Planar rotation, degree

To understand the function of a protein at the molecular level, it is important to know its three-dimensional stmcture. The diversity in protein stmcture, as in many other macromolecules, results from the flexibiUty of rotation about single bonds between atoms. Each peptide unit is planar, ie, oJ = 180°, and has two rotational degrees of freedom, specified by the torsion angles ( ) and /, along the polypeptide backbone. The number of torsion angles associated with the side chains, R, varies from residue to residue. The allowed conformations of a protein are those that avoid atomic coUisions between nonbonded atoms. 

Tetramethylene. With increasing chain length, the mrniber of rotational degrees of freedom increases and it becomes more and more difficult to discuss the structural dependence of SOC. However, some qualitative results may be obtained by following Michl [11] and viewing tetramethylene as "ethanologous" triplet ethylene (15) for the purpose of understanding the delocalization of the radical electrons. In order for condition (2) to be fulfilled, the ethylene substructure must not be planar. 

Nelsen and coworkers determined a barrier to inversion through the planar form in 2 and 3 to be approximately 2 kcalmol-1 by variable temperature ESR spectroscopy [59]. Gerson and coworkers found, also by ESR spectroscopy, that the frequency of electron exchange between the two sites in 4, which is equivalent to rotation about the central bond, can vary between < 106 and > 109 s-1 depending the degree of steric hindrance to planarity [60]. Recent calculations also provide very small barriers to inversion through the planar form [56,57]. It is apparent, therefore, that for most synthetic purposes most alkene radical cations can be considered as essentially planar with effective delocalization over the two sp2-hybridized C atoms, and they will be considered as such in this chapter. 

These studies suggested a planar ylidic carbon and definite participation of the P d orbitals in the description of the HOMO. The earliest ab initio study of methylenephosphorane found a very small rotational barrier [0.003 kcal mol-1 (1 kcal = 4.184 kJ)] about the P=C double bond64. These three points, the degree of pyramidalization at the ylidic carbon, the role of the P d orbitals and the P=C rotational barrier, remain the focal points of all theoretical studies of the ylides. A summary of the theoretical structures determined using ab initio techniques is given in Table 7. 

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