Fourth Overtone Research Articles

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.

Online inspection of blackheart in potatoes using visible-near infrared spectroscopy and interpretable spectrogram-based modified ResNet modeling.

Blackheart is one of the most common physiological diseases in potatoes during storage. In the initial stage, black spots only occur in tissues near the potato core and cannot be detected from an outward appearance. If not identified and removed in time, the disease will seriously undermine the quality and sale of theentire batch of potatoes. There is an urgent need to develop a method for early detection of blackheart in potatoes. This paper used visible-near infrared (Vis/NIR) spectroscopy to conduct online discriminant analysis on potatoes with varying degrees of blackheart and healthy potatoes to achieve real-time detection. An efficient and lightweight detection model was developed for detecting different degrees of blackheart in potatoes by introducing the depthwise convolution, pointwise convolution, and efficient channel attention modules into the ResNet model. Two discriminative models, the support vector machine (SVM) and the ResNet model were compared with the modified ResNet model. The prediction accuracy for blackheart and healthy potatoes test sets reached 0.971 using the original spectrum combined with a modified ResNet model. Moreover, the modified ResNet model significantly reduced the number of parameters to 1434052, achieving a substantial 62.71% reduction in model complexity. Meanwhile, its performance was evidenced by a 4.18% improvement in accuracy. The Grad-CAM++ visualizations provided a qualitative assessment of the model's focus across different severity grades of blackheart condition, highlighting the importance of different wavelengths in the analysis. In these visualizations, the most significant features were predominantly found in the 650-750 nm range, with a notable peak near 700 nm. This peak was speculated to be associated with the vibrational activities of the C-H bond, specifically the fourth overtone of the C-H functional group, within the molecular structure of the potato components. This research demonstrated that the modified ResNet model combined with Vis/NIR could assist in the detection of different degrees of black in potatoes.

Ease of excitation of black hole ringing: Quantifying the importance of overtones by the excitation factors

The excitation factors of black hole quasinormal modes quantify the ease of excitation of the quasinormal modes and are independent of the source of perturbation. We compute the excitation factors of Kerr black holes up to the 20th overtone and find that the fourth, fifth, and sixth overtones have the first three highest excitation factors for intermediate and high spin parameters. This provides an independent confirmation of the importance of overtones that has been confirmed by the fitting data analysis of numerical relativity waveforms beginning around the strain peak amplitude.

The period–luminosity relation for δ Scuti stars using Gaia DR2 parallaxes

We have examined the period-luminosity (P-L) relation for delta Scuti stars using Gaia DR2 parallaxes. We included 228 stars from the catalogue of Rodriguez et al. (2000), as well as 1124 stars observed in the four-year Kepler mission. For each star we considered the dominant pulsation period, and used DR2 parallaxes and extinction corrections to determine absolute V magnitudes. Many stars fall along a sequence in the P-L relation coinciding with fundamental-mode pulsation, while others pulsate in shorter-period overtones. The latter stars tend to have higher effective temperatures, consistent with theoretical calculations. Surprisingly, we find an excess of stars lying on a ridge with periods half that of the fundamental. We suggest this may be due to a 2:1 resonance between the third or fourth overtone and the fundamental mode.

Modelling long-period variables – I. A new grid of O-rich and C-rich pulsation models

We present a new grid of non-adiabatic, linear pulsation models of Long-Period Variables (LPVs), including periods and growth rates for radial modes from the fundamental to the fourth overtone. The models span a wide range in mass, luminosity, metallicity, C/O ratio and helium abundance, effectively covering the whole thermally-pulsing asymptotic giant branch (TP-AGB) evolution, and representing a significant update with respect to previous works. The main improvement is the inclusion of detailed atomic and molecular opacities, consistent with the models chemical mixture, that makes the present set of models the first to systematically account for variability in C-stars. We examine periods and growth rates in the models, and find that, while the fundamental mode is affected by the structure of the envelope, overtones are less sensitive to the interior and largely determined by the global properties. In the models, the frequency of the overtone with the largest degree of excitation is found to scale with the acoustic cut-off frequency at the stellar surface, a behaviour similar to that observed for the frequency of maximum oscillation power for solar-like oscillations in less evolved red giants. This allows us to provide a simple analytic prescription to predict the most-likely dominant mode as a function of stellar parameters. Best-fit relations for periods are also provided. By applying results of pulsation models to evolutionary tracks, we present a general picture of the evolution of long-period variability during the TP-AGB, that we find consistent with observations. Models are made public through a dedicated web interface.

Survey of non-linear hydrodynamic models of type-II Cepheids

We present a grid on non-linear convective type-II Cepheid models. The dense model grids are computed for 0.6M_Sun and a range of metallicities ([Fe/H]=-2.0,-1.5,-1.0), and for 0.8M_Sun ([Fe/H]=-1.5). Two sets of convective parameters are considered. The models cover the full temperature extent of the classical instability strip, but are limited in luminosity; for the most luminous models violent pulsation leads to the decoupling of the outermost model shell. Hence, our survey reaches only the shortest period RV Tau domain. In the Hertzsprung-Russel diagram we detect two domains in which period doubled pulsation is possible. The first extends through the BL Her domain and low luminosity W Vir domain (pulsation periods ~2-6.5 d). The second domain extends at higher luminosities (W Vir domain; periods >9.5d). Some models within these domains display period-4 pulsation. We also detect very narrow domains (~10 K wide) in which modulation of pulsation is possible. Another interesting phenomenon we detect is double-mode pulsation in the fundamental mode and in the fourth radial overtone. Fourth overtone is a surface mode, trapped in the outer model layers. Single-mode pulsation in the fourth overtone is also possible on the hot side of the classical instability strip. The origin of the above phenomena is discussed. In particular, the role of resonances in driving different pulsation dynamics as well as in shaping the morphology of the radius variation curves is analysed.

ON THE PULSATIONAL-ORBITAL-PERIOD RELATION OF ECLIPSING BINARIES WITH δ-SCT COMPONENTS

We have deduced a theoretical relation between the pulsation and orbital-periods of pulsating stars in close binaries based on their Roche lobe filling. It appears to be of a simple linear form, with the slope as a function of the pulsation constant, the mass ratio, and the filling factor for an individual system. Testing the data of 69 known eclipsing binaries containing δ-Sct-type components yields an empirical slope of 0.020 ± 0.006 for the P{sub pul}-P{sub orb} relation. We have further derived the upper limit of the P{sub pul}/P{sub orb} ratio for the δ-Sct stars in eclipsing binaries with a value of 0.09 ± 0.02. This value could serve as a criterion to distinguish whether or not a pulsator in an eclipsing binary pulsates in the p-mode. Applying the deduced P{sub pul}-P{sub orb} relation, we have computed the dominant pulsation constants for 37 δ-Sct stars in eclipsing systems with definite photometric solutions. These ranged between 0.008 and 0.033 days with a mean value of about 0.014 days, indicating that δ-Sct stars in eclipsing binaries mostly pulsate in the fourth or fifth overtones.

Polymerization of fluoro-containing acrylic monomers: Determination of monomer conversion from absorption spectra in the near IR range

For a series of polymers, including crosslinked polymers, based on fluoro-containing acrylic monomers, absorption coefficients are measured in the visible and near-IR ranges. The relationship between the intensities of observed absorption bands and the conversions of monomers during radical photopolymerization is revealed. Absorption bands at 0.85 μm are identified. It is found that the bands centered near 895 and 730 nm correspond to excitations of the fourth and fifth overtones of the stretching vibrations of C-H bonds. The absorption bands centered near 707 and 867 nm are related to the presence of C=C bonds in the monomers.

Measurement of the Fourth O−H Overtone Absorption Cross Section in Acetic Acid Using Cavity Ring-Down Spectroscopy

We report the absolute absorption cross sections of the fourth vibrational O-H (5ν(OH)) overtone in acetic acid using cavity ring-down spectroscopy. For compounds that undergo photodissociation via overtone excitation, such intensity information is required to calculate atmospheric photolysis rates. The fourth vibrational overtone of acetic acid is insufficiently energetic to effect dissociation, but measurement of its cross section provides a model for other overtone transitions that can affect atmospheric photochemistry. Though gas-phase acetic acid exists in equilibrium with its dimer, this work shows that only the monomeric species contributes to the acetic acid overtone spectrum. The absorption of acetic acid monomer peaks at ∼615 nm and has a peak cross section of 1.84 × 10(-24) cm(2)·molecule(-1). Between 612 and 620 nm, the integrated cross section for the acetic acid monomer is (5.23 ± 0.73) × 10(-24) cm(2)·nm·molecule(-1) or (1.38 ± 0.19) × 10(-22) cm(2)·molecule(-1)·cm(-1). This is commensurate with the integrated cross section values for the fourth O-H overtone of other species. Theoretical calculations show that there is sufficient energy for hydrogen to transition between the two oxygen atoms, which results in an overtone-induced conformational change.

Dynamics of Vibrational Overtone Excited Pyruvic Acid in the Gas Phase: Line Broadening through Hydrogen-Atom Chattering

The dynamics of overtone-excited pyruvic acid (PA) is studied using a combination of experimental and theoretical methods. It is experimentally observed that high overtone excitation of the OH-stretching mode of PA in the gas phase leads to a unimolecular decarboxylation reaction. An RRKM analysis of the rate is consistent with previous experiments for the thermal reaction but is inconsistent with the present overtone chemistry; from this it is concluded that the overtone-induced reaction is likely to be a direct reaction. Using a Fourier transform infrared spectrometer and a cavity ring-down spectrometer, the spectrum for the OH-stretch fundamental and overtone transitions is measured. We assign two conformers of PA in the spectrum, the Tc and Tt, corresponding to distinct orientations of the OH-group. The spectral peaks for the Tc-conformer broaden dramatically at the third and fourth overtones while those of the Tt-conformer remain relatively narrow. Using a three-mode quantum mechanical model for the vibrational states, the line positions and intensities are well reproduced by theory. The line widths, and the associated dynamical interpretation, are provided by a direct dynamics calculation, where the potential is computed "on-the-fly" and all degrees of freedom are included. It is found that the line broadening is due to the onset of H-atom chattering between the two O-atoms, an effect that occurs for the Tc-conformer but not the Tt-conformer. This H-atom-transfer process is the first step of the decarboxylation reaction mechanism, which subsequently involves breaking the C-C bond. The theoretical and experimental line widths agree but do not correspond to the full reaction time which is much longer than the initial chattering step.

Fluorosulfonic Acid and Chlorosulfonic Acid: Possible Candidates for OH-Stretching Overtone-Induced Photodissociation

We have calculated the stationary points and internal reaction coordinate pathway for the dissociation of fluorosulfonic acid (FSO3H) and chlorosulfonic acid (ClSO3H). These sulfonic acids dissociate to sulfur trioxide and hydrogen fluoride and chloride, respectively. We have calculated the frequencies and intensities of the OH-stretching transitions of FSO3H and ClSO3H with an anharmonic oscillator local mode model. We find that excitation of the fourth and third OH-stretching overtones provide adequate energy for photodissociation of FSO3H and ClSO3H, respectively. We propose that experimental detection of the products of OH-stretching overtone-induced photodissociation of FSO3H and ClSO3H would be easier than the sulfuric acid (H2SO4) equivalent. The photodissociation of H2SO4 is thought to be important in the stratosphere. The FSO3H and ClSO3H experiment could be used in proxy to support the recently proposed OH-stretching overtone-induced photodissociation mechanism of H2SO4.

Vibrational OH-Stretching Overtone Spectroscopy of Jet-Cooled Resorcinol and Hydroquinone Rotamers

We have measured the OH-stretching fundamental and overtone spectra of resorcinol and hydroquinone in a supersonic jet using nonresonant ionization detected infrared/near-infrared spectroscopy. Anharmonic oscillator local mode calculations of the OH-stretching frequencies and intensities and Boltzmann populations of the stable rotamers have been calculated at the B3LYP/6-311++G(3df,2pd) level to help interpret the observed spectra. Resorcinol has three stable rotamers and in the recorded second and third OH-stretching overtone spectra there is evidence of two distinguishable rotamers. Hydroquinone has two stable rotamers; however, the OH-stretching oscillators of each rotamer are so similar in nature that even up to the fourth OH-stretching overtone the transitions coincide. These results place a limit on the ability of the jet-cooled overtone spectroscopy technique to distinguish between rotamers.

Vibrational Overtone Spectroscopy of Three-Membered Rings

We have recorded vapor-phase photoacoustic spectra of cyclopropane, ethylene oxide, and ethylene sulfide in the third, fourth, and fifth CH-stretching overtone regions. We have used a harmonically coupled anharmonic oscillator local mode model to facilitate analysis of the spectra. Fermi resonance between the CH-stretching and HCH-bending vibrations is essential to explain the observed wide and multistructured CH-stretching overtone bands. A number of weak combination bands can account for the remaining experimental features observed to the blue of the CH-stretching regions. We have reassigned the fundamental spectra of these three-membered rings.

The pulsational stability of intermediate- and low-luminosity red giants in globular clusters

Some theoretical calculations of linear non-adiabatic pulsations of intermediate- and low- luminosity red giants in globular clusters have been carried out using a time-dependent theory of nonlocal stellar convection. As shown by the results, for all models with temperatures higher than 5400 K the modes up to the fourth overtone are pulsationally stable. With the increase of stellar luminosity, the low-order overtones also become pulsationally unstable. For red giants of intermediate and low luminosities, the pulsational stability is exceedingly low and is close to neutral stability. Therefore, they will be either non-variables or short-period variables ( P < 2 days) with extremely small amplitudes.

Weak Intramolecular Interactions in Ethylene Glycol Identified by Vapor Phase OH−Stretching Overtone Spectroscopy

Vapor phase OH-stretching overtone spectra of ethylene glycol were recorded to investigate weak intramolecular hydrogen bonding. The spectra were recorded with conventional absorption spectroscopy and laser photoacoustic spectroscopy in the first to fourth OH-stretching overtone regions. The room-temperature spectra are dominated by two conformers that show weak intramolecular hydrogen bonding. A less abundant third conformer, with no sign of hydrogen bonding, is also observed. Vapor phase spectra of the ethylene-d(4) glycol isotopomer were also recorded and used to identify an interfering resonance between CH-stretching and OH-stretching states in the fourth overtone. Anharmonic oscillator local mode calculations of the OH-stretching transitions have provided an accurate simulation of the observed spectra. The local mode parameters were calculated with coupled cluster ab initio methods. The calculations facilitate assignment of the different conformers in the spectra and illustrate the effect of the intramolecular hydrogen bonding.

Selective OD bond dissociation of HOD: Photodissociation of vibrationally excited HOD in the 5νOD state

Exclusively selective OD bond dissociation of HOD has been demonstrated by the ultraviolet photodissociation at 243.1 nm through the fourth overtone state of the OD stretching mode (5nu(OD)). Branching ratio between the OH and OD bond dissociation channels has been determined by detecting H and D atoms, utilizing a (2+1) resonance-enhanced multiphoton ionization (REMPI) process. The OD bond dissociation has been solely observed with the branching ratio phi(D+OH)/phi(H+OD)>12, which has been determined by the detection limit for the H atom. Time-dependent wave-packet calculations reveal two important features for the highly selective OD bond dissociation: (1) strong local-mode character of the 5nu(OD) state and (2) limitation of the total excitation energy lower than the saddle point between the OH and OD dissociation channels in the A state. Additionally, the recoil velocity and angular distribution of the nascent D atom are roughly evaluated by analyzing the Doppler-resolved REMPI spectrum. Based on these results, the dynamics of the selective OD dissociation has been discussed in detail.

Determining the vibrational pattern via overtone cold spectra: C–H methyl stretches of propyne

Vibrationally mediated photodissociation and photoacoustic (PA) spectroscopy were employed for studying the intramolecular dynamics of propyne initially excited to the first through fourth overtone of methyl C-H stretching modes. Room-temperature PA and jet-cooled action spectra, monitoring the absorption of the parent and the yield of the ensuing H photofragments, respectively, were obtained. The PA spectra exhibit mainly broad features, while the action spectra, due to inhomogeneous structure reduction, expose multiple peaks of recognizable shapes in the differing overtone manifolds. Symmetric rotor simulations of the band contours of the action spectra allowed retrieving of band origins and linewidths. The linewidths of the bands in each manifold enabled estimates for energy redistribution times out of the corresponding states to the bath states, the times ranging from 18+/-6 ps for two quanta of C-H excitation to subpicosecond for five quanta. The data were also analyzed in terms of a normal-mode model and a joint local-/normal-mode model. These models enabled determination of harmonic frequencies, anharmonicities, and interaction parameters reproducing the observed data in all monitored regions and provided spectral assignments. The measured Doppler profiles were well fitted by Gaussians with widths suggesting low average translational energies for the released H photofragments. These low energies and their similarities to those for dissociation of propyne isotopomers preexcited to acetylenic C-H stretches were ascribed to an indirect dissociation process occurring after internal conversion to the ground electronic state and isomerization to allene.

Resonance coupling in the fourth OH-stretching overtone spectrum of formic acid.

The room-temperature vibrational overtone spectra of the formic acid isotopomers HCOOH and DCOOH have been recorded in the third and fourth OH-stretching overtone regions with intracavity laser photoacoustic spectroscopy. Resonance coupling between the OH- and CH-stretching vibrations in HCOOH is clearly identified in the fourth overtone region. This is an example of strong coupling across bonds. In the third overtone region, no resonance is observed. Vibrational energies and intensities of the OH- and CH-stretching overtones and combination bands have been calculated with an anharmonic oscillator local mode model. The pure OH-stretching bright state carries almost all the intensity prior to resonance coupling.

Bond-selective photodissociation of partially deuterated ammonia molecules: photodissociations of vibrationally excited NHD(2) in the 5nu(NH) state and NH(2)D in the 5nu(ND) state.

Ultraviolet photodissociation of NHD(2) excited to the fourth overtone state of the NH stretching mode (5nu(NH)) and NH(2)D excited to that of the ND stretching mode (5nu(ND)) has been investigated by using a crossed laser and molecular beams method. Branching ratio between the NH and ND bond dissociations has been determined by utilizing a (2+1) resonance enhanced multiphoton ionization scheme of H and D atoms. For the photolysis of NHD(2) in the 5nu(NH) state, the NH dissociation cross section is 5.1+/-1.4 times as large as the ND dissociation cross section per bond. On the other hand, for the photolysis of NH(2)D in the 5nu(ND) state, the ratio of the NH dissociation cross section per bond to the ND dissociation cross section decreases to 0.68+/-0.16. In comparison with the branching ratios for the photolysis of vibrationally unexcited NH(2)D and NHD(2), the present results indicate that the excitation of the NH stretching mode enhances the NH dissociation with ca. two times larger NH/ND branching ratio, whereas the excitation of the ND stretching mode results in the preferential ND dissociation with ca. 3-4 times larger ND/NH branching ratio than that for the vibrational ground states. The mechanism of the bond-selective enhancement has been discussed in terms of the energetics and dynamics of wave packet.

The effect of NH2-inversion tunneling splitting on the NH-stretching overtone spectra of aniline vapour

The room temperature vibrational overtone spectrum of aniline vapour has been recorded by intracavity laser photoacoustic spectroscopy in the 9700 cm−1 to 16 600 cm−1 region. The NH-stretching overtone bands exhibit spectral structure due to the tunneling splitting of the amino group inversion states. We find that this tunneling splitting steadily decreases with increasing NH-stretching vibrational excitation, and at the fourth NH-stretching overtone the splitting is negligible. Wave numbers and intensities of the NH- and CH-stretching vibrational overtones were calculated with a harmonically coupled anharmonic oscillator local mode model to facilitate spectral assignment. The conventional liquid phase overtone spectra of aniline were recorded and the measured absolute intensities are in good agreement with the calculated intensities.