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.
Density Functional Theory (DFT) method of the type (B3LYP) and a Gaussian basis set (6-311G) were applied for calculating the vibration frequencies and absorption intensities for normal coordinates (3N-6) at the equilibrium geometry of the Di and Tetra-rings layer (6, 0) zigzag single wall carbon nanotubes (SWCNTs) by using Gaussian-09 program. Both were found to have the same symmetry of D6d point group with C--C bond alternation in all tube rings (for axial bonds, which are the vertical C--Ca bonds in rings layer and for circumferential bonds C—Cc in the outer and mid rings bonds). Assignments of the modes of vibration IR active and inactive vibration frequ
... Show MorePM3 and DFT (6-311G/ B3LYP) level calculations were carried out for the 5Radialene molecule, which is exhibit D5h symmetry. The obtained equilibrium geometry was applied for the calculation of all 3N−6 vibration frequencies, and for the analysis of its normal coordinates and symmetry species, in addition to some physical properties such as heat of formation, total energy, dipole moment and energy difference of HOMO and LUMO levels (ΔELUMO-HOMO), using Gaussian-03 program. The so calculated frequencies according to DFT (6-311G/ B3LYP) fall in the ranges;
CH2 str. (3016-3098 cm-1), C=C str. (1662-1709cm-1), ring (C-C str.) (1268-1464 cm-1). δCH2 (890-1317cm-1), (δCCC) (562-631cm-1), γCH2 (738-946cm-1) and γring (γCCC) (
DFT (3-21G, 6-31G and 6-311G/ B3LYP) and Semi-empirical PM3 methods were applied for calculating the vibration frequencies and absorption intensities for normal coordinates (3N-6) of the Tri-rings layer (6,0) Zigzag single wall carbon nanotube (SWCNT) at their equilibrium geometries which was found to have D6h symmetry point group with C-C bond alternation in all tube rings.as well as mono ring layer. Assignments of the modes of vibration were done depending on the pictures of their modes applying by Gaussian 03 program. The whole relations for the vibration modes were also done including (CH stretching, CC stretching, deformation in plane of the molecule (δCH, δring and δCCC), deformation out of plane of the molecule (CH and
... Show MoreIn this paper, we construct a new mathematical system as Multiplicative Cyclic Group (MCG), called a New Digital Algebraic Generator (NDAG) Unit, which would generate digital sequences with good statistical properties. This new Unit can be considered as a new basic unit of stream ciphers.
A (NDAG) system can be constructed from collection of (NDAG) units using a Boolean function as a combining function of the system. This system could be used in cryptography as like as Linear Feedback Shift Register (LFSR) unit. This unit is basic component of a stream cipher system.
A study of the emission spectra of isotopic for electronic states has been carried out. The energies of the vibration levels ( =0,1,..25) and the values of spectral lines R(J) and P(J) versus rotational quantum number (J=0,1..25). It was found that were an increase of the value of R(J) with the increase of the values of J was found while the value of P(J) decreases with decreasing of the values of J . It was found that corresponding to R(J) and P(J) the spectral line R(J) increases when the values of m increased.
The study showed flow rates and the interaction between the settlements served by applying the model of gravity theory to measure depending on the number of the population between city Najaf and the rest of the other settlements served and using three functions of disability, time and cost, as recorded an increase in the interaction index with some settlements like them Kufa, Abbasid and Manathira, while the indicator contrast was in other settlements, either when the application of the gravity model depending on trips and socio-economic characteristics accuracy rate was more pronounced.