Abstract We report the first examples of bound molecular electronic states computed using the primitive semiclassical approximation. This method is based directly on classical actions derived from classical trajectories, and as such is closely related to the Bohr method for atoms. The examples chosen are neutral one-electron diatomic molecules, with fractional nuclear charges; both polar and non-polar cases are considered. It is the reduction of the nuclear repulsion from that experienced by one-electron cations which allow this semiclassical method to find bound states. The errors in the bond length and energies decrease to less than a percent as the quantum numbers are increased; Rydberg states are computed with much higher accuracy. The implications for interpretation of chemical bonding are briefly discussed.