Helium bond order

The MO diagram shown in Figure 10-28 can be applied to any of the possible diatomic molecules or ions formed from the first-row elements, hydrogen and helium. Count the electrons of He2" , place the electrons in the MO diagram, and calculate the bond order. If the bond order is greater than zero, the species can form, under the right conditions. 

Electrical discharges through samples of helium gas generate He cations, some of which bond with He atoms to form Hc2 cations. These fall apart as soon as they capture electrons, but they last long enough to be studied spectroscopically. The bond dissociation energy is 250 kJ/mol, approximately 60% as strong as the bond in the H2 molecule, whose bond order is 1. 

The molecule He, is unknown since the number of antibonding electrons (2) is equal to the number of bonding electrons (2) and the net bond order is zero. With no bond energy14 to overcome the dispersive tendencies of entropy, two helium atoms in a "molecule will not remain together but fly apart. If it existed, molecular helium would have the electron configuration ... 

The noble gas hydride ions should have a bond order of one and tbe diatomic noble gas ions should have a bond order of one-half. Neither type cun be isolated in the form of salts of the type HeH+X or He, X- since the electron affinity of positive helium, etc. is greater than that of any appropriate species X, and so such salts would spontaneously decompose ... 

Table 3.3.2 summarizes the various properties of second-row homonuclear diatomic molecules. In the last column of the table, we list the bond order between atoms A and B in the molecule AB. Simply put, the bond order is a number that gives an indication of its strength relative to that of a two-electron single bond. Thus the bond order ofHf (cr ) is 1/2, while that of H2 (afs) is 1. For a system with antibonding electrons, we take the simplistic view that one antibonding electron cancels out one bonding electron. Thus the bond orders in lief (ofs o-j 1) and He2 (ofs aj s2) are 1 /2 and 0, respectively, and helium is not expected to form a diatomic molecule. 

There is no overall bonding, the two helium atoms are not held together, and He2 does not exist. Only if there are more electrons in bonding MOs than in antibonding MOs will there be any bonding between two atoms. In fact, we define the number of bonds between two atoms as the bond order (dividing by two since two electrons make up a chemical bond). 

We will now apply the MO model to the helium molecule (He2). Does this model predict that this molecule is stable Since the He atom has a Is2 configuration, Is orbitals are used to construct the MOs. Therefore the molecules will have four electrons. From the diagram shown in Fig. 14.29, it is apparent that two electrons are raised in energy and two are lowered in energy. Thus the bond order is zero ... 

Since the antibonding molecular orbital is raised more than the bonding is lowered, if we try to fill both molecular orbitals (with 4 electrons), the overall energy is increased compared to the isolated atoms. This is why helium does not form a diatomic molecule. With both the bonding and antibonding orbitals filled with two electrons, there is no net bond and the helium atoms drift apart. With three electrons, the antibonding orbital has just one electron in it, so the bond order of He2 is 1/2, resulting in a very weak bond. 

This situation gives a bond order of zero according to equation (2- 1) and thus it is not beneficial for two helium atoms to join and form a covalent bond. This is hence the answer to the question about why two hydrogen atoms form a molecule while two helium atoms do not. 

The charges sum to 0.5423 + 0.4579 = 1.000, the total charge on the molecule. The less positive charge on helium is in accord with the fact that electronegativity increases from left to right along a row of the periodic table. H He bond order For this we use Eq. (5.213) n,/j is summed for aU overlaps between basis functions on atoms A and B. There is only one such overlap, that between and 02, so... 

The hypothetical molecule Hc2 would have a bond order of 0. In fact, the overlap integral in the denominator of the energy-level equations. Equations (7.22) and (7.23), means that the ungerade symmetry MO destabilizes this system slightly more than the stabilization gained by filling the l(Tg+ level. Accordingly, Hc2 is unstable with respect to isolated He atoms, and so helium is a monatomic gas. 

Notice that the two additional electrons must go into the higher energy antibonding orbital. There is no net stabilization by joining two helium atoms to form a helium molecule, as indicated by the bond order ... 

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)]. 

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. 

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