Normal modes of oscillations of lattices

Polynomial equations are obtained for the solutions of the vibrational frequencies of a simple cubic, primitive orthorhombic and tetragonal Bravais lattices of finite size with particles connected to their nearest neighbours through both central and non-centrarl forces, but with arbitrary forces connecting the surface atoms to the rigid walls. The exact expressions of the different normal modes of oscillations and the amplitudes of vibration of different particles in various modes are obtained by solving three decoupled partial difference equations.     

Inelastic neutron scattering in Zr<Subscript>2</Subscript>NiH<Subscript>1.9</Subscript> and Zr<Subscript>2</Subscript>NiH<Subscript>4.6</Subscript>

In this paper we report the results obtained from inelastic neutron scattering measurements on Zr₂NiH_1.9 and Zr₂NiH_4.6 using triple-axis spectrometer at Dhruva reactor, Trombay. The spectrum up to 35 meV represents largely the lattice modes of Zr and Ni atoms. The vibrational frequencies of hydrogen atoms are expected predominantly at higher energies. The phonon spectra from 35–180 meV were recorded using a Be filter as analyser. In order to analyse the observed neutron spectra, we assume a set of Ein-stein modes due to the hydrogen atoms which are delta functions in energy. These delta functions are broadened by the resolution of the instrument. The vibrational frequencies obtained from the fitting of the observed phonon spectra have been assigned to various tetrahedral sites in both the compounds.     

Normal modes of oscillations of one-dimensional monoatomic and diatomic lattices

A polynomial equation is obtained for the solutions of the vibrational frequencies of one-dimensional monoatomic and diatomic lattices with particles connected by identical springs, but with arbitrary springs connecting the end particles to rigid walls. The exact expressions of the different normal modes of oscillations of the linear chain of particles for monoatomic, diatomic and defective lattices are derived in a straightforward way. As special cases of our problem we have considered the effects of different end springs on the vibrational frequencies. One interesting result is that very high frequencies are allowed when the ends of the diatomic lattice are rigidly fixed with the boundary walls.     

Direct targeting of adsorbate vibrations with mode-tracking

The normal modes and vibrational frequencies of a thiophenolate anion adsorbed on an Ag(1 1 1) surface are directly targeted employing the mode-tracking protocol. The adsorbate normal modes of three model systems are compared. These three models consist of an Ag₅₁ cluster with a thiophenolate in a fixed orientation attached to it and are geometry-optimized either completely or only with respect to the adsorbate structure or not at all. Vibrational normal modes and frequencies calculated with mode-tracking are found to be equal to the results of a full frequency analysis. The calculation of vibrational modes and frequencies in harmonic approximation is shown to be justified for partially optimized structures as long as only the harmonic frequencies of those modes are interpreted which solely involve movements of the atoms belonging to the optimized subsystem. Adsorption of the thiophenolate results in adsorbate frequency shifts which are reproduced equally well by any of the three geometrically different models.     

Low-frequency vibrations of bacteriochlorophyll

Frequencies and normal vibrational modes of bacteriochlorophyll are calculated using the semiempirical quantum-mechanical MNDO-PM3 method. To analyze the structure of normal modes, the indices of delocalization of the vibrations and the distribution functions of normal modes over atoms in the molecule are introduced. It is shown that normal vibrational modes of bacteriochlorophyll in the region from 3 to 20 cm^?1 represent “intermolecular” vibrational modes of phytol and tetrapyrrole macrocycle. As the vibrational frequency increases, the normal modes delocalized both on phytol and tetrapyrrole atoms alternate with the modes that are delocalized only on phytol atoms or only on tetrapyrrole atoms. The structural properties of some modes are considered in the aspect of their possible involvement in the formation of absorption spectra of the pigments of reaction centers in photosynthesis and in the formation in them of the coordinate of a primary reaction of the intermolecular electron transfer.     

Intramolecular vibrational modes of polychlorodibenzo-p-dioxines of the D 2h symmetry

The infrared and Raman spectra of the octachlorodibenzo-p-dioxine molecule are measured and all normal vibrational modes of the molecule are calculated. Each vibrational mode was assigned to the vibrations of certain functional groups of atoms in the molecule, taking into account the local symmetry characteristics of the vibration mode. A correlation of vibrational modes by their shape was established in a series of molecules: dibenzo-p-dioxine, 2,3,7,8-tetrachlorodibenzo-p-dioxine, and OCDX. The influence of substituents on vibrational frequencies was also examined.     

Possible Propagating Intrinsic Localized Vibrational Modes for One-Dimensional Klein-Gordon Lattice

A11 possible existed propagating intrinsic localized vibrational modes for the discrete Klein-Gordon lattice are obtained analytically in the whole w(q) space of the system by means of the so-called semidiscrete approximation, with which the carrier wave is treated explicitly while the envelope is described in the continuum approximation. Our investigation shows that, in general, both the pulse-like and kink (antikink) envelope types of the vibrational modes for the system can occur with certain carrier wavenumbers and frequencies in the separated parts of the ω(q) space. And the propagating velocity of the pulse-like modes is either subsonic or nearsonic, abd that of the kink (antikink) modes is either subsonic or supersonic. Our results are similar to or consistent with some results for Klein-Gordon lattice model or other related nonlinear lattice systems by some different methods.     

Phonon spectra and heat capacity of Li2B4O7 and LiB3O5 crystals

The results of calculations of the phonon dispersion, the vibrational density of states and the heat capacity of lithium tetraborate and lithium triborate crystals are presented. They are obtained in the framework of a potential model that takes into account the non-equivalence of boron atoms in different structural positions (BO3 and BO4 units). A symmetry analysis of the phonon modes at point was performed, and calculated frequencies are compared to experimental spectra. Analysis of Li contributions to the vibrational density of states reveals that the Li-O bonds in both crystals are relatively weak. This is in line with the experimentally observed high mobility of lithium ions at high temperatures. A good agreement between calculated and measured heat capacities from the literature was obtained.     

Can we rationalize the structure of small silicon-carbon clusters?

A theoretical study of clusters with using density functional theory is presented. Tests of various functionals demonstrate that local spin density approximation (LSDA) is the most adequate functional for the study of these systems. Structures, vibrational frequencies, and IR intensities of the lowest energy isomer of the studied clusters obtained using LSDA are described, and the unusual properties of the Si-C clusters are discussed. A quantitative analysis of the obtained structures was carried out, and relations between the coordinations, interatomic distances, and angles observed in the Si-C clusters were obtained through introduction of the notion of coordination. This analysis also shows that the carbon atoms mainly exhibit sp and sp² hybridizations, and that a majority of silicon atoms do not hybridize. This study is the fi rst step of the implementation of a semi-empirical potential, which would describe the moderately small Si-C clusters. Received: 20 October 1997 / Received in final form: 16 December 1997 / Accepted: 17 December 1997     

Theoretical study of the surface structure and vibrations of solid argon

The influence of zero-point oscillations on the equilibrium structures and the vibrational modes for the (001), (110) and (111) surfaces of solid Ar is investigated at zero temperature. The surface structures are determined by minimizing the total energy, the static lattice energy plus zero-point energy, where the zero-point energy is evaluated from Einstein frequencies. It is found that the interlayer distances near the surface are larger than the values for bulk argon and are also larger than the distances predicted by minimizing only the static lattice energy. Based upon the surface structures determined by each of these two different minimization schemes, the phonon dispersion curves have been calculated for 21 layer slabs. The qualitative features of the dispersion curves in each case are very similar but there is a significant overall reduction in the frequencies calculated using the structures determined by minimizing the total energy, including the zero-point contribution. The rms vibrational amplitudes of atoms near the surface are calculated from the Einstein frequencies and their values relative to the bulk amplitude are the same as those evaluated by Allen and De Wette [Phys. Rev. 179 (1969) 873] from the lattice dynamics of slabs.     

吸附氢分子的振动态及熵的计算

用第一性原理方法研究了H_2在(MgO)_9及(AlN)_(12)团簇上的吸附态、振动模式及熵.分析表明,吸附体系的振动中有六个简正模式可归为氢分子的振动;由于氢分子质量很小,零点能修正对吸附能有重要影响.利用振动配分函数计算了吸附氢分子的熵,表明吸附态H_2的熵主要决定于较低的同相振动的频率,并不完全与吸附强度相关;在标准大气压下70—350 K的温度范围内,吸附H_2的熵与气态H_2的熵之间存在很好的线性关系,吸附后H_2的熵减小约10.2R.     

Vibrational and electronic spectral analysis of 2,3-pyrazinedicarboxylic acid: A combined experimental and theoretical study

Fourier transform infrared and Raman spectra of 2,3-pyrazinedicarboxylic acid were recorded and analyzed using density functional theory. The complete assignments of the anharmonic vibrational modes have been performed based on potential energy distribution. The anharmonic frequencies were computed using vibrational second-order perturbation theory as well as vibrational self-consistent field and correlation corrected vibrational self-consistent field methods. Mode–mode coupling strength is also estimated using two-mode representation of quartic force field approximation. The intra- and intermolecular interactions were also studied in the dimer and trimer forms of the title molecule. The ultraviolet–visible absorption spectra in ethanol, methanol, and acetonitrile solvents were recorded and analyzed using time-dependent density functional theory involving the polarization continuum model. The observed and calculated results are well comparable. Molecular electrostatic potential and the highest occupied and the lowest unoccupied molecular orbital analyses are also reported.     

Vibrational frequency and force field constant calculation of CH3OH and its 9 isotopomers by GF matrix method

A total 75 observed vibrational frequencies from 8 isotopomers in methanol have been fitted to a least-squares programme and a set of force constants which includes 21 parameters are obtained. Using this set of parameters, the G and F matrix calculations yield the vibrational frequencies for 10 isotopomers of methanol. The calculated results also show that the different vibrational modes are mixed. This calculation can be readily extended to other similar molecules.     

Vibration of ZnO nanotubes: a molecular mechanics approach

We investigate the vibrational properties of two kinds of single-wall ZnO nanotubes. The simulations are carried out for three types of zigzag nanotubes (5,0), (8,0), (10,0) and armchair nanotubes (3,3), (4,4), (6,6). The natural frequencies are determined by means of the molecular mechanics approach with the universal force field potential. The first four natural frequencies are obtained for length/diameter ratio of about 5–20. The vibration modes associated with these frequencies have been computed. Closed-form analytical expressions have been derived using the continuum shell theory for the physical explanations of the simulations results. We observe that the natural frequencies decrease as the aspect ratios increase. The results follow similar trends with results of previous studies for carbon nanotubes (CNT). However, the magnitudes of the frequencies are lower from the corresponding CNT counterparts, indicating that ZnO nanotubes are comparatively less stiff.     

Quantum-mechanical calculations and analysis of vibrational modes in lead magnoniobate

The vibrational modes in lead magnoniobate have been calculated using the frozen phonon method. It has been shown that lead atoms participate in two radically different vibrational modes, namely, a nonpolar antiferrodistortive mode, which involves the antiphase motion of some lead atoms with respect to other lead atoms, and a polar mode, which includes the polar motion of lead atoms with respect to other atoms of the lattice. The nontrivial properties of lead magnoniobate have been discussed in terms of the unity and conflict of these modes.     

Geometry,vibrational frequencies,and ionization potentials for CO/Ni(100); explanation of the disappearance of the 5σ peak in pes

Using a cluster of 14 Ni atoms to model a Ni(100) surface, we used ab initio methods [generalized valence bond (GVB)] to study CO chemisorbed at the on-top site. Reported are the optimum geometry, vibrational frequencies, and ionization potentials. We propose a new explanation for the two lowest levels of free CO (5σ and 1π) reducing to one level of chemisorbed CO.     

Femtosecond dynamics of primary processes in visual pigment rhodopsin

The dynamics of the coherent photoisomerization of the 11-cis-retinal in bovine rhodopsin is studied by femtosecond time-resolved laser absorption spectroscopy with a resolution of 30 fs. Rhodopsin is excited with 500-, 535-, and 560-nm femtosecond pulses to produce different initial Franck-Condon states with different vibrational energies of the molecule in its electronically excited state. The time evolution of the photoinduced differential absorption spectra of rhodopsin is measured upon excitation with a femtosecond pulse in a spectral range from 400 to 720 nm. Oscillations in the time-resolved absorption of the rhodopsin photoproducts, such as photorhodopsin with a vibrationally excited all-trans-retinal and in its initial-state rhodopsin with a vibrationally excited 11-cis-retinal, are examined. It is demonstrated that these oscillations reflect the dynamics of coherent vibrational wavepackets. The Fourier transform of these oscillatory components yields frequencies, amplitudes, and initial phases of various vibrational modes involved in the motion the wavepackets in both photoproducts. The main vibrational modes manifest themselves at frequencies of 62 and 160 cm^?1 for photorhodopsin and 44 and 142 cm^?1 for initial-state rhodopsin. It is shown that these vibrational modes are directly involved in the coherent reaction under the study, with their amplitudes in the power spectrum produced by the Fourier transform of the kinetic curves being dependent on the wavelength of rhodopsin excitation.     

基于密度泛函理论的盐酸罂粟碱太赫兹振动光谱计算与分析

为了进一步探究太赫兹振动光谱的理论机理,为违禁药品的太赫兹光谱检测提供完善合理的科学依据,本文以盐酸罂粟碱为例,基于第一性原理的密度泛函理论计算方法,利用BLYP、LC-BLYP、B97-XD、B3LYP和CAM-B3LYP函数并结合6-311++G（d,p）基组,分别讨论其分子构象并对盐酸罂粟碱的光谱吸收特性和振动模式进行了表征和分析。计算结果表明,盐酸罂粟碱是以异喹啉N原子上的质子化阳离子和两个最低质子化构象的形式存在的。四个指纹峰中有三个是由能量最低的分子构象共振引起,另一个是由第二个最低能量的分子构象共振引起的。在该方法中,LC-BLYP函数被证明是五个函数中最合适的一个。研究表明,太赫兹时域光谱技术可以有效地检测非法药物,采用密度泛函理论合理计算振动频率,可以为今后违禁药品及各种衍生物的检验提供依据。     

Line phosphorescence spectrum of octachlorodibenzo-p-dioxine at 4.2 K

The line phosphorescence spectrum of octachlorodibenzo-p-dioxine (OCDX) is obtained and interpreted. The symmetry of the lowest triplet state of this molecule is established. The vibrational frequencies found from the vibronic phosphorescence spectrum at 4.2 k are assigned to the vibrational modes of certain symmetry related to individual functional atomic groups of the molecule. The relation between contributions from the spin-orbit (SO) and vibronic-spin-orbit (VSO) interactions to the phosphorescence rate constant k _ph of the OCDX molecule is found from the vibronic line intensities. It is found that the increase in the number of Cl atoms in OCDX compared to that in tetrachlorobenzo-p-dioxine results in the increase in the relative contribution of the VSO interaction to k _ph.     

On the validity of magnetohydrodynamics for ionic mixtures

The collective mode spectrum of the magnetized ionic mixture consisting ofs components is studied by starting from the microscopic balance equations and the fluctuation formulas for the microscopic densities. Apart from a heat mode ands-1 diffusion modes with frequencies of second order in the wavenumber, four modes with complex finite frequencies for vanishing wavenumber are found. If the mixture consist of particles with equal ratios of charge and mass, these four modes become similar to the gyroplasmon modes of the magnetized one-component plasma of which the frequencies are real in lowest order in the wavenumber. Green-Kubo relations are derived for the transport coefficients which appear in the frequencies of the heat mode and the diffusion modes. The long-time behavior of the integrands of the Green-Kubo expressions is evaluated with the help of mode-coupling theory. The static transport coefficients are found to be finite unless the mixture consists of species with equal ratios of charge and mass. It is concluded that the presence of species with different charge-mass ratios is essential for the validity of magnetohydrodynamics for an ionic mixture.