). By the relationship E = hn, higher frequency means higher energy. The same principle holds for atomic orbitals (right): An s orbital is spherically symmetrical, a p orbital has one nodal plane, and a d orbital has two nodal planes. The energy within one n level accordingly increases from s to p to d.

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