Dihydrogen cation

The hydrogen molecular ion, dihydrogen cation, or H+
2, is the simplest molecular ion. It is composed of two positively charged protons and one negatively charged electron, and can be formed from ionization of a neutral hydrogen molecule. It is of great historical and theoretical interest because, having only one electron, the Schrödinger equation for the system can be solved in a relatively straightforward way due to the lack of electron–electron repulsion (electron correlation). The analytical solutions for the energy eigenvalues are a generalization of the Lambert W function. Thus, the case of clamped nuclei can be completely done analytically using a computer algebra system within an experimental mathematics approach. Consequently, it is included as an example in most quantum chemistry textbooks.

The first successful quantum mechanical treatment of H+
2 was published by the Danish physicist Øyvind Burrau in 1927, just one year after the publication of wave mechanics by Erwin Schrödinger. Earlier attempts using the old quantum theory had been published in 1922 by Karel Niessen and Wolfgang Pauli, and in 1925 by Harold Urey. In 1928, Linus Pauling published a review putting together the work of Burrau with the work of Walter Heitler and Fritz London on the hydrogen molecule.

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