Molecules with three or more atoms have molecular orbitals that span the entire molecule. The MOs are derived from the overlap of AOs from all the atoms in the molecule. Both the MO wave functions and the structure of the energy-level diagram are much more complicated than for diatomic molecules, but mathematical techniques exist for calculating and displaying the electron densities that form chemical bonds. In this course we will not delve deeply into these more complicated cases except to make several general points:
- The number of MOs for a molecule equals the number of AOs on the atoms that make up the molecule.
- The energies of the MOs increase as the number of nodes in the MO increases.
- MOs can extend over the entire molecular structure; they are not necessarily confined to pairs of atoms.
Some of the molecular orbitals for a water molecule are shown here. Based only on what you know about the appearance of bonding and antibonding orbitals, rank these MOs from lowest-energy to highest-energy.
While MOs provide accurate physical information about the molecule, such as energies of the valence electrons involved in a reaction and precise geometries of the molecule, their visualization does not always provide intuitive chemical understanding. It is possible to “re-combine” the MOs in such a way that the electron densities are displayed as being localized between pairs of atoms or on individual atoms. This allows us to correlate MO derived electron densities with the more familiar Lewis structures, which represent electrons in chemical bonds as lines between pairs of atoms and electrons on a single atom as dots. We will discuss Lewis structures in more depth next.