A theory of some electron-levels in H 2

§ 1.Introduction . —Preparatory to a theoretical investigation of the Stark-effect in the hydrogen molecule, it was found necessary to undertake the present study of some excited electron levels. Suitable approximate wave functions must be determined in order to calculate the Stark-effect perturbations associated with neighbouring states. The functions must be appropriate for certain integrations in which the equilibrium nuclear separations are used. Kemble and Zener have employed a method which gives wave functions suitable for great inter-atomic separation. Their calculations for “equili­brium” energies show rather poor quantitative agreement with experimental values for the 2p ∏ states. In an unpublished study of the 2p Ʃ states, using the method of Kemble and Zener, the writer also found great discrepancies. Guillemin and Zener used a variation method and obtained moderately good agreement with the experimental results for the 2p 1 Ʃ state. A short time before the present paper was submitted for publication a paper by Hylleraas appeared. In it the energy curves for 2-quantum electron levels were determined. The results arrived at by Hylleraas agree well with the experimental data which he gives. In his paper Hylleraas does not discuss the methods by which his 2-quantum wave functions are constructed from the basic H2 + -like functions which he uses.