Methyl radicals, vibrationally averaged

Table 9.4 compares to experiment the isotropic h.f.s. values computed for and H in the methyl radical at the UMP2/6-311G(d,p) level both (i) at the UHF/6-31G(d) equilibrium geometry and (ii) as the expectation value over the umbrella mode vibrational wave function computed at this level. Also included are data for the monofluoromethyl radical CHiF, which is even more affected by vibrational averaging because it has a very shallow doublewell potential along the umbrella mode (i.e., the equilibrium structme is pyramidal, but the barrier to inversion is less than 1 kcal mol ), so that its vibrational wave function has large amplitude around a planar structure with smaller h.f.s. than for the equilibrium structure. 

Case Studies Vibrationally Averaged Properties of Vinyl and Methyl Radicals... 

In the following section, we will see that vibrational averaging plays a significant role in the computation of reliable hcc values for a number of interesting systems. Here, we just discuss vibrational averaging effects related to inversion at the radical center of typical n (methyl) and o (vinyl) radicals. 

If the hypothetical life-time of the excited acetyl radical is characterized by the average period of one vibration, then the acetone molecule directly decomposes into two methyl radicals and a CO molecule in this case there is no point in speaking about the acetyl radical at all. If, however, decomposition into CH3 and... 

As an example, consider the trifluoromethyl radical CF3. To determine the s-electron spin density on the carbon, one must measure the hyperflne coupling constant experimentally. This is found to be 271.6 G, which is 24% of a full 2s electron on the carbon. This implies near SP bonding in the radical and indicates that CF3 is tetrahedral and not planar. In contrast, the hyperflne coupling constant for the methyl radical CH3 is 38 G, which indicates only 3% s character. This is consistent with a near-planar structure for CH3. In fact, the time-average structure of CH3 is planar, but a small amount of s hybridization can arise from out-of-plane vibrations of the H atoms. 

When a substance is heated, the kinetic energy of atoms and molecules increases. E.g., if methane is heated, the kinetic energy of translation, vibration and rotation of methane molecules increases, as discussed in section 1.2. As heat is applied, higher vibrational states are increasingly populated. In higher vibrational quantum states, the average C-H bond distance increases until finally the C-H bond breaks. The result is the formation of a methyl radical and a hydrogen atom. 

---