Point groups high-symmetry

Note The group of SI. No. 32 is the most highly symmetrical of all the point group of symmetry. 

The electronic spectrum of the radical has been recorded long before a satisfactory theoretical explanation could be provided. It was realized early on that the system should be Jahn-Teller distorted from the perfect pentagon symmetry (D5/, point group). Recently, an extensive experimental study of the high-resolution UV spectrum was reported [76], and analyzed using Jahn-Teller formalism [73],... 

Molecules belonging to the 4 point group are very highly symmetrical, having 15 C2 axes, 10 C3 axes, 6 C5 axes, 15 n planes, 10 axes, 6 5io axes and a centre of inversion i. In addition to these symmetry elements are other elements which can be generated from them. 

The III character table is given in Table A.46 in Appendix A. The very high symmetry of this point group results in symmetry species with degeneracies of up to five, as in and... 

At higher frequencies (above 200 cm ) the vibrational spectra for fullerenes and their cry.stalline solids are dominated by the intramolecular modes. Because of the high symmetry of the Cgo molecule (icosahedral point group Ih), there are only 46 distinct molecular mode frequencies corresponding to the 180 6 = 174 degrees of freedom for the isolated Cgo molecule, and of these only 4 are infrared-active (all with Ti symmetry) and 10 are Raman-active (2 with Ag symmetry and 8 with Hg symmetry). The remaining 32 eigcnfrequencies correspond to silent modes, i.e., they are not optically active in first order. 

Crystals with one of the ten polar point-group symmetries (Ci, C2, Cs, C2V, C4, C4V, C3, C3v, C(, Cgv) are called polar crystals. They display spontaneous polarization and form a family of ferroelectric materials. The main properties of ferroelectric materials include relatively high dielectric permittivity, ferroelectric-paraelectric phase transition that occurs at a certain temperature called the Curie temperature, piezoelectric effect, pyroelectric effect, nonlinear optic property - the ability to multiply frequencies, ferroelectric hysteresis loop, and electrostrictive, electro-optic and other properties [16, 388],... 

For all but the few smallest clusters, the number of possible structures is virtually unlimited. In order to be able to treat the larger systems, quite restrictive assumptions about their geometry has to be made. For those clusters where well-defined equilibrium structures do exist, these are likely to possess a non-trivial point-group symmetry (in many cases the highest possible symmetry). It therefore seemed justified to focus the study on high-symmetric systems. Symmetry can also be used to simplify the calculation of electronic structure, and reduces the number of geometrical degrees of freedom to be optimized. 

Interpenetration of Reactants. A detailed structural examination (Figure 1) reveals the inherent difficulties in attempting to define a "contact" separation for reactants of the type considered here. In spite of the deceptively high symmetry (e.g., the Tg point group assumed in Figure 1 and (13)), the... 

The connection between the diffraction group and the point group is obtained from Table II. High symmetry diffraction groups are very useful. One or a few Zone-Axis Patterns are required to identify the point group. 

In the late 1970s no ab initio programs contained algorithms for directly computing IR frequencies or intensities. However, two groups independently (Kollmar and Staemmler and Hess and Schaad ) undertook the calculation of the IR spectrum of 1. This required a point-by-point calculation of the force-constant matrix, but fortunately the high symmetry (D2 ) of cyclobutadiene significantly... 

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