The Helium Molecule-Ion

The Helium Molecule and Molecule-ion.—The simplest example of a molecule containing a three-electron bond is the helium molecule-ion, in which a Is eigenfunction for each of two identical atoms is involved. The two unperturbed states of equal energy are He He+ and He-+ He. The formation of this molecule might be represented by the equation He Is2 >5 + He+ Is 5 —>- He (Is + ls) 2 Three dots in a horizontal line placed between the two atomic symbols may be used to designate a three-electron bond He He+. 

In Sections 42 and 43 we shall describe the accurate and reliable wave-mechanical treatments which have been given the hydrogen molecule-ion and hydrogen molecule. These treatments are necessarily rather complicated. In order to throw further light on the interactions involved in the formation of these molecules, we shall preface the accurate treatments by a discussion of various less exact treatments. The helium molecule-ion, He , will be treated in Section 44, followed in Section 45 by a general discussion of the properties of the one-electron bond, the electron-pair bond, and the three-electron bond. 

The Helium Molecule-Ion.—The simplest molecule in which the three-electron bond can occur is the helium molecule-ion, HeJ, consisting of two nuclei, each with one stable Is orbital, and three electrons. The theoretical treatment7 of this system has shown that the bond is strong, with bond energy about 55 kcal/mole and with equilibrium internuclear distance about 1.09 A. The experimental values for these qualities, determined from spectroscopic data for excited states of the helium molecule, are a bout 58 kcal/mole and 1.080 A, respectively, which agree well with the theoretical values. It is seen that the bond energy in He He4 is about the same as that in H H+, and a little more than half as great as that of the electron-pair bpnd in H H. 

M. THE HELIUM MOLECULE-ION AND THE INTERACTION OF TWO NORMAL HELIUM ATOMS... 

In the preceding sections we have discussed systems of two nuclei and one or two electrons. Systems of two nuclei and three or four electrons, represented by the helium molecule-ion Hef and by two interacting helium atoms, respectively, are treated in the following paragraphs. A discussion of the results obtained for systems of these four types and of their general significance in regard to the nature of the chemical bond and to the structure of molecules will then be presented in Section 45. 

The resonance of molecules among several electronic structures. The Nucleus (Northeastern Section, Am. Chem. Soc.) 9 (May 1932) 183—184. The normal state of the helium molecule-ions He2" and He2 . J. Chem. Phys. 1 (1933) 56-59. 

Helium molecule ion, He the helium molecule ion is considered as a combination of a helium atom and a helium ion He". It has three electrons in all. This molecule has the electron configuration (als) (a Is) ... 

Do He2 and He2 Exist One of the early triumphs of MO theory was its ability to predict the existence of Hc2, the helium molecule-ion, which consists of two He nuclei and three electrons. Let s use MO diagrams to see why He2 exists but He2 doesn t ... 

In Figure 3-2, the Is atomic orbital occupations for A -B and A- B are displayed for the helium molecule ion, Hc2. Because each of these valence-bond stmctures has only one unpaired electron, Pauling deduced that the length and... 

I believe that the explanation of these facts is provided by the three-8 W. Weizel, Z. Physik, 59,320 (1929). Weizel and F. Hund [ibid., 63, 719 (1930) ] have discussed the possible electronic states of the helium molecule. Neither one, however, explains why He Is2 + He+ Is form a stable molecule-ion, nor gives the necessary condition for the formation of a three-electron bond. In earlier papers they assumed that both atoms had to be excited in order to form a stable molecule [W. Weizel, ibid., 51,328 (1928) F. Hund, ibid., 51, 759 (1928)]. 

At this point the identity of X remains unspecified.. X could be, for example, the metastable 23S helium atom, in which case X represents a ground state He atom plus an electron. Alternatively X could be the He2+ molecule-ion, and X would then represent two ground state helium atoms. For simplicity we assume that under any one set of conditions only one excited helium species is dominant, although we can expect several processes occurring simultaneously. The natural lifetime of N2+ or 02+ is short compared with the time scale of the experiment, and thus the emission intensity is proportional to the rate of Reaction 1. If the concentration of nitrogen is uniform and constant along the tube, which should be the case after some distance of travel, the intensity... 

For the doubly charged helium molecule-ion, He +, a treatment Pased on the function 43-13 has been carried through,3 leading to the energy curve shown in Figure 43-5. It is seen that at large distances the two normal He+ ions repel each other with the force e2/r2. At about 1.3 A the effect of the resonance integrals... 

In the preceding sections we have discussed systems containing two nuclei, each with one stable orbital wave function (a Is function), and one, two, three, or four electrons. We have found that in each case an antisymmetric variation function of the determinantal type constructed from atomic orbitals and spin functions leads to repulsion rather than to attraction and the formation of a stable molecule. For the four-electron system only one such wave function can be constructed, so that two normal helium atoms, with completed K shells, interact with one another in this way. For the other systems, on the other hand, more than one function of this type can be set up (the two corresponding to the structures H- H+ and H+ H for the hydrogen molecule-ion, for example) and it is found on solution of the secular equation that the correct approximate wave functions are the sum and difference of these, and that in each case one of the corresponding energy curves leads to attraction of the atoms and the formation of a stable bond. We call the bonds involving two orbitals (one for each nucleus) and one, two, and three electrons the one-electron bond, the electron-pair bond, and the three-electron bond, respectively. 

---