We have discussed some general properties of the wave functions of ${\mathrm{H}}_2^{+}$ and its isoelectronic ions, in terms of confocal elliptic coordinates. Based on the asymptotic properties when the electron is far away from the nuclei, and the coalescence properties when it is close to one of the nuclei, we have developed simple, model wave functions for several states. These wave functions are simple enough to provide a clear insight into the structure of the wave functions, and yet accurate enough to provide energies close to the exact values.

• Received 10 May 2000

DOI:https://doi.org/10.1103/PhysRevA.62.052515