Canonical orientations

Figure 12.5. If desired, these small effects can easily be exactly included by letting the simulation program output all the relative energy levels for the experimentally used frequency and for the canonical orientation that corresponds to geff = 10.4, and then using these values in Equation 12.3. The outcome of Equation 12.3 for a given experimental temperature is required for spin counting (determination of the concentration of the S = 7/2 system) using the single-peak integration procedure explained in Section 6.2.

Figure 2. Time-resolved CIDEP spectrum of the lowest triplet of GAV at 77 K. a, Am = 2 transitions at half field, b, Ani = 1 transition at the canonical orientations. The strong emissive signal at g = 2 is due to phenoxy radicals.

Clark (1969, 1973) and others (Lakoff Johnson, 1980 see also Tversky, this volume) maintain that this asymmetry of linguistic structure is rooted in the asymmetries of perceptual space. The clearest form of this argument was given by Clark, who pointed out that the structure of our bodies and our movements in the world define three reference planes, two of which are asymmetrical. The only plane characterized by perceptual symmetry is the right-left plane. Two reference planes are asymmetrical the front-back plane, and the top-bottom (or head-feet) plane. Clark claimed that the front end of the front-back plane is positive because it is the direction of movement and the side toward which most of our perceptual receptors are oriented. Similarly, he reasoned that the top end of the top-bottom plane is positive because up-down is the canonical orientation of the body as well as the primary direction of observed movement (objects fall from up to down but never in the opposite direction). The asymmetric structure of perceptual space has since been confirmed... 

In all covalent electron donor-acceptor systems produced earlier, triplet states observed by EPR were formed via a spin-orbit intersystem crossing (SO-ISC) mechanism. Another possible mechanism of triplet formation is RP-ISC, mentioned above, which results from radical ion pair recombination, and which had been observed previously by time-resolved electron paramagnetic resonance spectroscopy (TREPR) only in bacterial reaction centers and in the green plant Photosystem I and II reaction centers. These two mechanisms can be differentiated by the polarization pattern of the six EPR transitions at the canonical orientations. In SO-ISC,... 

Fig. 2.26 (a) Q-band FSE EPR (EIE) spectrum of peridinin triplet (A) absorption, (E ) emission (b) Davies ENDOR pulse sequence (c) Q-band H ENDOR spectra recorded at the three canonical orientations Xn, Yn, Zn, which are marked with arrows in the ESR spectrum of panel (a) using the conditions in panel (b). At the proton Larmor frequency vh a narrow and intense line is visible resulting from nuclear transitions in the mg = 0 manifold. The frequency axis gives the deviation from Vh in the respective spectra. The excitation wavelength was 630 nm. Left numbering and spin density plot of peridinin in its excited triplet state. The orientation of the ZFS tensor axes X, Y, and Z is also given. The figure is adapted from [51] with permission from the American Chemical Society... 

Fig. 5. Zeeman energy level diagrams for (nn ) benzophenone in canonical orientations. Allowed (A, B) and forbidden (C) transitions are shown for a frequency of 9.6 GHz (Mucha, 1974).

Having established the coincidence of the principal axes of g and D, Eq. (18) may be solved in closed form to obtain the energies, wavefunctions, and resonance fields in the three canonical orientations. These are listed in Table 8. By combining the expressions for the A is = 1 resonance fields in each of the canonical orientations, expressions for each of the six magnetic... 

Fig. 9. High-field ODMR spectra using magnetic field modulation showing C hyperfine structure observed in canonical orientations of C-benzophenone-d,o in 4,4 -dibromo-diphenylether (Brode and Pratt, 1977).

The absolute signs of the hyperfine elements are easily determined if ENDOR transitions can be detected (and assigned) by monitoring both Aws = 1 lines near canonical orientations [Eq. (38)]. The principle of the method is illustrated in Fig. 14 for the case H x. Since the absolute zf scheme is known (Z > 0 > Y > AT), and since the sign of the C nuclear magnetic moment is positive (Ramsey, 1953), it is clear that if < v ... 

Isomorphic orientation functions differ only in the chosen atom numbering, they belong to essentially equivalent conformations. Thus, when generating conformations we would like to generate exactly one representative from each class of isomorphic orientation functions. This is achieved by defining canonic orientation functions. Within each class of isomorphic orientation functions, we declare one as canonic. Thus, an efficient test to recognize whether a given orientation function is canonic or not is necessary. 

Fig. 4.18 Canonical orientations of orbitals of two carbon atoms. The shaded regions represent boundary surfaces of the wavefunctions as in Fig. 2.5. The Vy z Cartesian coordinate system is centered on atom 1 with the y axis aligned along the interatomic vector. The transition gradient matrix elements VVn and V y are for the orientations shown in A, B and C, respectively. Matrix elements for an arbitrary orientation can be expressed as linear combinations of these canonical matrix elements...

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