Hybridization and orbital size

Instead, we believe the electronic structure changes are a collective effect of several distinct processes. For example, at surfaces the loss of the bulk symmetry will induce electronic states with different DOS compared to bulk. As the particle sizes are decreased, the contribution of these surface related states becomes more prominent. On the other hand, the decrease of the coordination number is expected to diminish the d-d and s-d hybridization and the crystal field splitting, therefore leading to narrowing of the valence d-band. At the same time, bond length contraction (i.e. a kind of reconstruction ), which was observed in small particles [89-92], should increase the overlap of the d-orbitals of the neighboring atoms, partially restoring the width of the d-band. 

In cases where there are no electronically driven distortions, the orbital description provides no better account of the chemistry than the bond valence model. Rather it tends to make an essentially simple situation more complex. For example, consider the phosphate and nitrate anions, and NOJ. In orbital models the P atom is described as sp hybridized and the N atom as sp hybridized, but these descriptions are just representations of the spherical and cylindrical harmonics appropriate to the observed geometries. They provide no explanation for why P is four but not three coordinate, or why N is three but not four coordinate. The bond valence account given in Chapter 6 is simpler, more physical, and more predictive. The orbital description is merely a rather complicated way of saying that the ions obey the principle of maximum symmetry but implying that the constraints are related in some unspecified way to the properties of one-electron orbitals rather than to the ionic sizes. 

As shown in Fig. 4.9 the hybrid sp2 orbitals all have basically the same shape. They are much more concentrated into regions that are in specific directions in space than are the simple atomic orbitals. For instance, simple atomic p orbitals have two regions in space, in opposite directions from the nucleus and located where the orbital would give a sizable electron density (Fig. 2.6). In ther/>2 orbitals, one of these regions has shrunk to a rather small size while the region in the oppo-... 

In 1985 chemists at Rice University in Texas used a high-powered laser to vaporize graphite in an effort to create unusual molecules believed to exist in interstellar space. Mass spectrometry revealed that one of the products was an unknown species with the formula Ceo- Because of its size and the fact that it is pure carbon, this molecule has an exotic shape, which the researchers worked out using paper, scissors, and tape. Subsequent spectroscopic and X-ray measurements confirmed that Ceo is shaped like a hollow sphere with a carbon atom at each of the 60 vertices. Geometrically, buckyball (short for buckminsterfullerene ) is the most symmetrical molecule known. In spite of its unique features, however, its bonding scheme is straightforward. Each carbon is xp -hybridized, and there are extensive delocalized molecular orbitals over the entire structure. 

Given these correlations, it seems that it should be possible to predictably turn on or off the stereochemical activity of the lead lone pair. To test this idea, Reger and co-workers prepared a series of lead complexes of polypyr-azolyl borate and polypyrazolyl methane ligands in which the number of donor atoms and the size of the ligand was systematically varied (177, 180, 183, 208). For a constant coordination number (6), only the bulkier hgand is holodirected (Fig. 12). This observation is consistent with the idea that the natural (i.e., energetically favored) state for Pb(ll) compounds is one in which the 6s and 6p orbitals are hybridized and the lone pair is stereochemically active, but that sufficient steric repulsion can overcome this effect and make the holodirected structure more stable. 

Figure 43 (a) Percent d orbital character in [M-H]+ bond and (b) size of nd and (n + 1)s orbitals for the transition metals (data taken from Ohanessian, G. Goddard, W. A., IIIAcc. Cherm. Res. 1990, 23, 386-392). (n + 1)s/nd hybridization is less effective for the metals of the 1 transition series because of the large difference in 4s and 3d orbital sizes. 

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