Rabbit-Ear Lone Pairs

6 THE VALENCE IONIZATION SPECTRUM OF H20 AND THE RABBIT-EAR LONE PAIRS 

Another argument that has often been invoked against VB theory and the hybridization concept is the fact that the water molecule has two experimentally measurable ionization potentials, in apparent contradiction with the classical representation of water with its lone electron pairs located in two equivalent 

let us express the polyelectronic wave functions, limited to the lone pairs, for the two apparently different representations. In the canonical MO representation, the polyelectronic wave function, P mo, is made of the doubly occupied n and p orbitals  

In the VB-hybridized representation, the equivalent hybrids are n + A,p and n — Xp (recall Exercise 3.7), leading to the polyelectronic wave function Pvb (omitting normalization)  

The wave functions fMo and vb can be compared with each other, by a simple expansion of Pvb in terms of elementary determinants as we did in Chapter 3 for the covalent and ionic parts of a bond wave function  

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There is little experience with the von Niessen method, but for most molecules the remaining three schemes tend to give very similar LMOs. The main exception is systems containing both a- and vr-bonds, such as ethylene. The Pipek-Mezey procedure preserves the cr/yr-separation, while the Edmiston-Ruedenberg and Boys schemes produce bent banana bonds. Similarly, for planar molecules which contain lone pairs (like water), the Pipek-Mezey method produces one in-plane cr-type lone pair and one out-of-plane yr-type lone pair, while the Edmiston-Ruedenberg and Boys schemes produce two equivalent rabbit ear lone pairs. 

It follows from the above analysis that the rabbit-ears and canonical MO representations of the water s lone pairs are both perfectly correct, as they lead to equivalent wave functions for the ground state of water, as well as for its two ionized states. Both representations account for the two ionization potentials that are observed experimentally. This example illustrates the well-known fact that, while the polyelectronic wave function for a given state is unique, the orbitals from which it is constructed are not unique, and this holds true even in the MO framework within which a standard localization procedure generates the rabbit-ear lone pairs while leaving the total wave function unchanged. Thus, the question what are the true lone-pair orbitals of water is not very meaningful. 

The orbital degeneracies noted in point 3 above and seen in Figure 2.4 reflect the symmetry of the molecule s nuclear framework. Notice that the conventional picture of two equal lone pairs in water, sometimes displayed as rabbit ears, is not supported by the energies of the two highest occupied MOs of water. In fact, the lone pairs resemble the proper group MOs shown in Figure 1.8. 

The term is not just whimsy on the author s part certain stereoelectronic phenomena arising from the presence of lone pairs on heteroatoms in a 1,3-relationship were once called the rabbit-ear effect , and a photograph of the eponymous creature even appeared on the cover of the Swedish journal Kemisk Tidskrift. History of the term, photograph Eliel EL (1990) From Cologne to Chapel Hill. American Chemical Society, Washington, DC, pp 62-64... 

The existence of two different ionization potentials in ethers, R-O-R, shows that their lone pairs are not equivalent. This experimental phenomenon is most easily rationalized by supposing that the oxygen is sp2 hybridized, as shown in 21.12 One of the lone pairs has then sp2 character and the other is a p orbital. When their electron densities are combined, a rabbit ear structure (22) is obtained. This often-used representation is incorrect (because it implies an equivalence of the lone pairs) but convenient, especially when the molecule is deformed slightly to make the oxygen perfectly tetrahedral. Below, we will see how the stability of an ether is increased when one of the lone pairs lies antiparallel to a low-lying neighboring o cx orbital. This is easily seen using representation 22, but less obvious with 21. We will use whichever of these representations is better adapted to the problem at hand. 

The experimental value of the dihedral angle25 in HOOH is 111°. The interactions between adjacent lone pairs are repulsive, but the other gauche effects result from attractive influences (see below). Had we use the rabbit ear structure 22, with equivalent lone pairs, the experimental structure would be hard to explain. 

If the two lone pair sp orbitals on oxygen are drawn in the customary skittle shapes, the major lobes in a Newman projection look like two rabbit s ears. The direct electrostatic effect of lone pair electrons was therefore dubbed the rabbits ears effect, but failed to find acceptance, as much from the overtones of Beatrix Potter as from the fact that the shape of electron density resembled not two, but one ear (Figure 2.11). 

Carbonyl compounds also have two nonbonding lone pairs on the oxygen atom. In organic chemistry texts, these are sometimes shown as two equivalent sp2-hybridized lobes (rabbit s ears). While hybridization has no effect on the total energy, the two degenerate nsp2 orbitals are inappropriate as a basis set to discuss one-electron properties such as ionization potentials or n,jt transitions. Rather, the symmetry-adapted lone pairs... 

In the initial publications (28, 198) concerning the rabbit ear effect, its electrostatic nature was emphasized, since electric dipoles were attributed to the atom-lone pair systems. Such point of view encouraged and enabled other workers to criticize this concept rather successfully (see Section III.B.l). 

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