John L. Johnson
Visualization of Wavefunctions of the Ionized Hydrogen Molecule JCE
John L. Johnson, The Pennsylvania State University
Mathcad and the Shooting Method, are used to solve the Schrodinger equation for the H2+ molecule. The angular portions of the wavefunctions are the spheroidal harmonics, which when plotted show the shapes of molecular orbitals. These exact solutions are compared with those obtained from the LCAO method, using hydrogenic orbitals as basis functions. Plot of the electronic charge densities show the concentration of charge that distinguishes bonding and anti-bonding states. The energies of the wavefunctions as a function of internuclear distance for the eight lowest molecular energy states are calculated.