Orbital interactions filled with unfilled

The standard method of explaining how such molecules can be stable is to invoke the interactions of filled p or hybrid orbitals on the ligands with an empty d orbital on the central element. Like any interaction of filled with unfilled orbitals, interactions with empty d orbitals are bound to be stabilising, but d orbitals are too high in energy relative to the p orbitals for their interaction to have any significant effect. 

Nevertheless, frontier orbital theory, for all that it works, does not explain why the barrier to forbidden reactions is so high. Perturbation theory uses the sum of all filled-with-filled and filled-with-unfilled interactions (Chapter 3), with the frontier orbitals making only one contribution to this sum. Frontier orbital interactions cannot explain why, whenever it has been measured, the transition structure for the forbidden pathway is as much as 40 kJ mol 1 or more above that for the allowed pathway. Frontier orbital theory is much better at dealing with small differences in reactivity. We shall return later in this chapter to frontier orbital theory to explain the much weaker elements of selectivity, like the effect of substituents on the rates and regioselectivity, and the endo rule, but we must look for something better to explain why pericyclic reactions conform to the Woodward-Hoffmann rules with such dedication. 

Figure 15. Canonical molecular orbital energy levels for [Rh(PH3)2(formamide)]+, showing the filled and unfilled orbitals with the woner symmetry to interact with C C jc and it-orbitals, seen on the right. Scale markings are in eV. All calculations were done at the B3LYP/LANL2DZ level.

CCI2 possesses both a high-energy filled molecular orbital in the o plane and a low-energy unfilled molecular orbital perpendicular to that plane (see discussion in the previous chapter). To interact optimally with the n electrons of an olefin, the carbene must orient itself in the following manner,... 

Molecular orbitals are characterized by energies and amplitudes expressing the distribution of electron density over the nuclear framework (1-3). In the linear combination of atomic orbital (LCAO) approximation, the latter are expressed in terms of AO coefficients which in turn can be processed using the Mulliken approach into atomic and overlap populations. These in turn are related to relative charge distribution and atom-atom bonding interactions. Although in principle all occupied MOs are required to describe an observable molecular property, in fact certain aspects of structure and reactivity correlate rather well with the nature of selected filled and unfilled MOs. In particular, the properties of the highest occupied MO (HOMO) and lowest unoccupied MO (LUMO) permit the rationalization of trends in structural and reaction properties (28). A qualitative predictor of stability or, alternatively, a predictor of electron... 

We cannot, then, expect this approach to understanding chemical reactivity to explain everything. Most attempts to check the validity of frontier orbital theory computationally indicate that the sum of all the interactions of the filled with the unfilled orbitals swamp the contribution from the frontier orbitals alone. Even though the frontier orbitals make a weighted contribution to the third term of the Salem-Klopman equation, they do not account quantitatively for the many features of chemical reactions for which they seem to provide such an uncannily compelling explanation. Organic chemists, with a theory that they can handle easily, have fallen on frontier orbital theory with relief, and comfort themselves with the suspicion that something deep in the patterns of molecular orbitals must be reflected in the frontier orbitals in some disproportionate way. 

The hosts outlined above generally utilize their metal centers to provide interactions with anions. The orbital overlap between unfilled heteroelement orbitals and filled anion orbitals yields bonding interactions. In the case of the mercury based receptors, the role of the metal atoms is partly structural, with their sp hybridization linear geometry specifically yielding large macrocyclic cavities of suitable diameters for anion encapsulation. The metal atoms have often been functionally used as an NMR handle on the anion coordination process. 

The interactions which do have an important energy-lowering effect are the combinations of filled orbitals with unfilled ones. Thus, in Fig. 2-18 and Fig. 2-19, we have such combinations, and in each case we see that the energylowering in the bonding combination is the usual one, and that the rise in energy of the antibonding combination is without effect on the actual energy of the system, because there are no electrons to go into that orbital. 

The soft-soft interaction of filled with empty orbitals is the major interaction in the transition state because there is little hard-hard attraction. In an unsubstituted system two soft-soft interactions stabilize the transition state The filled tl)2 molecular orbital of the diene interacts with the unfilled jt of the dienophile also the empty ips of the diene interacts with the filled Jt of the dienophile. Figure 12.19 gives the interaction diagram. 

This leads to a stabilizing effect called hyperconjugation. Hyperconjugation is what happens when there is an unfilled (antibonding or vacant) C-C ti orbital and a filled C-H a bond orbital next to each other. The result is that the filled C-H o orbital interacts with the unfilled C-C ti orbital and stabilizes the molecule. The more highly substituted the molecule, the more chances there are for hyperconjugation and thus the more stable the molecule is. 

Complexes with n Bonding. If the ligands have n orbitals, filled or unfilled, it is necessary to consider their interactions with the T2gd orbitals,... 

Even when a transition metal is coordinatively saturated, either filled or unfilled d-orbitals of suitable energy and orientation are available, which may interact with orbitals at the /S-position on the ligand. The existence of such interactions has been established by spectral studies (25). In the systems where the /8-position on the ligand is unsaturated, metal d-orbitals of suitable symmetry may be found that can weakly overlap with the vr-orbitals of the /8-substituent. If the /8-position is saturated, metal c/-orbitals may overlap with either an empty sp lobe of the /8-carbon or one of the sp carbon-substituent orbitals. These interactions are summarized in Fig. 9. 

Intermolecular Diels-Alder cycloaddition reactions usually fail with unactivated dienophiles as the energy of the LUMO of such dienophiles is normally high and therefore the interaction of this molecular orbital with that of the HOMO of the diene is poor (orbitals of similar energy interact more strongly). Filled-unfilled orbital interactions are crucial for successful Diels-Alder reactions, which are typically frontier-orbital controlled. See Section 3.1.1. 

There is thus a wide, continuous, and unfilled band of valence orbital energies. If we have a crystal of noble gas atoms (He, Ne, Ar, Kr, Xe, and Rn) on the other hand, every orbital taking part in the interaction arises from an orbital that was filled in the atom. Since the number of MOs created by the interaction must be the same as the original number of orbitals, all orbitals will be filled. The orbitals above the gap receive no electrons at T = 0. For example, in the case of neon, the valence band created from the 2s and 2p orbitals will be filled with 12 electrons. 

Finally, it is interesting to consider why the /7-effect is found to a greater extent with transition metals than with other elements. The answer probably lies in the fact that transition metals, even when they are conventionally considered to be co-ordinatively saturated, as in ML , have d orbitals, which may be filled or unfilled, but which are of suitable energy andposition to be involved in M- -position interactions. When transition metals are in a low oxidation state, their d orbitals extend further from the metal than for the higher oxidation states. It follows that the j7-effect would be expected to be more marked in low oxidation state complexes. 

Although ligands commonly coordinate to vacant metal d orbitals (i.e., n —s-dvi1 interactions), such coordination is also possible with the unfilled metal s orbital (i.e., hl->-Sm interactions) for metal ions with completely filled d shells. An example is Zn2+(d10s°), where the vacant 4s orbital serves as the acceptor orbital for donor-acceptor interactions of ni s/+ type. 

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