Lattice vibrational spectrum of diamond

The lattic dynamics of covalent crystals are discussed with reference to known models. The dispersion curves of diamond have been computed on the basis of the shell model of Cochran applicable to covalent crystals. Parameters have been determined using elastic constants and dispersion curves along the Δ and A directions from the neutron spectrometric data of Warren et al. In general there is good agreement between the calculated curves and experiment. The average error is about 4.8%. Although the calculated curves seem to be a definite improvement over the curves calculated by Smith there appears to be a certain discrepancy between theory and experiment. Plausible causes of this discrepancy are pointed out.     

The vibrational spectrum of fluorobenzene

The high resolution infrared spectra of three fluorobenzene isotopes were obtained and interpreted. Vibrational assignments of most bands were made and values for most of the fundamental vibrations were obtained. Accurate values for the infrared inactive a₂ vibrations were also obtained. Several major modifications of literature values for the fundamentals were made and a Fermi resonance interaction identified.     

Interpretation of the vibrational spectra of polycrystalline adenine

The infrared and Raman spectra of the tetramer of the adenine N₉H are calculated and analyzed. The vibrational spectra of polycrystalline adenine are interpreted. It is demonstrated that the method for calculating the vibrational spectra of molecular complexes formed by hydrogen bonds can be used for interpreting the vibrational spectra of polyatomic molecules in the solid state.     

Computer calculation of the vibrational spectrum of nanoparticles

A new method for calculating the vibrational spectrum of nanoparticles is proposed. The method is based on a molecular-dynamics simulation of the oscillations of the center of mass and of individual atoms and subsequent Fourier analysis of the obtained time series. It is shown by way of a concrete example that, depending on the dimensions of the nanocrystallite, the calculated spectrum of intrinsic vibrations can consist of one or more dominant harmonics. Correspondence of this method to the open resonator model and to calculations of longitudinal intrinsic vibrations of a rod in the theory of elasticity is demonstrated. Fiz. Tverd. Tela (St. Petersburg) 39, 2062–2064 (November 1997)     

The vibrational spectrum of crystalline KSCN

The spectrum is reported for the range 700 to 5000 cm^–1; the internal modes of the SCN^– ion are interpreted in terms of the C_s local symmetry group. The combinations of internal and external (lattice) modes are examined in terms of theD _2h factor group. The frequency of the translational mode is found to be 20 cm^–1.I am indebted to Academician A. N. Terenin for direction and encouragement, and to L. A. Gribov and D. S. Bystrov for discussions.     

Interpretation of vibrational IR spectrum of uracil using anharmonic calculation of frequencies and intensities in second-order perturbation theory

The anharmonic frequencies of fundamental vibrations, overtones, and combination vibrations, as well as the intensities of absorption bands in the IR spectrum of uracil, are calculated. The anharmonic quartic force field and the third-order dipole moment surface calculated by the DFT quantum-mechanical method (B3LYP/6-31+G(d,p)) are taken as the initial parameters. The anharmonic frequencies and intensities of vibrations are determined using the second-order perturbation theory in the form of contact transformations. Multiple Fermi resonances and polyads are determined by the diagonalization of a small interaction matrix of vibrations of different types (fundamental, combination, and overtone frequencies). The total experimental IR spectrum of matrix-isolated uracil is interpreted. It is shown that the used method of calculating anharmonic frequencies and intensities can form a basis for anharmonic calculations of vibrations of moderate molecules.     

Mechanical model of carbon dioxide vibrational spectrum

Classical dynamics methods have been used to study the nonlinear vibrations of a CO₂ molecule. Consideration includes not only the anharmonicity valence angle, which enables one to explain the Fermi resonance, but also the physical nonlinearity of the force field (stiffness and softness of springs). In the farthest neighbor approximation (with regard to oxygen–oxygen interaction), a set of nonlinear differential equations in the Lagrangian form has been derived. Their analytical solution has been derived using the method of invariant normalization. The occurrence of a strange attractor has been discovered by numerical simulation. Recommendations for the selection of initial conditions are given that take into account the possibility of regular beatings that change into to chaotic beatings.     

On the vibrational spectrum of a parallel dislocation array

The free vibrations of dislocation arrays of different types (monopole and dipole dislocation walls and a planar dislocation array) have been investigated on the basis of the dispersion equation derived within the self-consistent dynamic theory of dislocations. The relaxation spectrum of a planar dislocation array in the strong damping mode has also been analyzed.     

Raman scattering and the low-frequency vibrational spectrum of glasses

We present a theory of low-frequency Raman scattering in glasses, based on the concept that light couples to the elastic strains via spatially fluctuating elasto-optic (Pockels) constants. We show that the Raman intensity is not proportional to the vibrational density of states (as was widely believed), but to a convolution of Pockels constant correlation functions with the dynamic strain susceptibilities of the glass. Using the dynamic susceptibilities of a system with fluctuating elastic constants we are able for the first time to describe the Raman intensity and the anomalous vibration spectrum of a glass on the same footing. Good agreement between the theory and experiment for the Raman spectrum, the density of states, and the specific heat is demonstrated at the example of glassy As(2)S(3).     

Millimeter-wave spectrum of DCCCHO in the ground vibrational state

About 140 a- and b-type millimeter-wave transitions of propynal-d₁, DCCCHO, were measured in the ground vibrational state. The accurate rotational and centrifugal distortion constants were determined from the observed frequencies including the previous microwave measurements. Seven microwave transitions observed by infrared-microwave double resonance were also included in the analysis. The determined constants are A = 66778.016(12), B = 4463.8489(7), C = 4177.7950(7), Δ_J = 0.0015919(5), Δ_JK = −0.139214(13), Δ_K = 9.4328(18), δ_J = 0.0002885(4), δ_K = 0.03069(4), H_JK = −0.817(13) × 10⁻⁶, H_KJ = −9.62(4) × 10⁻⁶, H_K = 0.00255(8), h_J = 0.0047(3) × 10⁻⁶, in MHz.