Comparison of wave-functions for HeH++ and HeH

Before trustworthy predictions can be made concerning the reliability of various approximate wave-functions in the case of complicated molecules, it is necessary to study the simplest molecules in as great detail as possible. Such a study enables one to assess the merits and inaccuracies of the different approximations in a way that is impossible with the more complex systems. The simplest of all molecular problems is H+2, and this ion has been studied thoroughly by several writers (e.g. Dickinson 1933; Sandemann I935; Steensholt 1936 a, b). The simplest two-electron problem is that of H2, and a very complete knowledge of the wave-functions for this molecule has been obtained (e.g. Weinbaum 1933; Coolidge and James 1933; Coulson 1937a). In order of increasing complexity the next molecule is the two-electron ion H3+, which has been discussed by Coulson (1935), by Eyring, Rosen and Hirschfelder (1936) and Hirschfelder, Diamond and Eyring (1937). All these molecules are homonuclear, however, so that the binding is predominantly covalent; but the majority of molecules experimentally observed are heteropolar, and then the binding is largely ionic. The present paper, therefore, extends the calculations already made for H+2, H2 and H+3, and discusses in detail the two simplest heteronuclear molecules, viz. the ground states of the single-electron ion HeH++ and of the double-electron ion HeH+. The object of the paper is primarily to compare the different types of wave-functions, and for this purpose as many diverse methods as possible have been employed; it is not important, from this point of view, that the HeH++ ion is unstable and that the HeH+ ion is stable. This work may be regarded as the analogue, in the molecular sphere, of a recent paper by Baber and Hassé (1937) on He, in the atomic sphere. Some of the methods used for the single-electron bond have no immediate counterpart in the discussion of the two-electron bond, and accordingly the two problems are treated independently.