Abstract
The character table or the table of eigen values for the D7h point group, which is not found in the literature was constructed. The constructed table is used to classify all modes of the vibrational frequencies of the IR and Raman spectra for any compound or molecule that has the D7h symmetry in the Point Group. For that, it was used for classifying all the modes of vibrational frequencies of the [7] cyclacene (linear) monitoring molecule, possessing D7h symmetry. The constructed table was used to classify the symmetry species for the total degrees of freedom, total degrees of transition, total degrees of rotation and for the total degrees of modes of vibration (3N-6) for this tube. The character table was also used to determine the active and inactive modes of vibration in the IR and Raman spectra.Also,determining the polarized and non-polarized vibrational frequencies in the Raman spectrum, and used for describing the complete physical structure of the studied molecule after extracting its geometric shape. The methods of quantum mechanics calculations PM3 and DFT were used for this purpose applying the Gaussian 09 program.
Highlights
Each molecule has a Symmetry Group that specifies ownership or non-possession of the five symmetry elements: E (Identity), the proper rotation axis (n), the level of symmetry, the axis of rotation (n) and inversion center (i)
The character table or the table of eigen values for the D7h point group, which is not found in the literature was constructed
The constructed table is used to classify all modes of the vibrational frequencies of the IR and Raman spectra for any compound or molecule that has the D7h symmetry in the Point Group
Summary
Each molecule has a Symmetry Group that specifies ownership or non-possession of the five symmetry elements: E (Identity), the proper rotation axis (n), the level of symmetry (the plane of symmetry), the axis of rotation (rotation reflection axis) (n) and inversion center (i). Such planes are known as dihedral planes, d, if they bisect the angles between the v planes or bisect the angles between two secondary axes of C2. 4- The associated symmetry element is a rotation-reflection axis (sometimes known as an alternating axis of symmetry) The symbol for such an axis is Sm where the angle of rotation is (360/n)0, and the operation of rotation by (m x (360/n)0 with m reflections in the perpendicular plane is given the symbol Snm. 5- the identity of the object E, which could be regarded as rotation by 3600.
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