Molecular structure and vibrational analysis of 3-Ethylpyridine using ab initio HF and density functional theory (B3LYP) calculations

The FT-Raman and FT-IR spectra for 3-Ethylpyridine (3-EP) have been recorded in the region 4000-100 cm(-1) and compared with the harmonic vibrational frequencies calculated using HF/DFT (B3LYP) method by employing 6-31G(d,p) and 6-311++G(d,p) basis set with appropriate scale factors. IR intensities and Raman activities are also calculated by HF and DFT (B3LYP) methods. Optimized geometries of the molecule have been interpreted and compared with the reported experimental values of some substituted benzene. The experimental geometrical parameters show satisfactory agreement with the theoretical prediction from HF and DFT. The scaled vibrational frequencies at B3LYP/6-311++G(d,p) seem to coincide with the experimentally observed values with acceptable deviations. The theoretical spectrograms (IR and Raman) have been constructed and compared with the experimental FT-IR and FT-Raman spectra. Some of the vibrational frequencies of the pyridine are effected upon profusely with the C2H5 substitutions in comparison to pyridine and these differences are interpreted.     

FT-IR and FT-Raman spectra and vibrational investigation of 4-chloro-2-fluoro toluene using ab initio HF and DFT (B3LYP/B3PW91) calculations

FT-IR (4000-100 cm(-1)) and FT-Raman (4000-100 cm(-1)) spectra of solid sample of 4-chloro-2-fluoro toluene (4Cl2FT) have been recorded using Bruker IFS 66 V spectrometer. Ab initio-HF (HF/6-311++G (d, p)) and DFT (B3LYP/6-311++G and B3PW91/6-311++G (d, p)) calculations have been performed giving energies, optimized structures, harmonic vibrational frequencies, depolarization ratios, IR intensities, Raman activities. The vibrational frequencies are calculated and scaled values are compared with FT-IR and FT-Raman experimental values. The isotropic HF and DFT analyses showed good agreement with experimental observations. The differences between the observed and scaled wave number values of most of the fundamentals are very small in B3LYP than HF. Comparison of the simulated spectra provides important information about the ability of the computational method (B3LYP) to describe the vibrational modes. The influences of substitutions on the geometry of molecule and its normal modes of vibrations have also been discussed. The changes made by substitutions on the benzene are much responsible for the non-linearity of the molecule. This is an attractive entity for the future studies of non-linear optics.     

Vibrational spectroscopy (FT-IR and FT-Raman) investigation, and hybrid computational (HF and DFT) analysis on the structure of 2,3-naphthalenediol

The FT-IR and FT-Raman vibrational spectra of 2,3-naphthalenediol (C(10)H(8)O(2)) have been recorded using Bruker IFS 66V spectrometer in the range of 4000-100 cm(-1) in solid phase. A detailed vibrational spectral analysis has been carried out and the assignments of the observed fundamental bands have been proposed on the basis of peak positions and relative intensities. The optimized molecular geometry and vibrational frequencies in the ground state are calculated by using the ab initio Hartree-Fock (HF) and DFT (LSDA and B3LYP) methods with 6-31+G(d,p) and 6-311+G(d,p) basis sets. There are three conformers, C1, C2 and C3 for this molecule. The computational results diagnose the most stable conformer of title molecule as the C1 form. The isotropic computational analysis showed good agreement with the experimental observations. Comparison of the fundamental vibrational frequencies with calculated results by HF and DFT methods. Comparison of the simulated spectra provides important information about the capability of computational method to describe the vibrational modes. A study on the electronic properties, such as absorption wavelengths, excitation energy, dipole moment and Frontier molecular orbital energies, are performed by time dependent DFT approach. The electronic structure and the assignment of the absorption bands in the electronic spectra of steady compounds are discussed. The calculated HOMO and LUMO energies show that charge transfer occurs within the molecule. On the basis of the thermodynamic properties of the title compound at different temperatures have been calculated. The statistical thermodynamic properties (standard heat capacities, standard entropies, and standard enthalpy changes) and their correlations with temperature have been obtained from the theoretical vibrations.     

Vibrational investigation on FT-IR and FT-Raman spectra, IR intensity, Raman activity, peak resemblance, ideal estimation, standard deviation of computed frequencies analyses and electronic structure on 3-methyl-1,2-butadiene using HF and DFT (LSDA/B3LYP/B3PW91) calculations

FT-IR and FT-Raman (4000–100 cm⁻¹) spectral measurements of 3-methyl-1,2-butadiene (3M12B) have been attempted in the present work. Ab-initio HF and DFT (LSDA/B3LYP/B3PW91) calculations have been performed giving energies, optimized structures, harmonic vibrational frequencies, IR intensities and Raman activities. Complete vibrational assignments on the observed spectra are made with vibrational frequencies obtained by HF and DFT (LSDA/B3LYP/B3PW91) at 6-31G(d,p) and 6-311G(d,p) basis sets. The results of the calculations have been used to simulate IR and Raman spectra for the molecule that showed good agreement with the observed spectra. The potential energy distribution (PED) corresponding to each of the observed frequencies are calculated which confirms the reliability and precision of the assignment and analysis of the vibrational fundamentals modes. The oscillation of vibrational frequencies of butadiene due to the couple of methyl group is also discussed. A study on the electronic properties such as HOMO and LUMO energies, were performed by time-dependent DFT (TD-DFT) approach. The calculated HOMO and LUMO energies show that charge transfer occurs within the molecule. The thermodynamic properties of the title compound at different temperatures reveal the correlations between standard heat capacities (C) standard entropies (S), and standard enthalpy changes (H).     

A new class of multiset Wilf equivalent pairs

We say the pair of patterns (σ,τ) is multiset Wilf equivalent if, for any multiset M, the number of permutations of M that avoid σ is equal to the number of permutations of M that avoid τ. In this paper, we find a large new class of multiset Wilf equivalent pairs, namely, the pair (σ_n-2(n-1)n, σ_n-2n(n-1)), for n?3 and σ_n-2 a permutation of {1^x₁,2^x₂,…,(n-2)^x_n-2}. It is the most general multiset Wilf equivalence result to date.     

Properties of C60 polymerized under high pressure and temperature

60 polymers. Pure and mixed phase polymeric samples were synthesized by simultaneously subjecting microcrystalline C₆₀ powder or pellets to various pressures () and temperatures (). The optical spectra of the orthorhombic, tetragonal, and rhombohedral C₆₀ polymer phases are observed to be quite distinct and rich. These spectra exhibit numerous lines and an overall downshift in frequency relative to C₆₀ is observed, consistent with a loss of double bonds from the fullerene cage. The LDMS spectra of a sample synthesized at under hydrostatic conditions and , exhibited a succession of clear peaks at mass numbers corresponding to , similar to the LDMS data on the C₆₀ photopolymer. This is taken as further evidence for interfullerene bonds in these high-pressure polymers. The XRD pattern of this sample indicates the presence of a strong texture in the sample. Received: 14 November 1996/Accepted: 8 January 1997     

Frequency tunability and temporal characteristics of a DAMC distributed feedback dye laser

The frequency tunablity characteristics of a simple prism configuration distributed feedback dye laser (DFDL) pumped by a low pressure nitrogen gas laser are described. Tunability is studied as a function of the refractive index of the dye solution and also as a function of the angle of the interfering beams of the pump laser. The tunability range for the dye studied is from 440 to 480 nm with a spectral width of 0·1 Å and the time duration of the DFDL pulses was 50 ps.