Vibrational Calculations Research Articles

Isomer-Specific, Cryogenic Ion Vibrational Spectroscopy Investigation of D2- and N2-Tagged, Protonated Formic Acid Complexes Using Two-Color, IR-IR Photobleaching.

Here we analyze cryogenic ion vibrational spectra of tagged protonated formic acid (PFA) with electronic structure and anharmonic vibrational calculations to establish the isomers generated by electrospray ionization (ESI) followed by buffer gas cooling to ∼25 K. Two isomers are identified (the trans form (E,Z) and the cis form (E,E)) and generated in comparable abundance despite the fact that the calculated E,E structure lies 6.40 kJ mol-1 above the E,Z form. A large (∼60 kJ mol-1) barrier separates them such that the E,E form can be kinetically trapped upon cooling in the ion trap. The anticooperativity between the H-bonds of the OH groups is explored by measuring the shift in the D2-bound OH fundamental when a second D2 is attached. Both isomers are observed in the N2-tagged counterparts, displaying the expected red-shifted OH bands. These results indicate that ESI generates both isomers and both must be considered when analyzing cluster spectra based on the PFA core ion.

Extending the functional form of the methane PES in redundant coordinates for highly excited vibrational energy levels calculation

Potential energy surfaces (PES) of methanewhich are constructed using ten symmetrised combinations of four bond length and six interbond angles are referred to as (10S) PESs At high energy ranges, it was found that (10S) PESs permitted improving by factor of five the fit quality of ab initio electronic energies of methane versus standard nine symmetric coordinates (9S) PES representations both in internal, orthogonal or normal-mode coordinates. We extend predictions of vibrational band origins to spectral range above 10000 cm−1 to help future analyses of experimental spectra. Accuracy at high energies is increased without notable deterioration at low-E levels (rms deviation of 0.26 cm−1). Based on a comparison between various variants of (10S) PESs we expect that new theoretical band origins should have accuracy not worse than 1–3 cm−1 up to 13400 cm−1.

A novel multi-excitation transient vibration framework for coupling three- and one-dimensional pumped storage hydropower shafting systems

In vibration models of shafting systems, the hydraulic excitation is difficult to characterize due to the complex and changeable hydraulic factors. Thus, hydropower units are not well understood in terms of their dynamics and stability control under transient processes. A hydraulic–mechanical–electric multi-excitation transient vibration calculation framework is developed for analyzing the relationship between shafting vibration and internal flow regimes. First, the boundary data from penstocks, tailraces, and hydro-turbine are interacted with using one-dimensional and three-dimensional (1D–3D) coupling; Second, user-defined function secondary development is applied to achieve two-stage guide vane closure and the runner's variable speed rotation; Third, based on the computational fluid dynamics results, a multi-excitation vibration model is established to analyze shafting system characteristics. There is less than 1.2% error between the algorithm and the field test in terms of speed peak values. Under braking or reverse pumping modes, various vortice clusters are generated in the blade channel as well as the cascade, blocking the flow passage and leading to the runner's unbalanced force. Three sudden increases in vibration amplitudes of the shafting system have occurred in the radial direction under load rejection, each corresponded to the runner's stall rotations. The change trend in axial vibration amplitudes, however, is closely related to the change in axial hydraulic thrust. Furthermore, in braking and reverse pumping conditions, the axis trajectory is more complex under the action of multiple coupling factors than when only hydraulic factors are considered.

Control of deposits on pipeline systems by the method of free oscillations

RELEVANCE. There are a large number of heat exchangers in operation enterprises that operate under various temperature conditions. Steam, hot water, heated products of oil refining and other industries, which may contain oxides of iron, aluminum, calcium sulfate silicates, etc., are used as a heating agent. The efficiency of the heat exchange equipment depends on the condition of the heating surfaces. Contamination of these surfaces with various deposits dramatically reduces the heat transfer coefficient, which leads to a significant increase in heat consumption. The nature of the deposits depends on the properties of the heating agent and the heated medium.THE PURPOSE. The purpose is to assess the possibility of controlling deposits on the surfaces of heat exchange equipment by the free oscillation method. The presence of deposits changes the mass of structures and, consequently, the natural frequencies of vibrations, the analysis of which can determine not only the presence and thickness of deposits, as well as their appearance.METHODS. The paper shows the results of experimental studies conducted using a hardware and software package and calculations of natural vibrations of the surfaces of heat exchange equipment in the ANSYS software package to identify their dependence on the thickness and density of deposits. A plate, a pipe, and a pressurized pipe were modeled as heat transfer surfaces.RESULTS. The results obtained experimentally and computationally coincided, and it was concluded that the free oscillation method makes it possible to determine not only the presence of deposits on heat exchange surfaces, but their thickness and appearance.CONCLUSION. The free oscillation method can detect deposits in a timely manner and monitor their condition, which in turn will, reduce overall operating costs, increase energy efficiency and extend service life.

Computational study of the supramolecular complexation of azocompounds with cucurbit[7]uril: effects on the production and release of free radicals.

An inclusion complex between 2,2'-azobis(2-methylpropionamidine) dihydrochloride (AAPH), a widely employed azocompound, and cucurbit[7]util (CB[7]), has shown an increased yield of radicals derived from the homolytic cleavage of the azo bond. Aimed to get insights about the formation of complexes and their effect on the yield of radicals production, complexes of CB[7] with seven azocompounds were studied by computational methods. Molecular electrostatic surfaces and structural analysis showed that the inclusion of symmetrical azocompounds inside of CB[7] depends mainly on the charge density and position of the functional groups at the main chain of the azoderivative. Analysis of non-covalent interactions and thermodynamic outcomes revealed that positively charged azocompounds with amidinium or imidazolium groups presented strong favorable interactions (multiple hydrogen bonds) with the oxygens of CB[7] portals. Additionally, carbon-centered radicals generated from the complexes (azocompounds@CB[7]) were corroborated using the electron localization function (ELF). Results evidenced that the strength of the interactions and the level of inclusion (partial or complete) between the azocompound and CB[7] determined the final orientation of the radicals (located out- or inside of the CB[7] cavity). Obtained results could be employed to design new supramolecular systems based on the properties of azocomplound@CB[7] complexes for new scientific or industrial applications. First-principles calculations at B3LYP-D3BJ/6-311g(d,p) level theory in the gas phase and in solvent (PCM, water) were performed in Gaussian 16 software package. The dispersion energy correction was included through the Grimme's dispersion with Becke-Johnson damping D3(BJ). Thermodynamical data and the minimum character of all structures were obtained from vibrational frequency calculations. NBO, Multiwfn, Chemcraft, and NCIPLOT software were used to perform population analysis, analyze outcomes, visualize data, and display non-covalent interactions respectively.

Comparison of curvilinear coordinates within vibrational structure calculations based on automatically generated potential energy surfaces.

For floppy molecules showing internal rotations and/or large amplitude motions, curvilinear internal coordinates are known to be superior to rectilinear normal coordinates within vibrational structure calculations. Due to the myriad definitions of internal coordinates, automated and efficient potential energy surface generators necessitate a high degree of flexibility, supporting the properties arising from these coordinates. Within this work, an approach to deal with these challenges is presented, including key elements, such as the selection of appropriate fit functions, the exploitation of symmetry, the positioning of grid points, or elongation limits for different coordinates. These elements are tested for five definitions of curvilinear coordinates, with three of them being generated in an automated manner. Calculations for semi-rigid molecules, namely H2O, H2CO, CH2F2, and H2CNH, demonstrate the general functionality of the implemented algorithms. Additional calculations for the HOPO molecule highlight the benefits of these curvilinear coordinates for systems with large amplitude motions. This new implementation allowed us to compare the performance of these different coordinate systems with respect to the convergence of the underlying expansion of the potential energy surface and subsequent vibrational configuration interaction calculations.

Torsional vibration suppression of a gear-rotor system using an inerter magnet nonlinear energy sink

The novel inerter magnet nonlinear energy sink (IMNES) utilizes chiral compression-torsion coupling effects to achieve mass augmentation, effectively mitigating torsional vibrations in a gear-rotor system with gear meshing clearance. The positive stiffness generated by the piecewise linear beam combines with the negative stiffness produced by the permanent magnet pair, resulting in the establishment of the IMNES’s nonlinear stiffness. Subsequently, a dynamic model of the IMNES-gear-rotor system is developed. Optimal parameters for the IMNES are determined through analysis of vibrational response surfaces under both transient and steady-state conditions. The numerical calculation of torsional vibration in the IMNES-gear rotor system is conducted across various gear meshing clearances. The results demonstrate that across different gear mesh clearances, the IMNES effectively attenuates torsional vibrations in the gear-rotor system. Under transient excitation, implementation of the IMNES leads to an 87% reduction rate in displacement within the gear-rotor system. In terms of steady-state excitation, simulations show a significant enhancement with a 65% increase in vibration suppression percentage.

Neural-network-based molecular dynamics simulations reveal that proton transport in water is doubly gated by sequential hydrogen-bond exchange.

The transport of excess protons in water is central to acid-base chemistry, biochemistry and energy production. However, elucidating its mechanism has been challenging. Recent nonlinear vibrational spectroscopy experiments could not be explained by existing models. Here we use both vibrational spectroscopy calculations and neural-network-based molecular dynamics simulations that account for nuclear quantum effects for all atoms to determine the proton transport mechanism. Our simulations reveal an equilibrium between two stable proton-localized structures with distinct Eigen-like and Zundel-like hydrogen-bond motifs. Proton transport follows a three-step mechanism gated by two successive hydrogen-bond exchanges: the first reduces the proton-acceptor water coordination, leading to proton transfer, and the second, the rate-limiting step, prevents rapid back-transfer by increasing the proton-donor coordination. This sequential mechanism is consistent with experimental characterizations of proton diffusion, explaining the low activation energy and the prolonged intermediate lifetimes in vibrational spectroscopy. These results are crucial for understanding proton dynamics in biochemical and technological systems.

Experimental design for a sustainable society among motorcyclists: The influence of road types and speeds on whole-body vibration exposure and musculoskeletal disorders in motorcyclists

Motorcycles are very popular motorized vehicles and are widely used around the world. The main ergonomic hazard associated with the continuous use of motorcycles is the motorcyclist’s exposure to vibrations, which can potentially cause musculoskeletal disorders (MSDs). This can lead to significant health issues and may also heighten the risk of accidents due to increased driving discomfort. This study aims to investigate the impact of road type and motorcycle speed on WBV exposure and MSD complaints among motorcyclists. An experimental design method was used in this study, with samples subjected to a combination of treatments: riding a motorcycle on different road types and at different speeds. Vibration measurements and calculations were carried out using an accelerometer sensor based on ISO 2631-1, and MSD complaints were assessed using the Body Map Questionnaire (BMQ). The results of this study showed that riding on concrete roads resulted in a significantly higher vibration acceleration of 37.74% and a higher score of MSD complaints of 18.67% compared to asphalt roads. Riding at a speed of 50 km/h resulted in a significantly higher vibration acceleration of 31.03% and a higher score of MSD complaints of 9.49% compared to a speed of 30 km/h. This indicates that increased vibration exposure increased the risk of MSD complaints in this study. These findings highlight the need for measures to mitigate WBV exposure and its adverse health effects on motorcyclists, particularly when riding on rough road surfaces at higher speeds. Recommendations include limiting riding duration and implementing vibration-reducing technologies in motorcycle design.

Microwave Spectroscopy of Chiral Astrochemical Candidate Vinyloxirane: The Missing Gauche Conformer.

The recent detection of a chiral molecule, propylene oxide, in the interstellar medium provides impetus for investigation of related analogues as candidates for discovery of a second chiral species. Vinyloxirane (VO) shares many of the characteristics of propylene oxide that favored its remote detection such as modest size, appreciable dipole moment and modest adsorption to water ice. The microwave spectrum of vinyloxirane at room temperature has been studied in the 18 - 26 GHz region. Rotational transitions of the previously undetected gauche-1 conformer have been assigned and fitted. The quantum number range of anti conformer transitions has been greatly expanded, providing improved molecular constants. Vibrational satellite transitions were assigned and fitted for the lowest frequency ν27 torsion mode, for 2ν27, and for the ν26 C=CC bend of anti VO, along with ν27 satellites of gauche-1. The rovibrational analyses were assisted by anharmonic vibrational calculations at B3LYP-D3/aug-cc-PVTZ, B2PLYPD3/cc-pVTZ, and DSDPBEP86/cc-pVTZ levels. Experimental peak intensities provide a population ratio Ngauche-1/Nanti of 0.36 ± 0.06, corresponding to a Gibbs free energy difference of 2.5 ± 0.4 kJ mol-1 in favor of the anti conformer, in agreement with the density functional theory results. In the gauche-1 conformer, the torsional angle between vinyl group and oxirane ring, τC=CCM, is optimized at -35° to favor an intramolecular CvinylH11...O interaction. The gauche-2 conformer with τC=CCM of + 74° suffers from CvinylH11...HCcyclopropyl repulsion so that it is calculated to be 8-9 kJ mol-1 higher than gauche-1. Reinterpretation of earlier Raman spectra suggests that the gauche-2 conformer had not been observed as reported.

Performance of Effective Harmonic Oscillator Approach for the Calculations of Vibrational Transition Energies of Large Molecules.

The accuracy and performance of the effective harmonic oscillator approximation for the description of anharmonic vibrational structure calculations are tested for large molecular systems and compared with experimental values along with vibrational self-consistent field and second-order perturbation theories. The effective harmonic oscillator approach is an effective single-particle approximation where the variational parameters are the centroids and widths of the multidimensional Gaussian product functions posited as the vibrational wave functions. A comprehensive calculation for 849 transitions that include the fundamentals, two and three quanta overtone transitions, and several combination bands of three polyaromatic hydrocarbons and one DNA nucleobase with a total of 231 normal modes are assessed. A comparison of EHO results with the experimental values is done for the polyaromatic hydrocarbons, and a close agreement is found between the two results. It also offers anharmonic eigenstates and eigenfunctions that are nearly identical with vibrational self-consistent field theory. An extensive analysis on the resultant wave functions of the excited states is performed. The overall root-mean-square deviation (RMSD) between these two methods for 849 transitions understudy is only about 8.3 cm-1, suggesting the effective harmonic oscillator as a viable alternative for the reliable calculations of transition energies of large molecular systems.

Railway vibration – fast physics-based models for the prediction of ground vibration and the identification of track damage

The following applications of machine learning/AI for railway vibration will be discussed: 1. The prediction of the wave propagation from a railway line (completely physics based for surface lines, for tunnel lines (partially) physics-based ML for surface lines). 2. The track behaviour for the emission of train-induced ground vibration (physics based for homogeneous soil, ML for layered soil). 3. Track damage detection and quantification from FRF and moving load response. 4. Bridge damage detection and localisation from modal analysis and moving load response. 5. The use of axle-box acceleration for the identification of track/sub-soil condition and bridge resonances. Prediction calculation of railway vibration usually needs time-consuming finite element, boundary element and wavenumber domain calculations. For a user-friendly prediction software, fast calculations are needed. Several time-consuming detailed calculations should be used to develop simpler and fast models. The dynamic stiffness of isolated or un-isolated railway tracks from detailed calculations with a continuous soil is approximated with the simpler Winkler soil. The vehicle-track resonance (P2 resonance) rules the effect of the mitigation measures, and it can also be used for the on-board monitoring of the track and sub-soil condition. For the identification of track damage such as gaps between sleepers, track slabs and layers, detailed models with a continuous soil have been updated to get the best fit to the measured frequency response functions from hammer tests and the deformation pattern from the moving load response. Whereas the track damage can be locally identified, this is more difficult for bridges where the modal analysis gives mainly global information. The influence lines of the inclination for statically passing vehicles (locomotive, truck, compaction ) have been used to localise bridge damage (stiffness variations). The on-board monitoring of rail bridges needs special conditions (regular trains with special speeds) to excite and measure the bridge resonance.

On the rearrangement and dissociation mechanism of SiH4+ in its triply-degenerate ground state.

An abinitio molecular orbital study has been performed to explore the structural rearrangement and dissociation of SiH4+ radical cation at the X̃2T2 ground electronic state. All stationary points located on the lowest adiabatic sheet of Jahn-Teller (JT) split X̃2T2 state are fully optimized and characterized by performing harmonic vibrational frequency calculations. The structural rearrangement is predicted to start with JT distortions involving the doubly-degenerate (e) and triply-degenerate (t2) modes. The e mode reduces the initial Td symmetry of the SiH4+ ground state to a D2d saddle point, which eventually dissociates into the SiH3+(2A1) + H products via C3v local minimum. In turn, an e-type bending of αH-Si-H yields the SiH2+(2A1) + H2 products through the first C3v local minimum and then the Cs(2A') global minimum. In the alternative pathway, the t2 mode distorts the initial Td symmetry into a loosely bound C3v local minimum, which further dissociates into the SiH3+(2A1) + H asymptote via totally symmetric Si-H stretching mode, and SiH2+(2A1) + H2 products via H-Si-H bending (e) mode through the Cs(2A') global minimum. It is further predicted that the Cs global minimum interconverts equivalent structures via a C2v transition structure. In addition, the two dissociation products are found to be connected by a second C2v transition structure.

Evaluating the safety of the redesigned shafting system following the propeller redesign aimed at enhancing CII and EEXI

In July 2023, the International Maritime Organization (IMO) set a target to achieve net-zero greenhouse gas emissions by 2050, introducing key measures such as the Energy Efficiency Design Index (EEDI), the Energy Efficiency Existing Ship Index (EEXI), and the Carbon Intensity Indicator (CII). The maritime industry explored adaptations, including engine de-rating, energy-efficient technologies, and propeller modifications, and beyond. This study assessed the safety implication of a redesigned shafting system, resulting in a propeller redesign to enhance the CII and EEXI on a 6500 TEU container ship built in 2006. Through an analysis of annual output per TEU from 2000 to 2015, the study focused on container ships built from 2005 to 2007 with high-output engines (9.4–9.5 kW/TEU). After selecting a sample ship, the study determined engine power limits according to the EEXI regulations and assessed their impact on the CII. Subsequently, the study redesigned the shafting system, performing torsional vibration calculations and shaft alignment analyses to ensure the safety of the modified system. While an enhanced CII rating was predicted, the tightening CII regulations imply this benefit may be short-lived, lasting approximately two years. Thus, additional measures are essential to prolong the improved CII rating.

Influence of trailing edge radius of intake struts on excitation force and vibration of rotor blades

Adjusting the trailing edge radius of the intake struts may be advantageous in suppressing the vibration of compressor rotor blades. To explore the impact of the intake struts trailing edge radius on the excitation force and vibration, this study focuses on a compressor with intake struts, and fluid and vibration calculations were conducted. The study revealed that decreasing the trailing edge radius led to a reduction in separation near the strut’s trailing edge, resulting in a narrower wake and weakened mixing near the trailing edge. This caused the total pressure loss region induced by the wake to become more elongated in the low-frequency component, leading to a nonlinear decrease in total pressure amplitude with the reduction of the trailing edge radius. As the trailing edge radius decreased, the excitation force and vibration amplitude of the first-stage compressor rotor blades decreased, while the excitation force distribution showed little variation. The research findings provide insights for the design of intake struts.

Field measurement data set of wind turbine tower for enhanced calculation of vortex-induced vibration

Field measurement data set of wind turbine tower for enhanced calculation of vortex-induced vibration

Vibrational Self-Consistent Field (VSCF) and Post-VSCF Method Calculations Combined with the Reference Interaction Site Model Self-Consistent Field Method Coupled with the Constrained Spatial Electron Density Distribution: Applications to NaHCOO in Aqueous Phase.

Investigating vibrational behavior in solution is crucial for understanding molecular dynamics within a solvent environment. Notably, the analysis of Raman spectra for molecules in solution is important owing to its ability to unveil intricate solute-solvent interactions. Previous studies have effectively employed frequency calculations utilizing the reference interaction site model self-consistent field method in conjunction with constrained spatial electron density distribution (RISM-SCF-cSED) to understand molecular vibrations in solution, primarily focusing on fundamental vibrational modes. However, the oversight of overtones and combination tones in these studies prompted us to combine the vibrational self-consistent field (VSCF) and vibrational second-order Mo̷ller-Plesset perturbation (VMP2) methods with RISM-SCF-cSED to address these aspects theoretically. Illustrating the efficacy of this integrated approach, we computed the Raman spectra of sodium formate (NaHCOO) in water, revealing the necessity of accounting for molecular anharmonicity in solution vibrational analysis. Our findings underscore the potency of VSCF and VMP2 in conjunction with RISM-SCF-cSED as a robust theoretical framework for such calculations.

Structure of Molecular Chains of Poly(trimethylene terephtalate) Studied by Low-Frequency Vibrational Spectroscopy and Quantum Chemical Calculations: In Comparison with That of Poly(ethylene terephthalate) and Poly(butylene terephthalate) from the Point of Parity of Methylene Chain Length

Structure of Molecular Chains of Poly(trimethylene terephtalate) Studied by Low-Frequency Vibrational Spectroscopy and Quantum Chemical Calculations: In Comparison with That of Poly(ethylene terephthalate) and Poly(butylene terephthalate) from the Point of Parity of Methylene Chain Length

Method for vibration and acoustic radiation analysis of underwater stiffened plates with acoustic coatings

Based on the effective medium theory as well as the three-dimensional viscoelastic theory, a semi-analytical model of the three-dimensional underwater vibration and acoustic radiation with cavity-type stiffened plate structures covered with acoustic coatings is established to solve the issues related to underwater vibration and acoustic radiation calculation of the stiffened plate and shell structure with complex acoustic coatings. By comparing the far-field acoustic radiation characteristics of the proposed semi-analytical model and the finite element numerical model, this research verifies the validity and accuracy of the proposed model. On such a basis, this research preliminarily investigates the coupling effect exerted by stiffeners and parent plates in stiffened plates as well as the vibroacoustic characteristics of acoustic coatings, thereby providing a valuable idea for the prediction of vibroacoustic characteristics concerning underwater structures.

Eliminating Imaginary Vibrational Frequencies in Quantum-Chemical Cluster Models of Enzymatic Active Sites.

In constructing finite models of enzyme active sites for quantum-chemical calculations, atoms at the periphery of the model must be constrained to prevent unphysical rearrangements during geometry relaxation. A simple fixed-atom or "coordinate-lock" approach is commonly employed but leads to undesirable artifacts in the form of small imaginary frequencies. These preclude evaluation of finite-temperature free-energy corrections, limiting thermochemical calculations to enthalpies only. Full-dimensional vibrational frequency calculations are possible by replacing the fixed-atom constraints with harmonic confining potentials. Here, we compare that approach to an alternative strategy in which fixed-atom contributions to the Hessian are simply omitted. While the latter strategy does eliminate imaginary frequencies, it tends to underestimate both the zero-point energy and the vibrational entropy while introducing artificial rigidity. Harmonic confining potentials eliminate imaginary frequencies and provide a flexible means to construct active-site models that can be used in unconstrained geometry relaxations, affording better convergence of reaction energies and barrier heights with respect to the model size, as compared to models with fixed-atom constraints.