C2-symmetry

The n ==> n transition thus involves ground Ai) and exeited Ai) states whose direet produet (Ai x Ai) is of Ai symmetry. This transition thus requires that the eleetrie dipole operator possess a eomponent of Ai symmetry. A glanee at the C2v point group s eharaeter table shows that the moleeular z-axis is of A symmetry. Thus, if the light s eleetrie field has a non-zero eomponent along the C2 symmetry axis (the moleeule s z-axis), the n ==> 71 transition is predieted to be allowed. Light polarized along either of the moleeule s other two axes eannot induee this transition. 

The tetra alkyl amm onium salts of [B Hg] , formed by ion-exchange reactions, have proven to be useful synthetic reagents because of their thermal and air stabihties. The stmcture of the [B Hg] ion has been determined by an x-ray study (66) and shown to have the 2013 styx stmcture, C2 symmetry. Mechanisms for the formation of this ion have been proposed (67). Tetraborane(lO) can be easily obtained from salts of [B Hg] (eq. 9). 

Vibrational spectra including Raman data of 3,3-dimethyldiaziridine and its hexadeutero compound were recorded in the gas phase and in the crystalline state. Assuming C2 symmetry and employing isotopic shifts and comparison with azetidine, a classification of bands which regarded 33 normal modes could be given (75SA(A)1509). 

Identify segments containing nCL stereocenters which can be dissected to give precursors of C2-symmetry.36... 

The B3Hg ion (p. 166) is a triangular cluster of Cj (rather than C2 ) symmetry (see Fig. 6.15a) the bridging atoms are essentially in the B3 plane with Ht above and below. While it has been conventional to represent the cluster bonding in terms of two BHB and one B-B bond (Fig. 6.15b), recent high-level computations suggest the presence of a 3-centre BBB bond, as depicted approximately in Fig. 6.15c. 

Figure 15.23 Structure of the [S2l4] cation of C2 symmetry, showing the very short S S distance and the rather short I-I distances note also the S-I distances which are even longer than in the weak charge transfer complex [(H2N2CS)2l]+ (262.9 pm). The nonbonding I I distance is 426.7 pm.

The gaseous molecule of CI2O7 has C2 symmetry (Fig. 17.16) the CIO3 groups being twisted 15° from the staggered (C2v) configuration the C1-Om bonds are also inclined... 

The C2-symmetric epoxide 23 (Scheme 7) reacts smoothly with carbon nucleophiles. For example, treatment of 23 with lithium dimethylcuprate proceeds with inversion of configuration, resulting in the formation of alcohol 28. An important consequence of the C2 symmetry of 23 is that the attack of the organometallic reagent upon either one of the two epoxide carbons produces the same product. After simultaneous hydrogenolysis of the two benzyl ethers in 28, protection of the 1,2-diol as an acetonide ring can be easily achieved by the use of 2,2-dimethoxypropane and camphor-sulfonic acid (CSA). It is necessary to briefly expose the crude product from the latter reaction to methanol and CSA so that the mixed acyclic ketal can be cleaved (see 29—>30). Oxidation of alcohol 30 with pyridinium chlorochromate (PCC) provides alde-... 

Beckmann rearrangement of anthraquinone dioximes leads to 1.5-diazocine systems, a reaction which indirectly proves the C2-symmetry of the starting material.51,52 The reaction is induced preferentially by heating in polyphosphoric acid. 

The C2 symmetry of sulfide 13 means that a single diastereomer is formed upon alkylation (Scheme 1.10). Attack from the Si face of the ylide is preferred as the Re face is shielded by the methyl group cis to the benzylidene group (28). Metzner postulates that this methyl group also controls the conformation of the ylide, as a steric clash in 27b renders 27a more favorable [16]. However, computational studies by Goodman revealed that 27a was not particularly favored over 27b, but it was substantially more reactive, thus providing the high enantioselectivity observed... 

In the more successful reagents, the ligands have been selected in such a way that the metal center remains nonstereogenic, this has been achieved mainly by application of chiral diols with C2 symmetry or by introduction of two of the same alkoxy residues. 

Employing a C2 symmetry in the case of the thiirene 1-dioxide and remembering that the spiro-operator that mixes the fragment orbitals gives nonzero matrix elements only if these orbitals are symmetric to the C2 operation53, the net result is stabilizing. On the other hand, thiirene 1-oxide suffers a homoconjugative destabilization. 

As expected, the hexagonal chair form of Se with 03a symmetry, occurring in the solid hexasulfur, is the most stable form of hexasulfur, due to its minimal strain. The boat conformer of C2V symmetry is 50 kj mol less stable than the chair form [54]. The Dsa—>C2v interconversion requires to overcome a barrier of ca. 125 kJ mol A structure of C2 symmetry, which is a local minimum at the HF/3-21G level [49, 50], is not a stationary point at higher levels of theory [54, 55]. 

UB3LYP theory predicts four minima of Sg which possess Cj, Cjhy O2 d C2 symmetries. At the UMP2 level of theory, no stationary point corresponding to the C2 minimum can be located and two new local minima with and D2 symmetries appear. The Sg conformers are found to be very prone to pseudorotation and are predicted to interconvert readily. For this reason, Cioslowski et al. refer to Sg as a fluxional species [93]. Interestingly, they found that the structures corresponding to local minima are not directly interconvertible. 

In the monoclinic crystals of cyc/o-decasulfur the molecules occupy sites of C2 symmetry although the molecular symmetry is close to D2 [151, 158]. In-... 

Cyc/o-Undecasulfur Su was first prepared in 1982 and vibrational spectra served to identify this orthorhombic allotrope as a new phase of elemental sulfur [160]. Later, the molecular and crystal structures were determined by X-ray diffraction [161, 162]. The Sn molecules are of C2 symmetry but occupy sites of Cl symmetry. The vibrational spectra show signals for the SS stretching modes between 410 and 480 cm and the bending, torsion and lattice vibrations below 290 cm [160, 162]. For a detailed list of wavenumbers, see [160]. The vibrational spectra of solid Sn are shown in Fig. 23. 

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