Molecular orbitals of radicals

The advantage of this radiation chemical method is that the by-products of radical ions are scarcely generated, because the direct decomposition of solute molecules by ionizing radiation is negligible due to low solute concentration. Another advantage is that the molecular orbitals of radical ions are scarcely disturbed by their counterpart ions, because electrons or holes are captured by solute molecules after traveling more than 5 nm from the point of ionization [34]. 

FIGURE 11 10 The lowest energy tt molecular orbital of benzyl radical shows the interaction of the 2p orbital of the benzylic carbon with the TT system of the aromatic ring... 

Aromatic Radical Anions. Many aromatic hydrocarbons react with alkaU metals in polar aprotic solvents to form stable solutions of the corresponding radical anions as shown in equation 8 (3,20). These solutions can be analyzed by uv-visible spectroscopy and stored for further use. The unpaired electron is added to the lowest unoccupied molecular orbital of the aromatic hydrocarbon and a... 

Problem 15.10 I Show the relative energy levels of the seven 77 molecular orbitals of the cvclohepta-trienyl system. Tel) which of the seven orbitals are filled in the cation, radical, and anion, and account for the aromaticity of the cycloheptatrienyl cation. 

Draw an energy diagram for the three molecular orbitals of the cyclopropenyl system (C l I3). How ate these three molecular orbitals occupied in the cyclopropenyl anion, cation, and radical Which of the three substances is aromatic according to Hiickel s rule ... 

The rationale behind this choice of bond integrals is that the radical stabilizing alpha effect of such radicals are explained not by the usual "resonance form" arguments, but by invoking frontier orbital interactions between the singly occupied molecular orbital of the localized carbon radical and the highest occupied molecular orbital (the non-bonding electrons atomic orbital) of the heteroatom (6). For free radicals the result of the SOMO-HOMO interaction Ts a net "one-half" pi bond (a pi bond plus a one-half... 

Figure 13.3 The n molecular orbitals of the allyl cation. The allyl cation, like the allyl radical, is a conjugated unsaturated system. The shapes of molecular orbitals for the allyl cation calculated using quantum mechanical principles are shown alongside the schematic orbitals. 

Diagrams AS, ISA, and 2SA (S = MO symmetric with respect to the plane, A = MO asymmetric with respect to the C2 axis) represent the symmetries of three lowest unoccupied molecular orbitals of a phenoxy radical. The order of increasing energy AS < ISA < 2SA is chosen according to an extended Hiickel calculation. Consideration of the symmetry properties of these MO s led Sandner, Hedaya, and Trecker34 to the following conclusions ... 

In this particular example we could have avoided some of the labour involved in finding the combinations of hybrid orbitals which are equal to px and ptf, by using the 8 point group (to which the molecule also belongs). For this point group, the two-dimensional representation, the cause of all the trouble, can be expressed as two complex one-dimensionl representations. The orbitals p, and py are then just as easy to obtain as the s-orbital. Any complex numbers which result are eliminated at the end of the treatment by addition and subtraction of the orbitals formed. This is the technique which was used in 10-7 to find the 7T-molecular orbitals of the trivinylmethyl radical. It is, however, of no avail when dealing with point groups which have three-dimensional irreducible representations as in our next example, CH4. 

These spectroscopic techniques tie the states of [1.1.1 ]propellane to those of its radical cation and radical anion and are usually interpreted as semiquantitative indicators of the nature of occupied and unoccupied molecular orbitals of the neutral species, respectively, through the use of Koopmans theorem. 

The initial step of the Birch reduction is an electron transfer to the lowest unoccupied molecular orbital of the benzene tt system (see Figure 21-5) to form a radical anion ... 

Esr spectra are subject to exchange effects in the same way as nmr spectra. A specific example is provided by electron exchange between sodium naphthalenide and naphthalene. Naphthalene has a set of ten 77-molecular orbitals, similar to the six 7r-molecular orbitals of benzene (Figure 21-5). The ten naphthalene it electrons fill the lower five of these orbitals. In a solvent such as 1,2-dimethoxyethane, which solvates small metal ions well, naphthalene accepts an electron from a sodium atom and forms sodium naphthalenide, a radical anion ... 

---