Internal Vibrational Modes Research Articles

A new way of analyzing vibrational spectra. III. Characterization of normal vibrational modes in terms of internal vibrational modes

A new way of analyzing vibrational spectra. III. Characterization of normal vibrational modes in terms of internal vibrational modes

A new way of analyzing vibrational spectra. I. Derivation of adiabatic internal modes

A new way of analyzing measured or calculated vibrational spectra in terms of internal vibrational modes associated with the internal parameters used to describe geometry and conformation of a molecule is described. The internal modes are determined by solving the Euler–Lagrange equations for molecular fragments ϕn described by internal parameters ζn. An internal mode is localized in a molecular fragment by describing the rest of the molecule as a collection of massless points that just define molecular geometry. Alternatively, one can consider the new fragment motions as motions that are obtained after relaxing all parts of the vibrating molecule but the fragment under consideration. Because of this property, the internal modes are called adiabatic internal modes, and the associated force constants ka, adiabatic force constants. Minimization of the kinetic energy of the vibrating fragment ϕn yields the adiabatic mass ma (corresponding to 1/Gnn of Wilson's G matrix) and, by this, adiabatic frequencies ωa. Adiabatic modes are perfectly suited to analyze and understand the vibrational spectra of a molecule in terms of internal parameter modes in the same way as one understands molecular geometry in terms of internal coordinates. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 1–9, 1998

The Infrared and Raman Spectra of Tetracalcium Phosphate (Ca4P2O9)

The infrared and Raman spectra of tetracalcium phosphate (Ca4P2O9) were measured and interpreted on the basis of factor group analysis. Factor group splitting can be noted for the various internal vibrational modes of the PO4 3- ion. However, a fewer number of factor group-split bands can be seen than predicted because of either the weak intensities of these bands or the convolution of such bands for the various internal modes of vibration.

Electron-stimulated disordering in c(8 × 2) benzoate/Cu(110): a combined STM, LEED and HREELS study

We demonstrate a novel, negative-ion-mediated, electron-stimulated disordering process in LEED and, at nanoscopic scales, in the STM. Electron-stimulated disordering of the c(8 × 2) benzoate/Cu(110) structure in LEED is reversible, and HREELS shows that it is non-destructive to the adsorbed species. The disordering kinetics in LEED are pseudo first-order above a threshold between 5 and 7 eV with a large cross-section (∼ 10 −16cm 2). The threshold correlates with strong negative ion resonance scattering in HREELS centred at 7–8 eV. Defect-controlled kinetics in LEED are observed at 5 eV and correlate with the spatial dependence in the STM disordering, which initiates preferentially at domain boundaries and is inhibited at step edges. Both the STM- and electron-beam-induced disordering are consistent with a negative ion resonance mechanism for efficient energy transfer from the tunnelling/incident electron to adsorbate internal vibrational modes which then relax by excitation of the frustrated translation. The influence of field effects on the potential energy surface is also considered.

Pb2BiO2PO4, a New Oxyphosphate

Pb2BiO2PO4is orthorhombic with space groupPnma,a=5.930(4),b=9.079(10),c=11.473 (6) Å at room temperature,Z=4, and a congruent melting point of 860°C. The structure was solved from single crystal and powder diffraction data. The PO4ion can occupy two energetically equivalent positions causing two oxygen atoms to be disordered. The structure can be described on the basis of several motifs. Infinite chains of BiO2rectangular pyramids formed by edge-sharing parallel to theaaxis that are linked by lead atoms and phosphate anions. Bi can also be considered as present in a trigonal prismatic environment of oxygen atoms in which one corner of a triangular face is unoccupied. Presumably the 6s2lone pair extends toward that apex. Pb is bonded to six oxygen atoms forming a distorted octahedron when distances less than 3 Å are considered. When two additional oxygen ions at 3.20(9) and 3.24(5) Å are considered part of the coordination polyhedron it can be described as a bisdisphenoid. This structure is related to structures found in manyMII2BiXO6phases. The Raman spectrum shows the expected frequencies for PO4. In addition frequencies are observed that can be assigned to P–O–Bi and P–O–Pb linkages. Intense bands at 143 and 150 cm−1are attributed to internal vibrational modes of the BiO4pyramid.

Angular autocorrelation functions in molecular crystals: application to nuclear magnetic resonance relaxation and Raman spectra

The theory of hindered molecular motion (HMM) in crystals, extended by taking the molecular site symmetry into account, is used in the calculation of the angular autocorrelation functions (ACFs). The basic model of motion involves a molecular rearrangement by means of random angular jumps of an intramolecular vector according to a crystallographic point symmetry group G between the potential wells in which the probability density of the vector orientation is continuously distributed over the angles. New physical quantities, the dynamical weights of the irreducible representations of the group G, are introduced to relate the molecular site symmetry in the ACFs. The polycrystalline ACFs are convenient for describing the HMM in liquids. The ACFs of the second-rank unitary spherical tensors are presented in an explicit form for all the point groups of pure rotation. The surface-plot graphs of the ACF amplitude, drawn as functions of a dynamical weight and an angle of crystal orientation, make the features of the HMM description more comprehensible. The new ACFs are applied to processing the exponential magnetic relaxation of the dipole and quadrupole nuclei and the line shape of Raman scattering in molecular crystals. Quantitative data about the NH4 +-ion motion and its site symmetry are obtained from the anisotropic magnetic spin–lattice relaxation of protons and deuterons in ammonium chloride. The theoretical anisotropy of the Raman line intensities corresponding to the internal vibration modes is in accord with experiment and with the common methods of group-theoretical analysis in the vibration spectroscopy of molecular crystals.

Lie algebraic method for vibrational and rotational transitions in inelastic collisions of a molecule with a solid surface

The vibrational and rotational transitions of a diatomic molecule in inelastic gas-surface scattering have been studied using the Lie algebraic approach of Alhassid and Levine [Phys. Rev. A 18 (1978) 89]. We have build a Hamiltonian describing the molecule-surface scattering and used it to construct a dynamical Lie algebra h 6. The expressions for the wavefunction of the system near the surface ( z 2~ 0) are explicitly obtained. All the internal rotational and vibrational modes of a diatomic molecule and their coupling have been taken into account in the theoretical model. This wavefunction is applied to compute analytically the transition probabilities from an initial-vibrational state to another final one, for a model problem of H 2 scattering from the LiF(001) surface. The computed probabilities are in good agreement with those obtained using an accurate coupled-channel method.

Resonance Raman study of solvent dynamics in electron transfer. I. Betaine-30 in CH3CN and CD3CN

Raman excitation profiles for nine vibrational modes of the solvatochromic dye betaine-30 have been measured in CH3CN and CD3CN solution at wavelengths that span the S0→S1 charge transfer transition. Though the absorption spectra of the dye are the same in the protonated and deuterated forms of the solvent, Raman cross sections for all modes were found to be lower in CD3CN solution than in CH3CN. Wave packet theory has been applied to model the absorption and Raman profiles, using a solvent dephasing model which accounts for bimodal solvent dynamics. The solvent isotope effect on the Raman intensities is interpreted in terms of different amplitudes of the fast solvent response in the protonated and deuterated solvents, and possible coupling of low-frequency solute and solvent modes. The solvent reorganization energy greatly exceeds that due to internal vibrational modes of betaine-30, and most of the internal reorganization is due to the torsional modes of the solute.

Vibrational Characteristics of the Alkali Metal–Indium Double MolybdatesMIn(MoO4)2and TungstatesMIn(WO4)2(M=Li, Na, K, Cs)

Infrared and Raman spectra of polycrystalline alkali metal–indium double molybdatesMIn(MoO4)2(whereM=Na, K, Cs) and alkali metal-indium double tungstatesMIn(WO4)2(whereM=Li, Na, K) were measured in the range 40–1000 cm−1at room temperature. To determine the symmetries and nature of the observed modes a factor group analysis has been performed. The crystal structure of the compounds studied depends on the type of cation and changes from trigonal (for the caesium–indium molybdate) to monoclinic and triclinic (for the lithium and sodium derivatives). The character of the coordination sphere around the molybdenum and tungsten atoms changes from tetrahedral (for the studied double molybdates and KIn(WO4)2) to octahedral (for the LiIn(WO4)2and NaIn(WO4)2). The assignment of the observed bands to the respective internal and external vibrational modes is proposed.

Infrared profile of single molecules adsorbed on ionic substrates: Relaxational mechanism for the homogeneous linewidth

The homogeneous line shape of the infrared spectrum of a single molecule physisorbed on ionic substrates is determined on the basis of a renormalization technique of the total system Hamiltonian. The absorption profile can be written in terms of a limited cumulant series expansion of the dynamical couplings between the optical system formed by the vibration–orientation modes of the molecule, and the bath modes characterized by molecular translations and substrate phonons. The various causes of homogeneous broadening of the lines are studied, implying phase and population relaxations through intramolecular transfers. In this latter case, two situations are considered depending on whether the internal vibration modes of the admolecule are localized or resonant (quasi-resonant) with the substrate phonon modes. These situations are usual for small polyatomic molecules adsorbed on substrates with extended optical phonon bands. An application to the calculation of the Q*, P* and R* branch widths for CO, CO2 and NH3 molecules adsorbed on NaCl(001) and/or MgO(001) is extensively discussed. We show that, at low temperature T≲ 20 K, the homogeneous width is quite negligible and inhomogeneity must be invoked to interpret the measured width. By contrast, for increasing T values (T≳ 50 K), homogeneous broadening increases and contributes significantly (about to 50%) to the measured width for CO and CO2 molecules adsorbed on clean substrates.

Raman Scattering Study of Boson Peak in Barium Borate Glass

The borate anomaly in barium borate glass was studied using Raman scattering spectroscopy. The main features of the the boson peak were reproduced by the disorder induced model with an exponential correlation function. An additional peak appears in the shoulder of the boson peak at about 210 cm-1, and increases in intensity markedly above x m=0.32, where the sound velocity shows a maximum. The obtained intermediate correlation length l c is nearly equal to the Ba-Ba distance. The dependence of internal vibration modes on the composition of barium was also studied.

Molecular force fields of uracil and thymine, through neutron inelastic scattering experiments and scaled quantum mechanical calculations

Abstract Neutron inelastic scattering (NIS) data have been obtained from polycrystalline samples of pyrimidine nucleic bases, i.e. uracil (U) and thymine (T). These spectra and those previously recorded by optical techniques (Raman scattering and infrared absorption) led us to carry out ab initio quantum mechanical calculations (SCF + MP2) in using split-valence gaussian sets with different d-orbital polarization functions for carbon, nitrogen and oxygen. The F x matrices (interatomic force constant matrices on the basis of cartesian coordinates) derived from these ab initio calculations have been then described in terms of internal molecular coordinates, allowing vibrational normal modes to be assigned in the framework of the so-called Wilson GF-matrix method. In addition, atomic displacements estimated from the normal mode calculations have been used to simulate the first-order NIS intensities by only considering the fundamentals of the internal molecular vibrational motions. For both molecules (U and T), the internal vibrational modes are located at higher wavenumbers than the lattice vibrational modes (external vibrational motions). In order to scale the calculated vibrational modes the so-called Pulay method has been used. A good agreement between calculated and experimental data (vibrational wavenumbers as well as NIS intensities) has been obtained for most of the internal vibrational modes.

Effect of high external pressures on the vibrational spectra of biomedical materials: calcium hydroxyapatite and calcium fluoroapatite.

Infrared and Raman spectra of the principal mineral component of human hard tissue, calcium hydroxyapatite, Ca10(PO4)6(OH)2, or HAP, and the analogous calcium fluoroapatite, Ca10(PO4)6F2, or FAP, have been recorded, using a diamond-anvil cell, at pressures ranging from ambient to 30 kbar. For FAP, the absence of any discontinuities in the slopes of the nu (cm-1) versus P (kbar) plots for the observed bands indicates that no pressure-induced structural transition occurs in this material throughout the pressure range investigated. For the internal vibrational modes of HAP, however, there are distinct breaks at approximately 20 kbar in the nu versus P plots, suggesting the occurrence of a structural change at this pressure. The OH stretching mode of HAP shifts to higher wave numbers with increasing pressure while the associated OH librational mode shifts in the opposite direction. The pressure-induced structural transition in HAP is reversible and occurs at approximately 22 kbar upon decompression. Further evidence for a structural change taking place at approximately 20 kbar was provided by a parallel pressure-tuning Raman study. Hydrogen bonding does not occur, or is very weak, in HAP.

Vibrational spectra of ETS-4 and ETS-10

Raman and i.r. absorption spectra of ETS-4 and ETS-10 were measured at room temperature in the frequency range 200–1,400 cm −1 . The peaks observed in the spectra were identified through model calculations of the internal modes of vibration for clusters typical of the structure of these materials.

Characterization of gauche end-groups in α,ω-dibromoalkanes: vibrational properties of the 1,6-dibromohexane/urea inclusion compound

The vibrational properties of the 1,6-dibromohexane/urea inclusion compound have been investigated by Raman spectroscopy (between 90 K and room temperature) and IR spectroscopy (at room temperature). The internal vibrational modes for the urea molecules in the 1,6-dibromohexane/urea inclusion compound are similar to those for other urea inclusion compounds, consistent with the similar local structural properties of the urea molecules in these structures. However, significant structural and conformational differences are observed between the 1,6-dibromohexane/urea inclusion compound and other urea inclusion compounds. In particular, the wavenumbers of the lattice modes reflect the different crystallographic properties of these materials. In addition, the 1,6-dibromohexane molecule has two gauche end-groups in its urea inclusion compound while α,ω-CnH2nBr2 molecules in the urea inclusion compound with n > 6 are essentially ‘trans’. This material is therefore a model system for characterization of the vibrational properties of α,ω-dibromoalkane molecules in this conformation. Normal-mode calculations and force-field refinement are reported for the 1,6-dibromohexane molecule with both end-groups gauche(point group Ci).

Impulse approximation neutron scattering from N2

We present the results of a detailed investigation of the inelastic neutron scattering from diatomic N2, at wave-vector transfers in the range Q = 20–100 Å−1 (1Å = 10−10 m). At intermediate Q, the scattering shows structure arising from the vibrational modes of the molecule, while at large Q the scattering is well described by the impulse approximation for the individual atoms, despite the fact that the corresponding energy transfers are considerably less than the maximum molecular excitation energies. We find good agreement for all Q with a calculation incorporating the internal rotational and vibrational modes of the molecule explicitly.

Electron stimulated neutral and ion emission from single crystal NaNO 3

Quadrupole mass spectrometry of the neutral products accompanying irradiation of single crystal NaNO 3 with a pulsed beam of 1–3 keV electrons shows intense NO and O 2 emissions and smaller amounts of Na and NO 2. Time-of-flight and intensity measurements as a function of pulse width and temperature are consistent with NO emission via a thermally assisted, electronic emission mechanism. The activation energy for the thermally assisted process is about 0.11 eV -similar to the excitation energies for internal vibrational modes of the NO 3 − anion. The emission of neutral O 2 involves fairly complex reactions with dissociation products and is also thermally assisted at temperatures above 380 K. Mass-selected ion emission measurements indicate copious H + emission, where the temperature dependence of the H + intensity is similar to that of NO. We propose that H + emission is limited by the density of appropriate surface defect sites, and that these sites are directly related to NO 3 − dissociation.

Infrared Absorption Spectra and Their Correlation with the Ti-O Bond Length Variations for TiO2 (Rutile), Na-Titanates, and Na-Titanosilicate (Natisite, Na2TiOSiO4)

The mid-infrared absorption spectra (400–1200 cm−1) of four TiO2-bearing crystalline solids, in the form of rutile (TiO2), Na-titanates (Na2Ti6O13/ Na2Ti3O7), and natisite (Na2TiOSiO4), are presented, providing a clear illustration of their differences in IR band structure (band pattern). Two sharp characteristic peaks of IR absorption bands of natisite have been noted at 725 and 624 cm−1, representing the internal vibration modes of TiO5 (normal) and SiO4 structural units, respectively, and obtainable by comparison with that of Ca-titanosilicate (CaTiOSiO4), NTS glass (Na2O-TiO2-SiO2), and low-cristobalite (SiO2). The tested series of TiO2-bearing crystalline solids has been helpful in presenting a case study in support for the generalization of IR spectra/structure correlations, showing that vibrational spectroscopy can be useful for understanding the crystal chemistry of crystalline solids in terms of the geometric setting of molecular structural units and chemical bonds. It has been qualitatively demonstrated that the Ti-O bond length variations may be broadly correlated with the complexity of IR absorption bands of four TiO2-bearing solids having great diversity in both chemical composition and crystalline structure.

Raman study of oxygen deficient YVO 4 single crystals

Oxygen deficiency which is an inherent problem in melt grown YVO 4 single crystals was investigated by Micro-Probe Raman Spectroscopy (MPRS). External vibrational modes at 157cm −1, 162cm −1 and selected internal vibrational modes at 379cm −1, 840cm −1 of full Raman spectra were compared with different YVO 4 crystals grown by the Czochralski (CZ) technique both with and without annealing in an O 2 atmosphere as well as by top seeded solution growth technique (TSSG) in directly produced oxygen deficiency-free form. Special differences of above mentioned frequencies and over 1000cm −1 were observed in the Raman spectra, which could prove that the growth technologies generated different rates of oxygen deficiency in addition to critical intrinsic segregation effects in YVO 4 which significantly determine the crystal quality.

Phonon dynamics and relaxation processes in isotopically pure 35Cl2 and natural crystalline chlorine

We have measured the Raman spectrum of natural and 99% isotope 35 chlorine crystal, in the lattice and in the internal mode regions, using a high resolution Raman spectrometer. We report the temperature dependence of the linewidth for both the lattice and the internal vibrational modes. The data were analyzed in terms of anharmonic interactions and contributions from the isotopic disorder. The lattice phonons are little affected by the isotopic disorder, while the internal vibrons are extremely sensitive to the presence of isotopic impurities. In the latter case the linewidths of the Ag and B3g internal vibrons are about one and two orders of magnitude, respectively, larger in the natural than in the isotopically pure sample. The Raman spectrum of natural chlorine in the internal region is correctly reproduced by an harmonic lattice dynamics calculation weighted over the statistical distribution of the isotopic species in the lattice.