Vibrational Frequencies Research Articles

Analyzing cyclobutane: A vibrational hamiltonian approach using dynamical U(2) Lie Algebras

This study uses a one-dimensional Lie algebraic framework, precisely adapted to the symmetry of molecules, to investigate the vibrational frequencies of cyclobutane. A vibrational Hamiltonian is also constructed using one-dimensional Morse oscillators, preserving the D2d point group symmetry for each molecule. The analysis compares the calculated fundamental vibrational frequencies with the observed experimental frequencies, resulting in a root mean square deviation of 0.886 cm-1. The result highlights the exceptional precision of the U(2) Lie algebraic Hamiltonian in accurately predicting the vibrational frequencies and their combination bands at the sub-cm-1 level of precision. Specifically, this computational approach has the potential to achieve these results with lower computational costs compared to traditional theoretical approaches. The broader implications of our study suggest that the U(2) Lie algebraic framework can be effectively applied to a wide range of molecular systems, offering significant advantages in fields such as material science, drug design, and environmental monitoring by providing precise and efficient vibrational spectral analyses. KEY WORDS: Vibrational Hamiltonian, Vibrational frequencies, Morse oscillator, Cyclobutane, Lie algebraic method Bull. Chem. Soc. Ethiop. 2024, 38(6), 1887-1896. DOI: https://dx.doi.org/10.4314/bcse.v38i6.29

Synthesis, crystal structure, spectroscopic, electronic and vibrational properties of N′-[(E)-3-pyridinylmethylene]nicotinohydrazide trihydrate: Experimental and computational study

N′-[(E)-3-pyridinylmethylene]nicotinohydrazide trihydrate (C12H10N4O·3(H2O)) was synthesized and its structure was determined by single crystal X-ray diffraction method. X-ray analysis showed that the compound crystalized in the triclinic system P-1 with a = 7.1134 (3) Å, b = 10.0208 (4) Å, c = 10.3601 (4) Å, α = 96.386 (3)°, β = 96.995 (3)°, γ = 101.219 (4)°, V = 712.05 (5) Å3 and Z = 2 and exhibits that the title compound (I) consists of N′-[(E)-3-pyridinylmethylene]nicotinohydrazide (II) (C12H10N4O), and three water molecules of crystallization. The two water molecules are attached to the third water molecule through intermolecular two OH…O hydrogen bonds. At the same time, this water molecule is linked to the NH amide group of the hydrazone by an intermolecular NH…O hydrogen bond. Hirshfeld surface (HS) analyses were carried out are to visualise the intermolecular interactions in the crystals of Compound I. The geometric optimization of the titled compound has been carried out by different computational methods such as by Hatree Fock (HF) and Density Functional Theory (DFT) methods with the 6–311++G (d,p) basis set. The vibrational frequency, dipole moment (μ), polarizability (α), hyperpolarizability (β), and electronic properties including the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO–LUMO) of the compound have been calculated at the level of both theories. In the results of crystal analysis and geometry calculations of the compound I, it was observed that intermolecular hydrogen bonds, N2H2A…O3, O3H31…O2 and O3H32…O4, were formed. The energy band gap (Eg = ELUMO-EHOMO) values were also obtained by using ELUMO and EHOMO at the level of both theories. The value of equilibrium (ground state) dipole moment of the studied molecule was calculated to be 8.31 Debye in B3LYP and 7.55 Debye in HF. The calculated hyperpolarizability values at the B3LYP/6–311++G(d,p) of the compound are 2.53 × 10−30 esu and this value corresponds to 6.79 times the hyperpolarizability value of urea.

Selective incorporation of antimony into gallium nitride

Dilute concentrations of antimony (Sb) incorporation into GaN induce strong bandgap bowing and tunable room-temperature photoluminescence from the UV to the green spectral regions. However, the atomistic details of the incorporation of Sb into the GaN host remain unclear. In this work, we use first-principles calculations to understand the thermodynamics of Sb substitution into GaN and its effect on the optical and Raman spectra. Although it is empirically considered that Sb is preferentially incorporated as an anion (Sb3−) into the N sublattice, we demonstrate that Sb can also be incorporated as a cation (Sb3+, Sb5+) into the metal sublattice. Our thermodynamic analysis demonstrates that SbN0, SbGa2+, and SbGa0 can co-exist under Ga-rich conditions in n-type samples. We further confirm the dual incorporation of Sb by calculating the vibrational frequencies of different anionic and cationic substitutions to explain the origins of experimentally observed additional Raman peaks of Sb-doped GaN. Moreover, the calculated band structures of different Sb substitutions into GaN explain the experimental photoluminescence and optical absorption spectra. Overall, our analysis suggests that the coexistence of Sb3−, Sb3+, and Sb5+ substitutions into GaN explains the totality of experimental measurements. Our results demonstrate that the selective incorporation of Sb into GaN (and potentially other group-V elements such as As, P, or Bi) by tuning the growth conditions can drastically modify the electronic properties, for applications in visible light emitters and photocatalysis.

Rapid wideband characterization of viscoelastic material properties by Bessel function-based time harmonic ultrasound elastography (B-THE)

Elastography is an emerging diagnostic technique that uses conventional imaging modalities such as sonography or magnetic resonance imaging to quantify tissue stiffness. However, different elastography methods provide different stiffness values, which require calibration using well-characterized phantoms or tissue samples. A comprehensive, fast, and cost-effective elastography technique for phantoms or tissue samples is still lacking.Therefore, we propose ultrasound Bessel-fit-based time harmonic elastography (B-THE) as a novel tool to provide rapid feedback on stiffness-related shear wave speed (SWS) and viscosity-related wave penetration rate (PR) over a wide range of harmonic vibration frequencies. The method relies on external induction and B-mode capture of cylindrical shear waves that satisfy the Bessel wave equation for efficient fit-based parameter recovery. B-THE was demonstrated in polyacrylamide phantoms in the frequency range of 20–200 Hz and was cross-validated by magnetic resonance elastography (MRE) using clinical 3-T MRI and compact 0.5-T tabletop MRI scanners. Frequency-independent material parameters were derived from rheological models and validated by numerical simulations.B-THE quantified frequency-resolved SWS and PR 13 to 176 times faster than more expensive clinical MRE and tabletop MRE and have a good accuracy (relative deviation to reference: 6 %, 10 % and 4 % respectively). Simulations of liver-mimicking material phantoms showed that a simultaneous fit of SWS and PR based on the fractional Maxwell rheological model outperformed a fit on PR solely.B-THE provides a comprehensive and fast elastography technique for the quantitative characterization of the viscoelastic behavior of soft tissue mimicking materials.

Influences of ultrasonic vibration directions, amplitudes, and frequencies on sapphire polishing studied by molecular dynamics

The sapphire surface morphology, atom removal rate, temperature, polishing force, subsurface damage, dislocation, and stress were explored under different ultrasonic directions, frequencies and amplitudes through molecular dynamics (MD). For both vertical and horizontal vibration, the rising ultrasonic frequency and amplitude will reduce the tangential and normal force, and increase the subsurface temperature and the material removal rate (MRR). Higher frequencies promote the basal dislocation, thus reducing the subsurface damage. Higher amplitudes cause thinner subsurface damage layer under horizontal vibration. However, it is opposite at vertical vibration. The horizontal vibration can obtain a flatter polished surface and a thinner subsurface damage layer due to the longer trajectory and less impact on sapphire surface. This study can provide reference for sapphire high-quality polishing.

Research on screening effect and time-frequency characteristics of screen surface with additional striking beam

ABSTRACT In this study, a new flexible screen surface structure with an additional striking beam was proposed for improved efficiency and addressing the clogging issue while processing moist coal material. Vibration tests were used to analyze the time-frequency characteristics of the screen surface and the striking beam under no-load and load conditions. The effects of different process parameters on the elastic screening effect of viscous and wet materials were explored. Further, the industrial application of the equipment was preliminarily carried out. The results showed that the load did not affect the main vibration frequency of the elastic screen surface and the striking beam. When the axis distance was adjusted to 7.5 cm, the displacement from the feeding end to the discharge end gradually decreased, promoting the rapid loosening and stratification of the material group. Semi-industrial tests showed that the optimal screening effects had a screening efficiency of 92.16% and a total misplaced content of 5.95% when exciting force was 18 kN, the exciting frequency was 10.8 Hz, the feeding rate was 9.36 t/h, the distance was 7.5 cm, and the moisture content was 8.21%. The GQPSS1848 vibrating screen applied in the industry achieved a screening efficiency of 86.66% at a processing capacity of 85 t/h with a broad commercial prospect. The study aims to provide theoretical and technical support for the research and development of flexible screening equipment and the efficient classification of −3 mm sticky and wet materials.

Vibrational Frequencies of Tetrachloroethylene using Lie Algebraic Framework

This study employs a sophisticated computational approach to predict tetrachloroethylene's higher overtone vibrational frequencies (C2Cl4) up to the fourth overtone. We utilize a Lie algebraic framework within the context of the vibrational Hamiltonian. The method involves replacing tetrachloroethylene's carbon-chlorine (C-Cl) bonds with unitary Lie algebras. The resulting Hamiltonian is written in terms of Casimir and Majorana's invariant operators and parameters. The derived Hamiltonian operator effectively characterizes the stretching vibrations inherent to the molecular structure. This approach enhances our understanding of the vibrational dynamics of tetrachloroethylene at higher overtones, offering valuable insights for applications in diverse scientific and technological fields.

The Influence of Vibration Frequency and Vibration Duration on the Mechanical Properties of Zhanjiang Formation Structural Clay

The Influence of Vibration Frequency and Vibration Duration on the Mechanical Properties of Zhanjiang Formation Structural Clay

Modulating Wetting States of Molten Aluminum Droplets on SiO2 Surfaces via Vertical Sinusoidal Vibrations.

Vibration affects the wetting behavior of droplets, and it is feasible to use vibration to modulate the adhesion characteristics of droplets. In this paper, the effect of vertical sinusoidal vibrations on the wettability of molten aluminum droplets on the substrate surfaces of smooth and with nanopillars is investigated. The increase in the frequency or amplitude of the vibration leads to a rise in the interfacial potential energy between the molten droplets and the substrate, which in turn leads to the occurrence of the Wenzel-Cassie transition. Once the vibration frequency reaches the threshold values, the molten droplets leave from the substrate, that is, dewetting occurs. The molten droplets in the Wenzel state undergo a Wenzel-Cassie transition before dewetting occurs. A phase diagram describing the frequency thresholds at which the molten aluminum droplets undergo dewetting and the Wenzel-Cassie transition at different amplitudes is plotted. For a specific amplitude, the frequency of vibration required for dewetting to occur in molten aluminum droplets in the Young state is lower than that in the Wenzel state. The needed vibrational frequency for dewetting or the Wenzel-Cassie transition decreases with increasing amplitude.

Two-dimensional graphyne monolayers as substrate discs of piezoelectric nanogenerators: A hybrid atomistic-continuum model study

The different phases of α-, β-, and γ-graphyne, which are new types of two-dimensional carbon allotropes, hold promise as potential candidates for designing substrate discs in piezoelectric nanogenerators. Accurate modeling of the bending rigidity and stretching properties as well as resonance frequencies of these materials is crucial for engineering applications like nano-resonator and nanogenerator systems. This step is imperative in designing and advancing future applications involving these structures. This study aims to create a hybrid atomistic-continuum model for modeling graphyne monolayers used as substrate discs in nanogenerators. The model integrates the benefits of both atomistic and continuum approaches. Based on the results, α-graphyne is the least mechanically stable, while γ-graphyne is the most stable. However, in terms of vibration frequency, α-graphyne has the highest frequency while γ-graphyne has the lowest. Therefore, β-graphyne, with moderate stability and resonance frequency, is recommended as the ideal choice for the substrate disc in piezoelectric nanogenerators. It can function within the Q-F frequency range (30–140 GHz) and induce deformation in the piezoelectric shim as well as generation voltage.

A highly accurate analytical method for determination of the vibrational frequency of N/MEMS with electrostatic and van der Waals interaction forces

A highly accurate analytical method for determination of the vibrational frequency of N/MEMS with electrostatic and van der Waals interaction forces

Understanding spin-dependent vibrational frequencies in Fe(II) metal organic coordination complexes

We investigated the compositional and temperature (T) dependences of vibrational frequencies in Hofmann-type Fe(L)2[M(CN)4] spin-crossover (SCO) coordination polymers in which {M = Ni, Pd or Pt with L = pyridine (py)}, or {L = 3-Cl-py or 3-methylpy with M = Ni}, using Raman spectroscopy. The SCO-driven peak shifts (in wavenumber) ranged up to ∼170 cm−1, manifesting significant spin-dependent structural evolutions. Furthermore, there appear clear HS signatures even at T ≪ TSCO for L = 3-Cl-py or 3-methylpy implying the steric effects of the organic ligands on the HS trapping. Meanwhile, for L = py, such HS trapping at the low temperature was not significant although some spectra taken under high laser fluence exhibit light-induced excited spin state trapping (LIESST) effect. The mechanism of the LIESST is discussed in detail in terms of the M d – C 2sp hybridization effects.

Bulking up: the impact of polymer sterics on emulsion stability.

Encapsulation of hydrophobic active ingredients is critical for targeted drug delivery as water-insoluble drugs dominate the pharmaceutical marketplace. We previously demonstrated hexadecane-in-water emulsions stabilized with a pH-tunable polymer, poly(acrylic acid) (PAA), via a steric layer preventing particle aggregation. Using vibrational sum frequency scattering spectroscopy (VSFSS), here we probe the influence of steric hindrance on emulsion colloidal stability by tailoring the molecular weight of PAA and by adding an additional methyl group to the polymer backbone via poly(methacrylic acid) (PMAA) at pH 2, 4, and 6. At low polymer molecular weight (2 and 10 kDa), PAA adsorption is entropy driven and akin to surfactant-mediated stabilization. With 450 kDa PAA, the longer polymer chain emphasizes enthalpically favored polymer-oil interactions to initially coat the surface, and forms layers at increasing molecular weight (1000 and 4000 kDa). PMAA exhibits better oil-solubility than PAA at low concentrations but cannot accommodate the steric hindrance at higher concentrations leading to disorder. Finally, we connect our molecular-level understanding of PAA ordering with temperature-dependent dynamic light scattering experiments and observe that emulsions coated with PAA at pH 2 and 4 maintain colloidal stability from 0-90 °C, making PAA a promising polymer for hydrophobic drug delivery.

Hexa-Penta nanobelt: a novel stable structure with potential optical application

ABSTRACT We report a theoretical investigation of a new carbon nanobelt called Hexa-Penta-belt with molecular formula C 42 H 18 . Hexa-Penta-belt is a variation of the synthesised Methylene-bridged[6]cycloparaphenylene (M-b[6]CPP) with molecular formula C 42 H 24 . Hexa-Penta-belt consists of carbon pentagon and hexagon rings and was inspired by the Penta-belt (theoretically derived from the penta-graphene sheet), the [12]cyclophenacene, and the M-b[6]CPP synthesised by Itami and Segawa [1]. Using Density Functional Theory (DFT), we calculated Hexa-Penta-belt electronic, optical, and thermodynamic properties and their vibrational frequencies. Hexa-Penta-belt is a structurally and thermally stable molecule, as Quantum Molecular Dynamics (QMD) showed. The results exhibited that the Hexa-Penta-belt has excellent electronic stability comparable to C 60 , and it behaves as a semiconductor with a gap estimated at 0.89 eV. It absorbs in the ultraviolet and the visible region (corresponding to the violet, green, and red colours) presenting an absorption more consistent in the visible region than M-b[6]CPP, which could indicate application, for example, as an optical nanosensor. We verified through the carbon atom binding energy that Hexa-Penta-belt is an intermediate molecule between Penta-belt and [12]cyclophenacene.

Simulation and mechanism analysis of fretting wear of parallel groove clamps in distribution networks caused by Karman vortex vibration

PurposeThe phenomenon of friction and wear in parallel groove clamps under wind vibration in 10 kV distribution networks represents a significant challenge that can lead to their failure. This study aims to elucidate the wear mechanism of parallel groove clamps under wind-induced vibration through simulation and experimentation.Design/methodology/approachFLUENT software was used to simulate the flow around the conductor and the parallel groove fixture, and the Karman vortex street phenomenon was discussed. The stress fluctuations of each component under breeze vibration conditions were investigated using ANSYS, and fretting experimentations were conducted at varying amplitudes.FindingsThe results demonstrate that the impact of breeze vibration on the internal stress of the parallel groove clamps is considerable. The maximum stress observed on the lower clamping block was found to be up to 300 MPa. As wind speed increased, the maximum vibration frequency was observed to reach 72.6 Hz. Concurrently, as the vibration amplitude increased, the damage in the contact zone of the lower clamping block also increased, with the maximum contact resistance reaching 78.0 µO at a vibration amplitude of 1.2 mm. This was accompanied by a shift in the wear mechanism from adhesive wear to oxidative wear and fatigue wear.Originality/valueThis study presents a comprehensive analysis of the fretting wear phenomenon associated with parallel groove clamps under wind vibration. The findings provide a reference basis for the design and protection of parallel groove clamps.

The coupled vibrations of a rectangular frame and a flexible net subjected to waves and currents

Aquaculture cages are commonly used to culture fish in the open sea. The main structure of these cages consists of steel pipe frames. The frames are covered with flexible nets. Under the action of waves and currents, the frames and flexible nets may vibrate simultaneously. There is a dynamic interaction between them. In this paper, a rectangular frame is modeled using the Euler-Bernoulli beam theory, and the flexible net is simulated using the lumped-mass method. The hydrodynamic forces on the frame and net caused by waves and currents are calculated using Morison’s equation. A three-dimensional dynamic coupled model of the frame and flexible net is developed. The dynamic model is solved using numerical methods. After verifying the dynamic model, detailed analysis is conducted on the dynamic interactions between the frame and flexible net. The results show that under the action of waves and currents, the vibration amplitudes of the frame and flexible net become larger due to the interactions between them, while their vibration frequencies seldom change.

Vibrational and Rovibrational Spectroscopic Data for the Ground and First-Excited States of Phosgene (COCl2), Formic Acid (HCOOH), and Chloroformic Acid (ClCOOH).

While "black box" quantum chemical computations for the determination of rovibronic spectral data are not quite at hand, the present work utilizes the titular molecules to showcase how excited-state quantum chemical methods can be conjoined to quartic force field (QFF) anharmonic rovibrational treatments to provide novel and useful predictions for such data. This work employs hybrid QFFs with explicitly correlated coupled cluster theory along with the equation-of-motion formalism to generate harmonic force constants and time-dependent density functional theory (TD-DFT) to produce anharmonic force constants for the generation of electronically excited-state rovibrational spectral data, in effect, rovibronic spectral data. Specific spectroscopic results from this work show that the fundamental C═O stretch in phosgene as well as in cis- and trans-formic acid drop from the region of around 1800 cm-1 to close to 1100 cm-1 or less in the first excited states of each molecule. While such is expected for these n → π* excitations, this work provides quantitative predictions for these fundamental vibrational frequencies. The most notable theoretical result is that the TD-DFT-based QFFs can experience unexpected failures, and their inclusion in excited-state hybrid QFFs should require at least two functionals to be employed. The computation of DFT QFFs is relatively fast, and such a "doubling up" of the QFFs will not greatly increase the computational time.

Study on dynamic characteristics and wind-vibration control of transmission tower considering local damage and destruction

As existing transmission lines gradually approach their service life, health monitoring studies of in-service transmission towers are becoming increasingly important. In this study, relying on the 110 kV transmission line project of Neihuang Dichu to Er’an in Anyang, Henan Province, China, a refined finite element model of the transmission tower structure was established, and the accuracy of the numerical model was validated based on the health monitoring data of the actual engineering structure. Damage and destruction analyses of transmission tower structures considering vibration modes and frequencies were carried out, and the influence of local damage on the vibration reduction effectiveness of controlled structures under wind loads was discussed and analyzed. The results showed that the vibration mode of the local damage model was shifted along the damaged part, and its frequency changed within 15 %; in contrast, the dynamic characteristics of the local damage model changed more significantly. With the vibration mode as the judgment basis of the structural state, the obvious difference can be observed when the structure undergoes local damage, and the vibration mode should be used as the basis for determining the specific damage site of the transmission tower in the actual project. The adopted TMD can effectively reduce the dynamic response of the transmission tower under different wind attack angles and wind speeds, and its vibration reduction effectiveness performed the worst due to the significant change in the dynamic characteristics of the tower leg damage model, resulting in the detuning of the TMD.

Vibrational analysis of polyurethane-sandwiched bridge decks with variable skew angles

Bridge decks are the surface of bridges that carry the weight of the vehicles and pedestrians crossing over them. The design of bridge decks varies depending on the span, traffic volume, and material availability. But nowadays, the need for a sustainable approach is required. So, use of a sustainable material for construction and retrofitting purposes is the need of the hour. In the present study, a novel synthetic material polyurethane has been used in bridges. The study deals with the variation in skew angles to determine the response of the bridge deck. The response of natural frequencies on the bridge deck due to the variation in skewness and thickness of steel are analysed under simply supported and clamped boundary conditions. Further, the bridge deck is sandwiched using steel and polyurethane having different thicknesses, and the responses are recorded. Afterwards, a bridge deck is modelled using polyurethane as a special case, to pursue sustainability and justify the RRR (reduce, reuse, and recycle) concept of waste management. A comparative study is also performed between the isotropic steel deck and sandwiched deck by varying the skewness. The skew angle is varied from 0° to 60° with a difference of 10°, i.e., 0°, 10°, 20°, 30°, 40°, 50°, and 60°. The frequencies of the isotropic steel and sandwiched decks are increasing when the skewness is increased. Also, the decks may be modelled in a way to enhances the vibration behaviour by sandwiching the existing steel decks. The free vibration frequencies of the sandwiched decks are comparable to the steel deck of similar thickness, which shows the use of polyurethane as the core material does not affect the vibrational characteristics of the deck, while at the same time reducing the cost significantly. The research lays the groundwork for the creation of engineering recommendations that practitioners can use.

Kink effect on the lattice properties of one-dimensional carbyne nanocrystals under high temperature

Carbyne nanocrystal (CN), as a kind of one-dimensional (1D) sp-hybridized carbon allotrope, has attracted much attention due to its excellent optical and transport properties. However, the lattice properties of 1D CNs under high temperature remain unclear. In our work, we investigate the stability and lattice properties of 1DCNs based on the atomic-bond-relaxation (ABR) approach and first-principles calculations. We find the change of transverse vibration frequencies and bond kinks induced by the thermal effect plays a significant role in the mechanical properties of 1D CNs. We establish a relationship between kink angle and phonon vibration modes, giving a deep inside into high frequency and low-frequency vibration behavior of 1D CNs. Our results indicate the phonon vibration modes modulated by kinks under applied temperatures can lead to a negative thermal expansion behavior in the axial direction of 1D CNs, suggesting an effective way to control the thermal properties of 1D CNs for practical applications.