Degenerate conformations

For molecules with an even number of electrons, the spin function has only single-valued representations just as the spatial wave function. For these molecules, any degenerate spin-orbit state is unstable in the symmetric conformation since there is always a nontotally symmetric normal coordinate along which the potential energy depends linearly. For example, for an - state of a C3 molecule, the spin function has species da and E that upon... 

Figure 23 shows sections of with J fixed, C2 = 0 and various values of L/N, where V = 27 is the total polyad action. There is an obvious conical point, X, at K, L) = (7,0). In addition, the concentric contours degenerate to points Y and Z at K, L) = (—7, V). It is important for what follows to explore the character of the point X. As a preliminary, the Hamiltonian may be reduced from the above seven-parameter form, to one involving two essential parameters, both of which vary with the total action. The appropriate definitions [14, 28, 29], modified to conform with the present (7, K) notation, are... 

The observed degeneration of the stereodynamic pattern of these processes is due to the fact that all conformers containing the axial lone pair at the nitrogen atom are thermodynamically highly unfavorable. Calculations also confirmed that the axial position of the nitrogen lone electron pair is highly unfavorable (see Chart 3.15). 

The cyclopentyl cation (39) undergoes a rapid degenerate rearrangement which can be frozen out at cryogenic temperatures as shown by solid state CPMAS 13C NMR spectra.57 MP2/6-31G(d,p) calculations show that cyclopentyl cation has a twisted conformation 4058 in which the axial hydrogens are bend toward the carbocation center. This is due to the pronounced geometrical distortion caused by the hyper-conjugative interaction of the /i-cr-C-H-bond with the formally vacant 2pz-orbital at the C+ carbon of this secondary carbocation. 

Examples of the role of the lattice in generating radicals in a given conformation, and in selecting one among many nominally degenerate pathways, have been described (246). 

Studies of molecules containing pairs of OH or C=0 oscillators have provided the most direct application of the degenerate coupled oscillator model of VCD to determine molecular conformation in solution. 

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