Rotational angles, coupling relation

It is an essential feature of the sequence (Fig. 2.53) that only the x components of the doublet vectors 1 and 2 will be rotated by the 90° pulse in (f). The magnitudes of these components depend on the phase angle cp, which is related to the proton shift <5H. To conclude, the extent of polarization transfer (Fig. 2.53 (f-g)) is a function of proton chemical shift. After the first Fourier transformation in the t2 domain, carbon-13 signals with modulated amplitudes will be obtained when ty is varied. Chemical shifts of the attached protons are the modulation frequencies. Therefore, a second Fourier transformation in the lL domain provides maximum signals located at the chemical shifts b H and <5C of the coupling proton and carbon-13 nuclei. 

Besides this coordinate sets, other sets of orthogonal vectors have been considered in the literature. Kinematic Rotations by mass-dependent matrices allows to relate different particle couplings in the Jacobi scheme, and to build up alternative systems such as those based on the Radau-Smith vectors and hyperspherical coordinates [1,3]. The Radau-Smith vectors RSi, RS2 and the angle cos Urs (0 < )rs < n), showed in Figure 3 (the D point is defined by OD = OE x OA, where O is the center-of-mass of the BC couple, E is the center-of-mass of the three particles and A is the position of the A particle), can be calculated from the Jacobi vectors xa and X using ... 

It was also found by H-NMR spectroscopy that the phenyl ring in arylidenebarbiturates (5) is twisted in relation to the plane of the ylidenebarbi-turate.114115 A detailed analysis of chemical shifts of particular aromatic protons and their coupling constants with the vinyl proton leads to the conclusion that the value of the dihedral angle 6 (Fig. 9) depends on the nature and position of substitution in the aromatic ring. Ortho substitution in the phenyl ring, where steric effects predominate, results in hindrance to rotation. Thus of the two possible conformations conformer A (Fig. 10) is favored. Moreover, for o-nitro substituted derivative 5 the dihedral angle is 43°.115... 

When the expectation value of (II.4) is taken over the product of the ground state wave functions for molecules a and b, the result is the sum of coupling energies for the permanent electric moments in the two molecules. If the moments are known, or taken as parameters, the electrostatic interaction energy is known for a chosen orientation, and can be compared for d and I species. By forming averages over angles we can make the calculation for molecules in relative rotational motion. First it is useful to examine the symmetry restrictions imposed by chiral character, and to see how the moments in one chiral enantiomer are related to those in the other. 

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