C, symmetry

In the present calculations, the molecule is restricted to Cs symmetry. There are five internal degrees of freedom fthe out-of-plane mode is excluded to preserve C, symmetry). Nuclear configurations will be denoted R = (R(H -O). / (0-H ), / (h2-H ), corresponding to the... 

The hi orbitals would maintain their identity going to a" symmetry. Thus Bi and A2 (both A" in Cs symmetry and odd under reflection through the molecular plane) can mix. The system could thus follow the A2 component of the C( P) + H2 surface to the place... 

The mirror plane is defined by the dummy atoms. The migrating hydrogen H le is not allowed to move out of the plane of symmetry, and must consequently have the same distance to C4 and C5. A minimization will locate the lowest energy structure within the given Cs symmetry, and a subsequent frequency calculation will reveal that the optimized structure is a TS, with the imaginary frequency belonging to the a" representation (breaking the symmetry). 

In addition to the branched rings and chains, cyclic Ss conformations of lower symmetry than Did are also likely components of liquid sulfur. For example, the following exo-endo isomer of Ss (Cs symmetry) is by just 28 kJ mor (AG°29s) less stable than the ground state conformation and therefore its relative concentration in liquid sulfur and sulfur vapor at the boiling point will also be 1% of all Ss species [35]. 

The free Sy molecule is of Cs symmetry but in its various solid allotropes it occupies sites of Ci symmetry [154]. In any case, in these point groups all fundamental modes are infrared and Raman active and no degeneracies occur. Four allotropes of Sy (a, p, y, S) have been identified by Raman spec-... 

The intense yellow rodlike crystals of S14 contain molecules of approximate Cs symmetry on sites of Ci symmetry [165]. Their Raman spectra recorded at -100 °C exhibit the expected pattern Stretching modes give rise to lines between 440 and 485 cm. This rather narrow region reflects the very narrow bond distance distribution in S14 molecules (204.7-206.1 pm). As usual, the bending, torsional and lattice modes show up below 300 cm (see Table 11 and Fig. 26). 

The symmetrical thiosulfoxide isomer of tetrasulfane (HS)2S=S is also of Cs symmetry and by 123 kJ mol" less stable than the chain-like ground state of C2 symmetry (at the MP2/6-31GV/HF/4-31G level of theory) [51]. However, at the much higher G3(MP2) level the energy difference is only 93 kJ mol [52]. Similarly, the two hexasulfane isomers (HSS)2S=S (Cs symmetry) and (HS)(HSSS)S=S (Q symmetry) have recently been calculated at the G3X(MP2) level to be by 53 and 54 kJ mol respectively, less stable than the helical chain of C2 symmetry [52]. The decreasing energy difference be-... 

Vibrational spectroscopy and in particular Raman spectroscopy is by far the most useful spectroscopic technique to qualitatively characterize polysulfide samples. The fundamental vibrations of the polysulfide dianions with between 4 and 8 atoms have been calculated by Steudel and Schuster [96] using force constants derived partly from the vibrational spectra of NayS4 and (NH4)2Ss and partly from cydo-Sg. It turned out that not only species of differing molecular size but also rotational isomers like Ss of either Cy or Cs symmetry can be recognized from pronounced differences in their spectra. The latter two anions are present, for instance, in NaySg (Cs) and KySg (Cy), respectively (see Table 2). 

For CP50B, it was reported [97] that the molecules have exact Cs symmetry as a consequence of their location on crystallographic mirror symmetry planes. The cyanophenyl group is perpendicular to the mirror plane, whereas the other phenyl ring and the carbonyloxy group are coplanar and located in... 

The allyl radical [115] trapped in an argon matrix can be photolytically (A = 410 nm) converted into the cyclopropyl radical [116] (Holtzhauer er a/., 1990). Dicyclopropane and cyclopropane were formed when the photolysed matrix was warmed from 18 to 35 K. The intermediate [116] was shown to be a cr-type (Cs symmetry) and not a rr-type symmetry) radical. Normal coordinate analysis of the radical [116] has been carried out and the IR band at 3118 cm has been assigned to the stretching vibration of the C—H bond at the radical centre. 

Oxirane is an important Lewis base in the present context. The O atom carries two equivalent n-pairs of electrons, as it does in H20, but oxirane has the advantage over water in that it is possible to determine both angles 0 and 9 for its complexes with HC1 and ClF because the non-zero off-diagonal element Xab(Cl) of the Cl nuclear quadrupole coupling tensor is available. The corresponding Lewis base in which an S atom carries two equivalent n-pairs is thiirane. Each of the pair of complexes (CL S- -HC1 and (CL S- -ClF has Cs symmetry and here it is the off-diagonal element Xac(Cl) that is non-zero... 

Fig. 28. Schematic of potential energy surfaces of the vinoxy radical system. All energies are in eV, include zero-point energy, and are relative to CH2CHO (X2A//). Calculated energies are compared with experimentally-determined values in parentheses. Transition states 1—5 are labelled, along with the rate constant definitions from RRKM calculations. The solid potential curves to the left of vinoxy retain Cs symmetry. The avoided crossing (dotted lines) which forms TS5 arises when Cs symmetry is broken by out-of-plane motion. (From Osborn et al.67)...

The SOMO in these radicals is expected from extended Hiickel MO calculations27-29 to be primarily cobalt 3dyz in character. In the Cs symmetry of the radicals, dyz belongs to the a" representation and d-hybridization is possible only with dxy. Assuming that such hybridization is negligible, the g-matrix... 

These systems have been extensively studied over the past 40 years with the majority of the reports appearing in the literature prior to 1996. Thus, readers are referred to Sections 4.38 of CHEC(1984) <1984CHEC(4)1049> and 8.32.4 of CHEC-II(1996) <1996CHEC-II(8)833> for full accounts of the previous work in this area. Thus, this chapter focuses primarily upon new developments in this field of research. First, the long-standing question of the whether these compounds have C2v or Cs symmetry will be addressed. Second, novel reactivity of these systems will be explored. Finally, new methods for their synthesis will be presented. 

The next debate in the literature was whether these molecules have C2v or Cs symmetry. The nuclear motion of a C2v symmetric structure would be described by a single-well potential (see Figure 10). The alternative is a rapid interconversion of two valence tautomers, each of Cs symmetry. This would occur via the C2v structure as transition state (see Figure 11). In this case the motion of the central sulfur would be described by a double-well potential, and dioxathiapentalene and trithiapentalene would be misnomers for (3//-l,2-oxathiol-3-ylidene)acetaldehyde 180 and (3/7-1,2-dithiol-3-ylidene)thioacetaldehyde 181. One advantage of C2v symmetry is aromatic stabilization from the 1071 electrons <2001CRV1247>. The alternative Cs symmetry has the advantage of avoiding a hypervalent sulfur. 

A calculation approach to this question is ongoing, but it has been noted that the conclusion depends on the level of approximation <1999JMT1>. According to Hartee-Fock calculations, the most stable structure of l,6,6aA-trithia-pentalene 175 has Cs symmetry, with the structure 8.7 or 10.7 kcal mol 1 higher in energy <1991JA6449>. 

By contrast, the synthesis of syndiotactic PP, s-PP, is generally catalyzed by Cs-symmetry ansa- metallocenes. For example, (16)/MAO affords PP with a pentad (rrrr) content of 86% at 25 °C.77 The stereoselectivity is highly sensitive to ligand variation. For example, substitution at the 3-position of the Cp ring with a methyl group affords heterotactic PP,78 whilst the Bu analog favors i-PP production.50,75,79... 

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