On the Two-Quantum Σ-States of the Hydrogen Molecule

A wave function in the form of a series with coefficients to be determined by the variational method is used to calculate the dissociation energies of the hydrogen molecule in two of its excited states: 1sσ2sσ 3Σg+ and 1sσ2pσ 1Σu+. In the former case an 11-term wave function gives an energy less than 0.02 e.v. from the most probable experimental value and lying within the limits of experimental error. For the second state an energy less than 0.08 e.v. from experiment is obtained by means of a function comprising 18 terms. The interelectronic distance has been introduced explicitly into the wave function and the role that it plays in reducing the energy is discussed at length. The limits of accuracy of the calculation with reference to convergence and nuclear motion are considered. Explicit wave functions are given for the two states.