Delocalized electrons molecular orbital description

Pyridine, symmetry group C2v, has six electrons in a system delocalized around the ring, and two lone-pair electrons in an orbital localized at the Nitrogen atom. The Is electrons, as well as the electrons in orbitals describing the a bonds, need not be considered explicitly in describing the resonance stabilization and low-lying excited states of pyridine. The simple molecular orbital description has the following characteristic assumptions ... 

This picture can qualitatively account for the g tensor anisotropy of nitrosyl complexes in which g = 2.08, gy = 2.01, and g == 2.00. However, gy is often less than 2 and is as small as 1.95 in proteins such as horseradish peroxidase. To explain the reduction in g from the free electron value along the y axis, it is necessary to postulate delocalization of the electron over the molecule. This can best be done by a complete molecular orbital description, but it is instructive to consider the formation of bonding and antibonding orbitals with dy character from the metal orbital and a p orbital from the nitrogen. The filled orbital would then contribute positively to the g value while admixture of the empty orbital would decrease the g value. Thus, the value of gy could be quite variable. The delocalization of the electron into ligand orbitals reduces the occupancy of the metal d/ orbital. This effectively reduces the coefficients of the wavefunction components which account for the g tensor anisotropy hence, the anisotropy is an order of magnitude less than might be expected for a pure ionic d complex in which the unpaired electron resides in the orbital. 

Conjugated enones are more stable than nonconjugated enones for the same reason that conjugated dienes are more stable than nonconjugated dienes (Section 14.2). Interaction between the ir electrons of the C=C bond and the ir electrons of the C=0 group leads to a molecular orbital description for a conjugated enone that shows a partial delocalization of the it electrons over all four atomic centers (Figure 23.3, p. 944). 

The TT electrons in 1,3-butadiene are delocalized over four sp carbons. In other words, there are four carbons in the rr system. A molecular orbital description of... 

The actual E of a particular system is often not as informative as is the comparison of the delocalized system with a reference system having localized orbitals. Figure 4.11 shows the reference system for allyl a double bond separated by an imaginary barrier from a p orbital that may have 0 (cation), 1 (radical), or 2 (anion) electrons. The molecular orbital description of that system, then, is simply a sum of the HMOs of the double bond and of the p orbital. Again, it does not matter whether we are talking about the cation, radical, or anion in Figure 4.11. The HMOs of the reference system are simply those of ethene (E = a -H /3, = a — /8) superimposed on the one HMO for an isolated p orbital (E = a). 

VALENCE-BOND THEORY FOR BcH2 The molecular-orbital description of BeHj has the four electrons delocalized over all three atoms, in orbitals resembling the boundary-... 

The valence-bond description of the ground state of BFs is comparable to the molecular-orbital description. Three equivalent hybrid orbitals are formed first by mixing together the 2s, Ipx, and Ipy boron orbitals, as shown in Fig. 4-9- Each sp hybrid orbital has one-third / and two-thirds p character. These three sp orbitals are then used to make three electron-pair a bonds with the Ipz fluorine orbitals. In addition, the Ipz boron orbital can be used to make a tr bond with any one of the three fluorine Ipy orbitals. Thus there are three equivalent resonance structures for BFs, as shown in Fig. 4-10. Notice that the three resonance structures move the electron-pair 7T bond around the ring this is analogous to having two electrons in the delocalized irp molecular orbital. 

Delocalized bonding was described in the valence-bond method by use of the concept of resonance. In the molecular orbital description, delocalized LCAOMOs are used. For example, in the benzene molecule, six of the electrons occupy delocalized orbitals. 

In Summary Allylic radicals, cations, and anions are unusually stable. In Lewis terms, this stabilization is readily explained by electron delocalization. In a molecular-orbital description, the three interacting p orbitals form three new molecular orbitals One is considerably lower in energy than the p level, another one stays the same, and a third is higher in energy. Because only the first two are populated with electrons, the total it energy of the system is lowered. 

A delocalized molecular orbital description of 4-electron 3-centre bonding is also widely used , and we shall describe three examples of the molecular orbital theory here. 

In this chapter, we have used both Heitler-London and molecular orbital descriptions of electron-pair bonds on different oecasions. For example, a doubly occupied bonding molecular orbital (namely ) has been used to describe the electron-pair A-B bond of the standard Lewis structure (4), but when we delocalize a Y electron of structure (4) into the antibonding A-B orbital (vp ), the resulting wave-function (neglecting electron spin and indistinguishability)... 

Again it is instructive to compare this with the traditional MO approach, taking the CH4 molecule as an example. The MO single determinant description (RHF, which is identical to UHF near the equilibrium geometry) of the valence orbitals is in terms of four delocalized orbitals, each occupied by two electrons with opposite spins. The C-H bonding is described by four different, orthogonal molecular orbitals, each expanded in... 

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