Unpaired electron energies

The negative sign in equation (b 1.15.26) implies that, unlike the case for electron spins, states with larger magnetic quantum number have smaller energy for g O. In contrast to the g-value in EPR experiments, g is an inlierent property of the nucleus. NMR resonances are not easily detected in paramagnetic systems because of sensitivity problems and increased linewidths caused by the presence of unpaired electron spins. 

Notice lh il Ihc orbiuls nc riol paiied, >.(/i"does n ol liiivc Ihc siimc energy as An unrestricted wave ftinction like this is a natural way of representing system s with unpaired electron s, such as the doublet shown here or a triplet state ... 

The degree to which allylic radicals are stabilized by delocalization of the unpaired electron causes reactions that generate them to proceed more readily than those that give simple alkyl radicals Compare for example the bond dissociation energies of the pri mary C—H bonds of propane and propene... 

Iron carries half the charge of a whole electron. The calculation produces a set of molecular orbitals appropriate for this pseudowave function. HyperChem then assigns the unpaired electron its proper spin (alpha), substitutes this electron in the orbital formerly occupied by the half electrons, and calculates energy and other properties. 

DE, since the 7c-electron energy is 4a + 4/3, the same as that for two independent double bonds. Thus, at this level of approximation, HMO theory prediets no stabilization for eyelobutadiene from delocalization and furthermore predicts that the molecule will have unpaired electrons, which would lead to very high reactivity. In addition, cyclobutadiene would suffer angle strain, whieh is not present in benzene. The extreme instability of eyelobutadiene is then understandable. Higher-level MO ealculations modify this picture somewhat and predict that eyelobutadiene will be a rectangular molecule, as will be diseussed in Chapter 9. These ealculations, nevertheless, agree with simple HMO theory in... 

It is of interest to be able predict the stability of such fiised-ring compounds. Because Huckel s rule applies only to monocyclic systems, it cannot be applied to the fiised-ring compounds, and there have been many efforts to develop relationships which would predict their stabihty. The underlying concepts are the same as for monocyclic systems stabilization should result from a particularly stable arrangement of MOs whereas instability would be associated with unpaired electrons or electrons in high-energy orbitals. 

The molecular orbital description of the bonding in NO is similar to that in N2 or CO (p. 927) but with an extra electron in one of the tt antibonding orbitals. This effectively reduces the bond order from 3 to 2.5 and accounts for the fact that the interatomic N 0 distance (115 pm) is intermediate between that in the triple-bonded NO+ (106 pm) and values typical of double-bonded NO species ( 120 pm). It also interprets the very low ionization energy of the molecule (9.25 eV, compared with 15.6 eV for N2, 14.0 eV for CO, and 12.1 eV for O2). Similarly, the notable reluctance of NO to dimerize can be related both to the geometrical distribution of the unpaired electron over the entire molecule and to the fact that dimerization to 0=N—N=0 leaves the total bond order unchanged (2 x 2.5 = 5). When NO condenses to a liquid, partial dimerization occurs, the cis-form being more stable than the trans-. The pure liquid is colourless, not blue as sometimes stated blue samples owe their colour to traces of the intensely coloured N2O3.6O ) Crystalline nitric oxide is also colourless (not blue) when pure, ° and X-ray diffraction data are best interpreted in terms of weak association into... 

Radical stability can often be explained in the same way as ion stability molecules that delocalize unpaired electrons tend to be more stable. Display spin density surfaces for 1-propyl and 2-propyl radicals. In which is the unpaired electron more delocalized Is this also the lower-energy radical ... 

Examine spin density surfaces for l-bromo-2-propyl radical and 2-bromo-l-propyl radical (resulting from bromine atom addition to propene). Eor which is the unpaired electron more delocalized Compare energies for the two radicals. Is the more delocalized radical also the lower-energy radical Could this result have been anticipated using resonance arguments ... 

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