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Abstract

In this paper we, present some MATLAB and GAP programs and use them to find the automorphism group of the Euclidean graph of the C80 fullerence with connectivity and geometry of Ih symmetry point group. It is proved that this group has order 120 and is isomorphic to Ih≊Z2×A5, where Z2 is, a cyclic group of order 2 and A5 is the alternating group on five symbols.

Abstract

Pentacene have recently become the subject of intense studies due to their physical properties which follow from the states of their outer-shell electrons that are able to take part in molecule bonding. The symmetry of these molecules provides the classification of quantum states according to the group theory method. In this paper, we apply a molecular state-space factorization scheme for the classification of pentacene molecules based on the structure of their electron states.

1 Introduction Group theory is important in organic chemistry in studying symmetry of molecules [ 2 ]. Usually, all the molecules are symmetric and rotations and vibrations of bonds are important [ 3 ]. For example, from the symmetries of molecular orbital wave functions one can figure out the information about the binding [ 4 ]. From the symmetries, we can explain the transition and change the bands [ 3 , 4 ]. Symmetry elements and symmetric operations are important concepts in group theory and if we apply any operation on a molecule and the molecule remains

, groupoids and higher-dimensional analogues and various symmetry aspects of polygones (tilings), polyhedra (tesselations) and polytopes, are also considered. Furthermore, symmetry concepts for the description of the symmetry of molecules, liquids, crystals and quasicrystals as well as symmetry representation of phase transformations are treated. The contributions of part II cover a wide range of symmetry studies, such as — detection of symmetry by the human eye-brain system — symmetry aspects of living matter — symmetry in free markets — symmetry in music — description of

certainly. I have come across cases where other physi- cal scientists have made gross errors of interpretation be- cause they had an insufficient grasp of the crystallography of their sample. Of prime importance are the symmetry aspects. Chemists appreciate point symmetry of molecules but often do not appreciate the effects of translational symmetry. I think something that is becoming a problem and will increasingly become more of a problem is that many people are using standard crystallographic software packages without having more than a cursory knowledge of what the

), as well as methods of nonlinear coherent Raman spectroscopy. Furthermore, the methods near-infrared spectroscopy, vibrational optical activity, infrared reflection, attenuated total reflection (ATR), time-resolved FTIR, high pressure techniques, and spectrometric determination of sample temperature are in- troduced. The character table follows from the section 7. This table lists all the possible different irreducible representations (species) of a point group describing the symmetry of molecules and molecular vibrations as well as their activity in infrared

different irreducible representations (species) of a point group describing the symmetry of molecules and molecular vibrations as well as their activity in infrared absorption and/ or Raman scattering. An extensive literature index and a subject index are given at the end of this monograph. This book gives a unique in theory, sophisticated experimental features, and examples for the application of these important spectroscopic methods, including many applications of non-classical Raman spectroscopy and spectroscopy under extreme conditions. It is the merit of the editor

, b la,b 6a « Ac2Q 8a o - 7a 9a Scheme 2. Due to the structural symmetry of molecule 9a, its 'H NMR spectrum has a very few signals. The values of coupling constants J2,3 (J2o,3a = 8 . 3 and J2ai3p = 4.5 Hz) and J5,6 (J5a,6a = 8.3 and J5o,6p = 4.5 Hz) displayed the exo relative stereochemistry of C-2 pyridine and C-6 phenyl groups in this bicycle.14 Electronic density of 366 J.R. Castro et al. Heterocylcic Communications pyridine and phenyl rings of rigid molecule 9a affect equally on the protons at C-2 and C-6, which resonate at 4.10 ppm. A triplet

probably never reached the compartmentalized synthesis sites in intact forms. Feeding of [2-13CJ—glycine resulted in the enrichment of all the carbons in gonyautoxin—II, , but in this case, C-ll and 0-12 were enriched significantly higher than the rest of the carbons (Fig. :3). The pathway shown in Fig. 1 can provide a plausible explanation for this rather unexpected enrichment of the neighboring carbons from the single labelled precursor. Glycine was first introduced into the TCA cycle via the glyoxalate pathway. In the TCA cycle, the symmetry of molecule will be lost

arrangement, because the twofold symmetry of molecules cause the same packing problem as that described in the previous case. Case ACB'D'. The space group here is P2i/a; individual molecules are centrosjmimetric. The refinement was performed using the same least-squares procedure as before. The R value for refinement with weights inversely proportional to the square of the standard deviation of the individual structure factors (calculated from counting statistics) was 0.021. There was a strong correlation between atoms related by pseudo- mirror planes and the difference map