Vibrational Interaction Research Articles

Density matrices and iterative natural modals in vibrational structure theory

ABSTRACTIt is demonstrated how the second-quantisation formulation of multi-mode dynamics leads to expressions for vibrational density matrices. The properties and different representations of these matrices are discussed. Diagonalising the one-mode density matrices defines a set of natural modals for each vibrational mode. The theory and first implementation of the iterative natural modals (ItNaMo) method for correlated vibrational structure models is presented. In the ItNaMo method, natural modals are used as basis functions for a subsequent correlated calculation. This optimisation of the one-mode basis is repeated until the changes in the basis functions become sufficiently small. Ground-state and excited-state energy calculations are presented for water, formaldehyde and ethylene. It is shown that using optimised coordinates for the water calculation makes the occupation numbers converge to zero much faster and thereby allows for large reductions in the required number of basis functions. For the higher-order wave-function models the ItNaMo method results in smaller energy errors compared to full vibrational configuration interaction and thereby facilitates a more accurate description of the wave function.

Experimental and analytical vibration serviceability assessment of an in-service footbridge

This paper discusses vibration serviceability assessment of a highly trafficked local footbridge based on the experimental tests and analytical studies. The selected bridge is an approximately 60 m (196 ft) long multi-span steel structure with a continuous reinforced concrete slab supported on two longitudinal steel girders. The experimental study consists of ambient vibration and pedestrian interaction tests to describe the dynamic characteristics of the selected bridge structure. The fundamental frequency of the bridge in the vertical direction obtained through ambient vibration tests was within the critical range described by available design guidelines. This required further analysis to assess the performance of the bridge relative to the maximum acceleration thresholds. In addition to the peak dynamic response obtained from the pedestrian interaction tests, peak acceleration values were calculated analytically based on current design guidelines and compared to the comfort limits. Results from both experimental and analytical studies suggest that the footbridge possesses satisfactory serviceability performance under low and dense traffic conditions, but the comfort level under very dense traffic loads was classified as minimum according to the results of the analytical calculations.

Assessment of electron-vibrational interaction (EVI) parameters of YAG:Ce3 +, TAG:Ce3 + and LuAG:Ce3 + garnet phosphors by spectrum fitting method

The electron–vibrational interaction (EVI) in 4f↔5d optical transitions of Ce3+ ions in YAG, TAG and LuAG garnet phosphors have been analysed in this work. The main EVI parameters that have been estimated and reported here are Huang-Rhys factor, effective phonon energy, Stokes shift, red shift and Zero-phonon line position. The EVI parameters were estimated from the room temperature photoluminescence results that were recently reported. The spectrum fitting method was employed to determine the EVI parameters. An emission band was modelled with the aid of the calculated EVI parameters. The agreement between the modelled emission bands with the experimentally obtained ones validated the estimated values of EVI parameters.

High‐Q Plasmonic Fano Resonance for Multiband Surface‐Enhanced Infrared Absorption of Molecular Vibrational Sensing

Realizing strong plasmon–vibration interactions between infrared‐active vibrational bands and resonating plasmonic metasurfaces opens up the possibilities for ultrasensitive label‐free detection of chemical and biological agents. The key prerequisites for exploiting strong plasmon–vibration interactions in practical spectroscopy are structures, which provide giant field enhancement that highly depends on the line‐width and line‐shape of the plasmonic resonances supported by these structures. Here, multiband surface‐enhanced infrared absorption (SEIRA) of poly(methyl methacrylate) (PMMA) is demonstrated. The line‐width and line‐shape of the proposed plasmonic metasurface can be readily tuned to match the multiple vibrational modes of the PMMA to sense the prohibitively weak fingerprints. The tightly coupled system exhibits mode splitting in the optical spectrum resulting in new hybrid plasmon–phonon modes of PMMA. Such a strong interaction of high‐Q Fano resonances to multiple phonon modes in ultrathin film analytes over a broadband spectral range could be step forward towards ultrasensitive sensing of biological and chemical molecules.

Ethylene-1-13C (13C12CH4): First analysis of the ν2, ν3 and 2ν10 bands and re–analysis of the ν12 band and of the ground vibrational state

High-resolution FTIR ro-vibrational spectra of the 13C12CH4 molecule in the region of 600–1700cm−1, where the bands ν3, ν12 and ν2 are located, were recorded and analyzed with the Hamiltonian model. This model takes resonance interactions between these three bands as well as strong interactions with six neighboring bands, ν10, ν8, ν7, ν4, ν6, and 2ν10 into account. More than 3800 ro-vibrational transitions belonging to the bands ν3, ν12, ν2 and 2ν10 were assigned (for the first time for the ν2, ν3 and 2ν10 bands) with the maximum values of quantum numbers Jmax./Kamax. equal to 22/8, 52/18, 30/11 and 27/12, respectively. On this basis, a set of 62 vibrational, rotational, centrifugal distortion and resonance interaction parameters was obtained from the weighted fit. These parameters reproduce 1562 initial “experimental” ro-vibrational energy levels obtained from unblended lines with the rms error drms=2.6×10−4cm−1. Furthermore, ground state parameters of the 13C12CH4 molecule were improved.

Vibrational Interaction of Two Rotors with Friction Coupling

A lumped parameter model is presented for studying the dynamic interaction between two disks in relative rotational motion and in friction contact. The contact elastic and dissipative characteristics are represented by equivalent stiffness and damping coefficient in the axial as well as torsional direction. The formulation accounts for the coupling between the axial and angular motions by viewing the contact normal force a result of axial behavior of the system. The model is used to investigate stick-slip behavior of a two-disk friction system. In this effort the friction coefficient is represented as an exponentially decaying function of relative angular velocity, varying from its static value at zero relative velocity to its kinetic value at very high velocities. This investigation results in the establishment of critical curve defining two-parameter regions: one in which stick-slip occurs and that in which stick-slip does not occur. Moreover, the onset and termination of stick-slip, when it occurs, are related to the highest component frequency in the system. It is found that stick-slip starts at a period nearly equal to that of the highest component frequency and terminates at a period almost three times that of the highest component frequency.

Crystal field splitting of 5d states and luminescence mechanism in SrAl2O4:Eu2+ phosphor

A stoichiometric SrAl2O4:Eu2+nanosized powder was synthesized by combustion method using urea at 500°C and calcinated at 1000°C. The measurements of the luminescent properties of SrAl2O4:Eu2+ were carried out; additionally, theoretical study of the crystal field splitting of the Eu2+ 5d levels at two crystallographically different Sr positions in the SrAl2O4 lattice was performed. Two luminescence bands at 450nm and near 520nm were observed at lower temperatures. The luminescence mechanism and peculiar temperature dependence of bands intensities are discussed on the basis of the crystal field theory (within the exchange charge model) combined with the vibronic approach. The latter involves the electron vibrational interaction in two kinds of the Eu2+ centers as well as the interaction between these centers in the host lattice. A simplified single-mode model was adopted for each center and the section of the bi-dimensional adiabatic potential of the Eu2+ dimer along an effective “out-of-phase mode” is considered. This original approach qualitatively explains the temperature dependence of the emission bands intensities by the non-radiative redistribution of excitations between two neighboring Eu2+ centers occupying two crystallographically different Sr positions in the SrAl2O4 lattice .

Adsorption Forms of CO2 on MIL-53(Al) and NH2-MIL-53(Al) As Revealed by FTIR Spectroscopy

Adsorption of CO2 on MIL-53(Al) and NH2-MIL-53(Al) has been studied by Fourier transform infrared (FTIR) spectroscopy at different temperatures and equilibrium pressures. For better interpretation of the spectra 13CO2 was also utilized. It is established that with both samples at low coverages CO2 forms O-bonded complexes with the structural OH groups (OH···O12CO). These species are characterized by ν3(12CO2) at 2337–2338 cm–1 and two ν2(12CO2) modes around 662 and 650 cm–1. Simultaneously, the ν(OH) modes of the hydroxyl groups are red-shifted, while the δ(OH) modes are blue-shifted. At higher coverages (OH···O12CO)2 dimeric species are formed and this leads to a decrease of the ν3(CO2) frequency by 2–4 cm–1. This change is due to vibrational interaction as proven by the observation that the frequency remains practically unaffected for (OH···O12CO) (OH···O13CO) dimeric species. Interaction between dimers leads to additional slight decrease of the value of ν3(CO2). In parallel with the CO2 adsorption a pa...

Vibrational Response of Methylammonium Lead Iodide: From Cation Dynamics to Phonon-Phonon Interactions.

The dynamic evolution of the vibrational interactions in the prototypical CH3 NH3 PbI3 was studied through a comprehensive experimental and theoretical investigation with a focus on the interactions between the organic cations and the inorganic cage. To date, no clear picture has emerged on the critical and fundamental interactions between the two perovskite components, despite the relevance of phonons to the electronic properties of several classes of perovskites. For the first time, we have monitored the IR and nonresonant Raman response in the broad frequency range 30-3400 cm-1 and in the temperature interval 80-360 K. Strong changes in the energies of different vibrational modes with temperature are observed and examined in the framework of phonon-phonon interactions considering a significant anharmonic contribution to the phonon relaxation process. The vibrational relaxation of the bending modes and their reorientation activation energies identify that such mechanisms are governed by medium-to-strong hydrogen bonds in the orthorhombic phase; however, any ferroelectric ordering in the orthorhombic phase is governed mostly by dipole interactions. These changes imply that charge localization mechanisms play a primary role, and our study enriches the fundamental knowledge of phonon interactions and charge transport in CH3 NH3 PbI3 for the further development of optoelectronic applications.

Tensor decomposition in potential energy surface representations.

In order to reduce the operation count in vibration correlation methods, e.g., vibrational configuration interaction (VCI) theory, a tensor decomposition approach has been applied to the analytical representations of multidimensional potential energy surfaces (PESs). It is shown that a decomposition of the coefficients within the individual n-mode coupling terms in a multimode expansion of the PES is feasible and allows for convenient contractions of one-dimensional integrals with these newly determined factor matrices. Deviations in the final VCI frequencies of a set of small molecules were found to be negligible once the rank of the factors matrices is chosen appropriately. Recommendations for meaningful ranks are provided and different algorithms are discussed.

Free vibrations of circular cylindrical shells with a small added concentrated mass

The effect of a small added mass on the frequency and shape of free vibrations of a thin shell is studied using shallow shell theory. The proposed mathematical model assumes that mass asymmetry even in a linear formulation leads to coupled radial flexural vibrations. The interaction of shape-generating waves is studied using modal equations obtained by the Bubnov–Galerkin method. Splitting of the flexural frequency spectrum is found, which is caused not only by the added mass but also by the wave-formation parameters of the shell. The ranges of the relative lengths and shell thicknesses are determined in which the interaction of flexural and radial vibrations can be neglected.

The algebraic cluster model: Structure of 16O

We discuss an algebraic treatment of four-body clusters which includes both continuous and discrete symmetries. In particular, tetrahedral configurations with Td symmetry are analyzed with respect to the energy spectrum, transition form factors and B(EL) values. It is concluded that the low-lying spectrum of 16O can be described by four α particles at the vertices of a regular tetrahedron, not as a rigid structure but rather a more floppy structure with relatively large rotation–vibration interactions and Coriolis forces.

Instability of a poppet valve: interaction of axial vibration and lateral vibration

The dynamics of axial vibration and lateral vibration coexisting in a poppet valve were studied. It is found that the axial movement affects the lateral movement of the poppet via three ways, including the axial displacement, the valve chamber pressure as well as collisions between the poppet and the valve seat. However, the impact of the lateral vibration on the axial one is only by means of collisions between the poppet and the valve seat. The influenced lateral or axial vibration undergoes a transition and sometimes changes from a damped vibration to a chaotic vibration.

Soliton dynamics in the three-spine $$\alpha $$ α -helical protein with inhomogeneous effect

We study a three-coupled variable-coefficient nonlinear Schrodinger equation, which describes soliton dynamics in the three-spine \(\alpha \)-helical protein with inhomogeneous effect, and analytically obtain multi-soliton solutions, whose formation originates from the dynamical balance between the dispersion owing to the resonant interaction of intrapeptide dipole vibrations and the nonlinear interaction provided by those vibrations with the local displacements of the peptide groups. Using these analytical solutions as initial solutions, we discuss the dynamical behaviors of solitonic interactions and the influence of the protein inhomogeneity on shape-changing collisions of solitons by direct numerical simulations.

Surface‐directed molecular assembly of pentacene on aromatic organophosphonate self‐assembled monolayers explored by polarized Raman spectroscopy

Organophosphonate self-assembled monolayers (SAMPs) fabricated on SiO2 surfaces can influence crystallization of vapor-deposited pentacene and thus can affect device performance of pentacene-based organic thin film transistors. Polarized Raman spectroscopy is demonstrated to be an effective technique to determine the degree of anisotropy in pentacene thin films deposited on three structurally different, aromatic SAMPs grown on silicon oxide dielectrics. Vibrational characterization of pentacene molecules in these films reveals that the molecular orientation of adjacent crystalline grains is strongly correlated on the SAMP-modified dielectric surface, which results in enhanced interconnectivity between the crystallite domains, well beyond the size of a single grain. It is found that vibrational coupling interactions, relaxation energies, and grain size boundaries in pentacene thin films vary with the choice of SAMP. This information clearly shows that molecular assembly of pentacene thin films can be modulated by controlling the SAMP-modified dielectric surface, with potentially beneficial effects on the optimization of electron transfer rates. Copyright © 2016 John Wiley & Sons, Ltd.

Balancing accuracy and efficiency in selecting vibrational configuration interaction basis states using vibrational perturbation theory

This work describes the benchmarking of a vibrational configuration interaction (VCI) algorithm that combines the favourable computational scaling of VPT2 with the algorithmic robustness of VCI, in which VCI basis states are selected according to the magnitude of their contribution to the VPT2 energy, for the ground state and fundamental excited states. Particularly novel aspects of this work include: expanding the potential to 6th order in normal mode coordinates, using a double-iterative procedure in which configuration selection and VCI wavefunction updates are performed iteratively (micro-iterations) over a range of screening threshold values (macro-iterations), and characterisation of computational resource requirements as a function of molecular size. Computational costs may be further reduced by a priori truncation of the VCI wavefunction according to maximum extent of mode coupling, along with discarding negligible force constants and VCI matrix elements, and formulating the wavefunction in a harmonic oscillator product basis to enable efficient evaluation of VCI matrix elements. Combining these strategies, we define a series of screening procedures that scale as O(Nmode6)−O(Nmode9) in run time and O(Nmode6)−O(Nmode7) in memory, depending on the desired level of accuracy. Our open-source code is freely available for download from http://www.sourceforge.net/projects/pyvci-vpt2.

Study of Falling Roof Vibrations in a Production Face at Roof Support Resistance in the Form of Concentrated Force

One of the main reasons of roof support failures in production faces is mismatch of their parameters and parameters of dynamic impact on the metal structure from the falling roof during its secondary convergences. To assess the parameters of vibrational interaction of roof support with the roof, it was suggested to use computational models of forces application and a partial differential equation of fourth order describing this process, its numerical solution allowed to assess frequency, amplitude and speed of roof strata movement depending on physical and mechanical properties of the roof strata as well as on load bearing and geometry parameters of the roof support. To simplify solving of the differential equation, roof support response was taken as the concentrated force.

Effects of unequal electrode pairs on an x-strip thickness-shear mode multi-channel quartz crystal microbalance

We study the thickness-shear vibrations of an x-strip monolithic piezoelectric plate made from AT-cut quartz crystals with two unequal electrode pairs. The Tiersten-Smythe scalar differential equations for electroded and unelectroded quartz plates are separately employed, resulting in free vibration distributions and frequencies of operating modes. The vibrations of these operating modes are mainly trapped in the electroded regions. The loss of the structural symmetry can lead to a weak vibration interaction between two electroded regions. The influences of electrode difference on the vibration and frequency interference between two adjacent resonators are investigated in detail. The obtained results provide a fundamental reference to the design and optimization of multi-channel quartz crystal microbalance.

Experimental values of the rotational and vibrational constants of deuterated silyl fluoride

ABSTRACTAccurate experimental values of the αA and αB rotation–vibration interaction, and ωi, xij and gij vibrational constants have been extracted from the most recent high-resolution Fourier transform infrared and millimetre-wave measurements in the spectra of the prolate symmetric top SiD3F, between 400 and 2000 cm−1. From the experimental values of the ground state rotational and rovibrational interaction parameters, accurate equilibrium rotational constants have been derived: Ae = 1.432326 (12) cm−1 and Be = 0.4112012 (45) cm−1 for silyl fluoride. The effective ground state structure has also been determined from the observed moments of inertia of SiD3F: r0(Si-D) = 1.4755 (29) Å; r0(Si-F) = 1.5931 (26) Å; θ0(DSiD) = 110.47 (32)° and θ0(DSiF) = 108.45 (56)°. A merge of equilibrium moments of 28SiH3F and 28SiD3F yielded an experimental equilibrium structure of silyl fluoride. This geometry has been found in good agreement with semi-experimental median values, as well as with the recent semi-experimental ab initio equilibrium structure obtained using all data available of the various isotopic species of silyl fluoride.

Vibrational dynamics of nitromethane mixed with IR780 dye studied by coherent anti-stokes Raman spectroscopy

Vibrational coupling between different kinds of molecules in liquid mixture is studied by multiplex coherent anti-Stokes Raman spectroscopy (CARS). To identify vibrational coherence, fs-probe with high time resolution and narrowband-probe with high spectral resolution are adopted in CARS experiments. Using liquid nitromethane (NM) mixed with organic dye IR780 perchlorate as the sample, we can clearly observe the interference between different vibrational modes. The intermolecular vibrational interaction between NM and IR780 molecules results in the vibrational coherence transfer (VCT) in the form of a change of phase correlation. Compared with symmetric bending vibration of NO2, coherence transfer is found to be easier to take place between C―N bond of NM and vibrations of IR780, which indicates the selectivity of intermolecular vibrational interaction. The selectivity is deduced to be related to the coordination between intramolecular and collective motion of molecules. Copyright © 2016 John Wiley & Sons, Ltd.