Q symmetry

The tetrameric macrocycle of 21 has Q-symmetry and its conformation is similar to that of 18 with one opposite pair of imidazole rings in the plane of the molecule, and the other pair perpendicular to it. In 22 all five imidazole rings are almost perpendicular to the molecular plane, so that a CH2CI2 molecule can be included in the cavity of the pentamer. Unfortunately, compounds 19-23 are unstable under influence of air and moisture [33]. 

The trisulfane molecule exists as two conformers which have been termed as cis- and trans-HzSi. While the trans-form is a helical molecule of C2 symmetry with the motif ++ (or — for the enantiomer), the cfs-form is of Q symmetry with the motif +- (identical to -+). Both forms have been detected by rotational spectroscopy [17, 45, 46]. The motif gives the order of the signs of the torsion angles at the SS bonds. The geometrical parameters [17] are presented in Table 4. The trans-isomer is by only 1 kj mol more stable than the cfs-form but the barrier to internal rotation from tmns to cis is 35 kJ mor [46]. The dipole moments were calculated by ab initio MO theory at the QCISD/TZ+P level as 0.68 D (trans) and 2.02 D (cis) [46]. For geometrical parameters of cis- and trans-trisulfane calculated at the MP2/6-311++G> > level, see [34]. 

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-... 

The molecular structures of the isolated polysulfide monoanions 8 with n=2-9 have been studied by density functional calculations and those of the smaller ions also by ab initio MO calculations. Compared to the neutral 8 molecules the extra electron occupies an antibonding orbital resulting in longer 88 bonds. The species 83 is bent and of C2V symmetry (a=115°) [140, 141]. 84 was calculated to be a planar ion of C2V symmetry (similar to the neutral molecule 84) but the planar C2h structure is only slightly less stable [140, 141]. The most stable isomer of 85 is a chain of Q symmetry sim-... 

The hfs (or quadrupole) tensors of geometrically (chemically) equivalent nuclei can be transformed into each other by symmetry operations of the point group of the paramagnetic metal complex. For an arbitrary orientation of B0 these nuclei may be considered as nonequivalent and the ENDOR spectra are described by the simple expressions in (B 4). If B0 is oriented in such a way that the corresponding symmetry group of the spin Hamiltonian is not the trivial one (Q symmetry), symmetry adapted base functions have to be used in the second order treatment for an accurate description of ENDOR spectra. We discuss the C2v and D4h covering symmetry in more detail. 

The NMR spectra of C qHR exhibits 37 resonances of the fuUerene carbons, with two of them in the sp region, proving Q-symmetry for the C oHR adducts. This is consistent with an addition to a double bond of a pole corannulene imit (1,2-addition), leading to l,2-dihydro[70]fullerene derivatives. These particular [6,6] bonds of Cyg, located between the carbons of the sets A and B, have almost the same bond length as the [6,6] bonds in Cjq [30], and the pole corannulene unit also exhibits bond alternation with longer [5,6] bonds. NMR data imply that the initial attack of the nucleophile occurred on C-1 and the protonation on C-2. 

From the satellites in the ESR spectra, the symmetry of the radicals as well as the information about the localization of the unpaired electron in RGgp can be obtained (Figure 6.2). In BuGgQ, for example, ten pairs of G satellites are clearly resolved (Figure 6.1). A Q-symmetry can be deduced from their relative intensities and splittings [1, 12]. The unpaired electron is mostly located on two fused six-membered rings of the Gjq surface, which rules out an extensive delocalization on the Ggo framework. 

Since a single anti-Bredt rule compound is neccessarily asymmetric, combination of two of them should afford double anti-Bredt rule compounds ( bridgehead dienes ) either of Cs (or Q) symmetry or of C2 symmetry depending upon the ways in which the enantiomers are combined to make up the molecules. 

Similarily, the 4,14-dicarboxylic acid 56 with C2-symmetry could also be resolved via its 1-phenylethylamine salts and its configuration unambiguously correlated with the monocarboxylic acid 55 through the monobromo derivative 5878). Accordingly 55 and 56 with the same sign of optical rotation have the same chirality. Many racemic and optically active homo- and heterodisubstituted 4,12- and 4,14-disubstituted [2.2]metacyclophanes have been prepared and chemically correlated 78,79) mainly to study their chiroptical properties78). Whereas 4,12-homodisubstituted compounds have a center of inversion ( -symmetry) and are therefore achiral meso-forms , the corresponding 4,14-isomers are chiral with C2-symmetry. All heterodisubstituted products are chiral (Q-symmetry see also Section 2.9.4 for the discussion of their chiroptical properties and their use as models for the application of the theory of chirality functions). 

Introduction of nitrogen into the anulene ring (e.g. of 95) leads to a methano-azaanulene 107 121) with Q-symmetry which is therefore chiral (like its mono- or disubstituted derivatives)118). The low basicity of 107 (pKa 3.20) prevented its optical resolution by conventional methods (e.g. through salts with optically active acids). Excellent results were obtained, however, (as also in the case of the two isomeric carbocyclic methylesters 97 and 101 and of several derivatives of azaanulene) by chromatography on microcrystalline triacetyl cellulose in ethanol at 7 bar 1221 (see also Section 2.7.1). In many cases base line separations were accomplished to give both (optically pure) enantiomers. Enantiomeric relations were confirmed in all cases by recording the CD-spectra of both fractions. Some results of these separations are shown in Fig. 4 together with the optical rotations ([a]D in ethanol) of the enantiomers. 

A crystal structure of the complex (20) has been reported329 and it is seen that the complex possesses a distorted Q symmetry, with a trans arrangement of the ligands. 

A crystallographic determination of the [Znl4]2- anion structure has been reported in its salt with the 2,4-dimethyl-17/-l,5-benzo diazepinium cation.1041 It possesses rigorous Q symmetry (Zn—I = 2.60 A) with deviations from the highest tetrahedral symmetry being due to packing forces. 

One of the advantages of (3) in asymmetric synthesis is its Q, symmetry. The anion of its dithiepine derivative (4) is used as a chiral version of the formyl anion [11]. 

A similar study has been carried out for the self-association of l,8a-dihydro-l, 8-naphthyridine derivatives using DFT methods (B3LYP/6-31+G and B3LYP/ 6-311++G ) [28]. Two possible dimers can be obtained from chiral 1,8a-dihydro-1,8-naphthyridine derivatives homochiral C2 dimers and heterochiral Q symmetry... 

C3 is isomorphic with the permutation group S3) to the internal coordinate R, leads to the Q symmetry coordinates... 

---