Vibrational Spectral Densities Research Articles

Dynamic response of a pipe with geometrical restriction subjected to gas-liquid internal flow

Due to the potential hazard of deepwater oil exploration, the Brazilian industry has an ever-increasing concern for reliability during hydrocarbon production. A major source of concern is mechanical failure in devices, such as safety valves, which can fail without warning, putting both the operation and the environment at risk. A possible reason for malfunction and failure could be the permanent occurrence of vibrations induced by internal two-phase flow during the extraction of fluids from the well. An experimental campaign is proposed to better understand these phenomena. Twenty two-phase flow conditions were tested, with superficial velocities ranging from 0.1 m/s to 2.0 m/s for water, and 0.33 m/s to 7.47 m/s for compressed air. The experiments were carried out in a restricted pipe and a pipe without any restriction to evaluate and compare the vibrations produced by two-phase flow (2-FIV). Three accelerometers positioned downstream of the restriction were used to collect vibrational amplitude spectral density data, 2-D acceleration magnitudes, and RMS values of acceleration. Among the main findings are the roles played by the gas volumetric fraction and the mixture velocity, which strongly influence the vibrational amplitude of both tubes, and the observation that the gas phase is the main responsible for vibrational amplitudes at low frequencies, while the liquid phase acts mainly at high frequencies. Furthermore, the flow pattern is also considered a key feature in determining the vibration level, as 20- and 12-fold increments have been observed for the same volumetric fraction when comparing elongated bubbles and severe slug patterns. Finally, it was demonstrated that the presence of an internal restriction strongly influences the structural response.

Exciton dynamics from the mapping approach to surface hopping: comparison with Förster and Redfield theories.

We compare the recently introduced multi-state mapping approach to surface hopping (MASH) with the Förster and Redfield theories of excitation energy transfer. Whereas Förster theory relies on weak coupling between chromophores, and Redfield theory assumes the electronic excitations to be weakly coupled to fast chromophore vibrations, MASH is free from any perturbative or Markovian approximations. We illustrate this with an example application to the rate of energy transfer in a Frenkel-exciton dimer, showing that MASH interpolates correctly between the opposing regimes in which the Förster and Redfield results are reliable. We then compare the three methods for a realistic model of the Fenna-Matthews-Olson complex with a structured vibrational spectral density and static disorder in the excitation energies. In this case there are no exact results for comparison so we use MASH to assess the validity of Förster and Redfield theories. We find that Förster theory is the more accurate of the two on the picosecond timescale, as has been shown previously for a simpler model of this particular light-harvesting complex. We also explore various ways to sample the initial electronic state in MASH and find that they all give very similar results for exciton dynamics.

Method of spectral response to stochastic processes for measuring the nonreciprocal effective interactions.

The theoretical background of the nonperturbative method of spectral response to stochastic processes (SRSP) for measuring the nonreciprocal interparticle effective interactions in strongly coupled underdamped systems is described. Analytical expressions for vibrational spectral density of confined Brownian particles with a nonreciprocal effective interaction are presented. The changes in the vibrational spectral density with varying different parameters of the system (nonreciprocity, viscosity, ratios of particle sizes, and intensities of random processes acting on each particle) are discussed using the example of a pair of nonidentical particles in a harmonic trap. The SRSP method is compared to three other nonperturbative methods. The SRSP method demonstrates an undeniable advantage when processing particle trajectories with errors in particle tracking.

Upper bound for the power outputs of linear vibrational power harvesters: translational vs. rotational geometries

Inertial harvesters utilize the motion of a translating or rotating mass to scavenge power from ambient vibrations. For translational harvesters, analytical expressions describing the influence of size on the output power of these harvesters have been derived previously by modeling vibrations as sinusoids or white noise. In this paper, we present a general method to estimate the size-dependent power outputs of both translational and rotational harvesters for vibrations with an arbitrary power spectral density. Using the heights and widths of the peaks in the vibrational power spectral density, we derive simple analytical expressions for the maximum power output of harvesters and the minimum harvester size required to achieve it. To illustrate an application of these estimates, we analyze the case of walking-induced vibrations produced at the hip-pocket and upper-arm locations. We find that rotational designs can outperform translational ones only when the harvester is larger than 26 cm and 8 cm for the hip-pocket and arm locations, respectively.

Comments on the optical lineshape function: application to transient hole-burned spectra of bacterial reaction centers.

The vibrational spectral density is an important physical parameter needed to describe both linear and non-linear spectra of multi-chromophore systems such as photosynthetic complexes. Low-temperature techniques such as hole burning (HB) and fluorescence line narrowing are commonly used to extract the spectral density for a given electronic transition from experimental data. We report here that the lineshape function formula reported by Hayes et al. [J. Phys. Chem. 98, 7337 (1994)] in the mean-phonon approximation and frequently applied to analyzing HB data contains inconsistencies in notation, leading to essentially incorrect expressions in cases of moderate and strong electron-phonon (el-ph) coupling strengths. A corrected lineshape function L(ω) is given that retains the computational and intuitive advantages of the expression of Hayes et al. [J. Phys. Chem. 98, 7337 (1994)]. Although the corrected lineshape function could be used in modeling studies of various optical spectra, we suggest that it is better to calculate the lineshape function numerically, without introducing the mean-phonon approximation. New theoretical fits of the P870 and P960 absorption bands and frequency-dependent resonant HB spectra of Rb. sphaeroides and Rps. viridis reaction centers are provided as examples to demonstrate the importance of correct lineshape expressions. Comparison with the previously determined el-ph coupling parameters [Johnson et al., J. Phys. Chem. 94, 5849 (1990); Lyle et al., ibid. 97, 6924 (1993); Reddy et al., ibid. 97, 6934 (1993)] is also provided. The new fits lead to modified el-ph coupling strengths and different frequencies of the special pair marker mode, ωsp, for Rb. sphaeroides that could be used in the future for more advanced calculations of absorption and HB spectra obtained for various bacterial reaction centers.

Vibrational spectral investigations and density functional theory study of 4-Formylbenzoic acid

An accurate assignment of the vibrational spectra of 4-Formylbenzoic acid in solid state was carried out. For this purpose density functional calculations (DFT) were performed to clarify wavenumber assignments of the experimentally observed bands for the first time. A scaling of the wavenumbers was carried out to improve the calculated values. Good reproduction of the experimental wavenumbers is obtained and the % error is very small in the majority of cases. The NBO analysis was carried out, and it reveals hyper conjugative interaction, ICT and stabilization of molecules.

Electron-nuclear double resonance study of molecular librations of nitroxides in molecular glasses: Quantum effects at low temperatures, comparison with low-frequency Raman scattering

Pulsed electron-nuclear double resonance applied to 15N nitroxide spin probes in molecular glasses is shown to be very sensitive to measurement of the A(XX) principal value of the hyperfine interaction tensor. For molecules experiencing fast restricted orientational motions (molecular librations), this provides a precise tool to determine the motion-averaged <A(XX)> value. For nitroxides in glycerol and o-terphenyl glasses, the observed <A(XX)> temperature dependence below 40 K may be readily interpreted as arising from quantum effects in librations, when the thermal energy of a librating molecule becomes comparable with the elementary quantum of the oscillator. The estimated elementary quanta for nitroxide librations, approximately 60 cm(-1) in glycerol and approximately 90 cm(-1) in o-terphenyl, are found to match the characteristic frequencies of the vibrational spectral densities seen in low-frequency Raman scattering for these glasses. Above approximately 80 K in glycerol and above approximately 120 K in o-terphenyl, the <A(XX)> temperature dependences manifest a kink with a slightly smaller slope than at lower temperatures.

Vibration spectra of soliton boundaries separating nanostructured 2D hexagonal lattice domains

We investigate the vibration spectra at domain boundaries called heavy and superheavy solitons that separate phase domains in hexagonal two dimensional lattices. The breakdown of translation symmetry in the 2D plane, normal to a soliton domain boundary, gives rise to localized vibration effects. The matching method is used to calculate the characteristic vibration Green functions, spectral densities, and densities of states, for the vibration components of the individual atomic sites that constitute a complete representation of the heavy and superheavy soliton domain boundaries. The variations of these vibration spectra due to changes in the homogeneous elastic constraints in the soliton domain boundary are calculated. It is shown that the calculated vibration spectra are sensitive and explicit signatures for the softening and hardening effects. The theoretical results yield criteria under certain experimental conditions, as regards the interpretation of the measurements of the elastic constraints in the domain boundaries.

Ab initio centroid path integral molecular dynamics: application to vibrational dynamics of diatomic molecular systems.

An ab initio centroid molecular dynamics (CMD) method is developed by combining the CMD method with the ab initio molecular orbital method. The ab initio CMD method is applied to vibrational dynamics of diatomic molecules, H2 and HF. For the H2 molecule, the temperature dependence of the peak frequency of the vibrational spectral density is investigated. The results are compared with those obtained by the ab initio classical molecular dynamics method and exact quantum mechanical treatment. It is shown that the vibrational frequency obtained from the ab initio CMD approaches the exact first excitation frequency as the temperature lowers. For the HF molecule, the position autocorrelation function is also analyzed in detail. The present CMD method is shown to well reproduce the exact quantum result for the information on the vibrational properties of the system.

Vibrational dynamics at a surface atomic well

AbstractWe investigate the dynamical phenomena at the inhomogeneous boundary of an extended atomic well in crystalline solid surfaces. The surfaces are considered as a semi‐infinite slab of two coupled atomic layers, and the well as a single atomic chain. This simplified geometric configuration models an atomic well in a surface. The breakdown of translation symmetry in the direction parallel to the surface and normal to the extended well gives rise to localized vibrational modes in its neighborhood. The matching method is used in this study, it may be applied to analyze both the vibrational and the scattering dynamical phenomena for surface inhomogeneities. Characteristic vibrational Green functions and spectral densities are calculated for this system, in particular for the atomic sites which constitute a representative ensemble for the well. The variations of these spectra are presented as a function of the variation of the elastic parameters of the well. This illustrates the variation of the spectra for the softening and the hardening situations of the surface atomic well. The calculated spectra could yield, in comparison with experimental results to come, useful information concerning the elastic parameters of such a surface atomic well.

Time averaging the semiclassical initial value representation for the calculation of vibrational energy levels. II. Application to H2CO, NH3, CH4, CH2D2

A method recently developed for calculating vibrational spectral densities of molecules, previously tested successfully on H2O, is applied here to several larger molecules. The method relies on use of a time averaging procedure in the conventional semiclassical (SC) initial value representation (IVR) expression for the spectral density. The convergence of the SC-IVR average over the phase space of initial conditions (of classical trajectories) is greatly enhanced by time averaging and is generally achieved with as few as 1000 trajectories per degree of freedom. Furthermore, meaningful results can be obtained with only a single trajectory propagated for a long time. (For systems with chaotic dynamics, however, the phase space average converges more slowly.) Results for vibrational energy levels of H2CO, NH3, CH4, and CH2D2 are reported and compared with quantum mechanical calculations available in the literature. The accuracy of the time-averaged SC-IVR is very encouraging, with the vibrational energy levels consistently in agreement with the quantum results to a few parts in a thousand.

Bridge Mediated Electron Transfer: A Unified Description of the Thermally Activated and Superexchange Mechanisms

Donor-acceptor electron transfer (D-A ET) through a linear molecular bridge is studied for the particular case of large electronic couplings among the molecular fragments inside the bridge. This makes it possible to choose a description in terms of extended bridge states, whereas the weak coupling of the bridge levels to the D and A centers guarantees the individuality of these terminal sites. Since fast vibrational relaxation within the D and A centers as well as within the system of bridge levels is provided, we can utilize our recently developed coarse graining description of ET (Petrov et al., J. Chem. Phys. 2001, 115, 7107). In particular, it is demonstrated that the whole ET process can be reduced to single-exponential kinetics for the electronic level populations characterized by an effective D -A transfer rate. This rate contains contributions from the overall superexchange and the overall thermally activated rate. The ratio of both contributions is calculated in the framework of the Song and Marcus model valid for a vibrational spectral density describing a single active vibrational mode. Taking reasonable parameters for the D-A ET reaction, it is demonstrated that the thermally activated mechanism can dominate the superexchange ET, even though the population of the bridge by the transferred electron is extremely small. And this dominance increases with increasing bridge length. Drawing the overall ET rate versus the number of bridge units, a novel behavior is predicted. First there is a strong decay of the rate up to a certain bridge length. But it is followed by a remarkable increase which is continued by a modest further increase or an in dependence on the bridge length. Furthermore, simple analytic expressions are given to decide which mechanism may work in a given experiment. Finally, it is underlined that ET pathways along hydrogen bonds or the key amino acids in proteins are extremely favorable for the thermally activated mechanism, while the pathways along covalent bonds are generally realized via the superexchange mechanism even at a small energy gap.

Mesoscopic thermal transport through a weak link

We consider mesoscopic thermal transport between two bulk dielectrics joined by a narrow wire or weak mechanical link. In the “tunneling” regime where the phonon transmission probability through the link is small and the thermal conductance is much less than πk B 2 T/6ℏ, the thermal current is determined by a product of the local vibrational spectral densities of the two bodies. We derive an expression for the thermal current that is a thermal analog of the well-known formula for the electrical current through a tunneling barrier.

Nonlinear Models for Double-Wall Systems for Vibrations and Noise Control

A theoretical model is developed for active control of vibrations and noise transmission of nonlinear double-wall systems to random wideband inputs. A velocity feedback control mechanism is integrated into governing nonlinear equations of motion using piezoelectric materials as sensors and actuators. The nonlinear von Karman thin plate theory is used to model vibrations of the face plates. A soft elastic core of the double wall is used. The nonlinear panel response is obtained by utilizing modal analyses and Monte Carlo simulation techniques. Transmitted noise inside a rectangular enclosure is obtained by solving the linearized acoustic wave equation subject to time-dependent boundary conditions of the vi- brating interior panel. Numerical results include vibration response time histories, spectral densities, rms responses, and noise reduction. The feasibility of using piezoelectric velocity feedback actuators for active control of nonlinear vibrations and noise transmission to random inputs is demonstrated.

Calculation of absolute spectral densities via stochastic estimators of [formula omitted

The calculation of absolute vibrational spectral densities, tr{δ(E - H ̂ )} , is investigated utilizing the stochastic trace estimator technique of Hutchinson. The spectral density is evaluated by a Monte Carlo scheme in which random vectors are sequentially sampled, their spectral density profiles computed and averaged. The requisite matrix elements of δ(E - H ̂ ) are evaluated using a Lanczos projection algorithm. The issue of distinguishing degenerate and replicated eigenvalues generated by the Lanczos algorithm is addressed and can be overcome using a recently-developed filter diagonalization scheme. The resulting method is simple, efficient and converges the density of states remarkably quickly for dense spectra. Illustrative calculations are presented for one- and two-dimensional test cases and finally for nitrogen dioxide in the energy range 0–12000 cm −1 using the V 11 diabatic surface of Hirsch et al.

Calculation of the vibrational spectral density of NO 2 via density correlation functions

The spectral density has been calculated for nitrogen dioxide in the energy range 0–12000 cm −1 using the density correlation method of Smith and Jeffrey. The V 11 diabatic surface of Hirsh et al. was employed with a 3-dimensional discrete variable representation. Promising comparison with experimental results is obtained.

Interplay of multiple vibrational spectral densities in femtosecond nonlinear spectroscopy of liquids

The multimode Brownian oscillator model of nonlinear response functions is generalized to include a multielectronic level system interacting with several spectral densities representing solvent and vibrational coupling to electronic energies, transition dipoles, and permanent dipoles. Applications to resonant and off-resonant transient grating as well as to infrared and fifth-order Raman photon echoes illustrate how the various spectral densities may be probed separately.

Probing the Microscopic Molecular Environment in Liquids: Intermolecular Dynamics of CS2 in Alkane Solvents

The femtosecond optical-heterodyne-detected optical Kerr effect/Raman-induced Kerr effect (OHD OKE/RIKE) dynamics of CS2 dissolved in a series of alkane solvents are reported. The data reveal that the nondiffusive (subpicosecond) dynamics of simple molecular liquids are determined largely by the details of the local, microscopic environment, rather than by the bulk solution properties, with no correlation observed between the short-time, nondiffusive dynamics and the bulk solution viscosity. For each solvent investigated, the vibrational spectral density is observed to narrow and shift to lower frequency with increasing dilution. While the same general trend is observed for each solvent, deviations of magnitude are observed for the longer-chain n-alkanes. This, coupled with the markedly nonexponential decay of the orientational anisotropy observed for the higher-alkane dilutions, suggests the presence of two distinct environments in which isolated pockets of CS2 exist. The observed spectral evolution is d...

Interrogation of Vibrational Structure and Line Broadening of Liquid Water by Raman-Induced Kerr Effect Measurements within the Multimode Brownian Oscillator Model

The method used to deduce the spectral density distribution of intermolecular and intramolecular (vibrational) degrees of freedom in the liquid state from optical heterodyne detected optical (Raman-induced) Kerr effect (OHD-RIKE) measurements is reexamined within a multimode Brownian oscillator model. The ramifications of nonlinear coupling of the nuclear degrees of freedom to the medium polarizability are explored for discrimination between “homogeneous” and “inhomogeneous” contributions to the vibrational spectral density. Under physically reasonable assumptions, an estimation of the homogeneous contribution to the vibrational line shape can be made from the OHD-RIKE observable (if nonlinear coupling is nonnegligible). The model is developed generally, and calculations are applied specifically to temperature-dependent OHD-RIKE measurements of liquid water. The results indicate that the line broadening in the low-frequency vibrational distribution due to the hydrogen-bonded network structure of liquid wa...

Calculation of high resolution electron and helium energy loss cross sections using surface vibration spectral densities

It is shown that vibrational eigenvectors (outputs of a slab calculation) are not required for the calculation of high resolution electron energy loss spectra (EELS) or helium energy loss spectra. Instead, vibrational spectral densities (outputs of a Green's function calculation) may be input directly to such calculations. This facilitates the treatment of scattering from bulk phonons as well as from surface phonons.