Symmetry effects

FIGURE 5.5 Typical pattern of a sulfide-bridge in the cat pheromone Felinine. (Cartesian RDF, 128 components). Two typical distances, 1.84 and 2.75 A, are a characteristic feature for the presence of the sulfide bridge. 

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Stanley R J, King B and Boxer S G 1996 Excited state energy transfer pathways in photosynthetic reaction centers. 1. Structural symmetry effected. Phys. Chem. 100 12 052-9... 

C3.2.2.4 BRIDGE ORBITAL SYMMETRY EFFECTS IN CHEMICAL SYSTEMS... 

It is beyond the scope of these introductory notes to treat individual problems in fine detail, but it is interesting to close the discussion by considering certain, geometric phase related, symmetry effects associated with systems of identical particles. The following account summarizes results from Mead and Truhlar [10] for three such particles. We know, for example, that the fermion statistics for H atoms require that the vibrational-rotational states on the ground electronic energy surface of NH3 must be antisymmetric with respect to binary exchange... 

We note that 02 4 vanishs if two of the four the frequency arguments Wq, wi, u>2, W3 become zero. For the case that three frequency arguments are equal (third harmonic generation) both mixed-symmetry effective frequencies w 2 vanish. The coefficients Amsi Bms, etc. 

Qualitatively, all proposals indicate a linear dependence on ml (linewidth over a hyperfine pattern increases from low to high field or vice versa cf. Figure 9.4) plus a quadratic dependence on m, (outermost lines more broadened than inner lines). Multiple potential complications are associated with the lump parameters A, B, C, notably, their frequency dependence (Froncisz and Hyde 1980), partial correlation with g-strain (Hagen 1981), and low-symmetry effects (Hagen 1982a). The bottom line quantitative description of these types of spectra has been for quite some time, and still is, awaiting maturation. 

Figure 9. Dyads used for investigating orbital symmetry effects on ET rates. Centre Orbital symmetries of the active MOs involved in the ET processes for 2(8) and 4(8).

The second example (Figure 9) of orbital symmetry effects concerns photoinduced charge separation in the norbornylogous dyads, 5(7) and 6(7), which is symmetry forbidden in the former system but symmetry allowed in the latter. In these systems, orbital symmetry effects are more pronounced than in 2(8) and 4(8), amounting to a 28-fold modulation in the magnitude of Vj201... 

A. M. Oliver, M. N. Paddon-Row, J. Kroon, J. W. Verhoeven, Orbital Symmetry Effects on Intramolecular Chaige Recombination , Chem. Phys. Lett. 1992, 191, 371-377. 

The phenomenon of asymmetric hfs tensors was first discussed by McConnell134). Later, Kneubiihl135,136) proved the existence of asymmetric g and A tensors in paramagnetic systems with low symmetry. Evaluation of the asymmetry of A using EPR and ENDOR spectroscopy has been treated by several authors132,137 141). Recently, low-symmetry effects in EPR have been covered in a comprehensive review article by Pilbrow and Lowrey142). 

An interesting illustration of the importance of orbital symmetry effects is the contrasting stability of azo compounds 16 and 17. Compound 16 decomposes to norbomene and nitrogen only above 100°C. In contrast 17 eliminates nitrogen immediately on preparation, even at —78°C.221... 

According to the generalized Woodward-Hoffmann rule, the total number of (4q + 2)s and (4r)0 components must be odd for an orbitally allowed process. Thus, Eq. (14) is an allowed, and Eq. (13) a forbidden sigmatropic rearrangement. The different fluxional characteristics of tetrahapto cyclooctatetraene (52, 138) and substituted benzene (36, 43, 125) metal complexes may therefore be related to orbital symmetry effects. 

In terms of the Dewar-Chatt model of bonding, for v metal complexation one double bond is effectively removed from the fullerene conjugation system due to extensive interaction between metal d orbitals and the fullerene HOMO and LUMO (7). The remaining 29 double bonds then behave almost identically to uncomplexed C60 with their IR, Raman, UV-vis, and 13C NMR spectra showing only slight perturbations, mainly as a result of diminution of symmetry effects. Nevertheless, it is important to state that the fullerene metal interaction is not confined purely to the former s HOMO and LUMO, and that other molecular orbitals are energetically suitable for interaction 89,90). The spectroscopic evidence cited for the preceding statement is as follows ... 

The second transformation is again Schofield s, and the first one has been added to assure the exact reproduction of the quantum mechanical ideal gas behavior if particles exchange symmetry effects may be neglected [318, 286]. 

It is obvious that independently of the rate of exchange the NMR spectrum of a system subject to a dynamic equilibrium depends on the relative concentrations of the components present. These may be expressed as mole fractions or, in the case of intramolecular exchange, as conformer populations. Sometimes the populations are governed by symmetry effects alone and are independent of the experimental conditions. This is always the case for mutual exchange when the process does not alter the chemical identity of a molecule. Examples of such exchange may be drawn from rotations of the t-butyl group in (CH3)3C-C(R1)(R2)(R3), and those about the CO-N bond in N,N-dimethyl-substituted amides (CH3)2N-C(=0)R. Other examples include ring inversions such as those in 1,2-ds-dimethylcyclohexane, 1,3-trans-... 

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