Molecular Orbitals

Even with additional parameters, parity symmetry in diatomic molecules implies we will have symmetric and antisymmetric wavefunctions for single electrons. The symmetric or bonding state has a larger probability to be between the two nuclei, sees more positive charge, and is therefore lower energy. As in our simple model of a molecule, the kinetic energy can be lowered by sharing an electron.

There is an axis of symmetry for diatomic molecules. This means \bgroup\color{black}$L_z$\egroup commutes with \bgroup\color{black}$H$\egroup and \bgroup\color{black}$m_\ell$\egroup is a good quantum number. The different \bgroup\color{black}$m_\ell$\egroup states, we have seen, have quite different shapes therefore bond differently. Imagine that a valence electron is in a \bgroup\color{black}$d$\egroup state. The \bgroup\color{black}$m_\ell=0,\pm 1,\pm 2$\egroup are called molecular orbitals \bgroup\color{black}$\sigma,\pi,\delta$\egroup respectively. Each has a bonding and an antibonding state.

Pictures of molecular orbitals are shown for \bgroup\color{black}$s$\egroup and \bgroup\color{black}$p$\egroup states in the following figure. Both bonding and antibonding orbitals are shown first as atomic states then as molecular. The antibonding states are denoted by a *.


Jim Branson 2013-04-22