Local Mode Behavior Research Articles

Novel Criteria to Provide a Locality/Normality Degree in Molecules and Their Relevance in Physical Chemistry.

In contrast to the traditional analysis of molecules using local mode behavior, where the degree of locality is given through a function in terms of Morse potential parameters, new criteria for locality/normality (LN) suitable for application to any molecular system are proposed. The approach is based on analysis of the connection between the algebraic normal and local mode representations. It is shown that both descriptions are equivalent as long as the polyad (total number of quanta) in the local representation is not conserved. The constraint of a local polyad conservation naturally provides a criterion for assigning an LN degree in quantitative form, without an analogue in configuration space. The correlation between the different parameters reveals the physical properties of molecules. A clear connection between the LN degree (based on the fundamentals) and spectroscopic properties is also presented, suggesting a promising approach for identifying mixtures of isotopologues.

Dynamical and Mechanical Insights into the Li(2 S)+ HCl( ) Reaction: A Detailed Quantum Wavepacket Study.

Quantum wave packet dynamics of the Li(2 S)+HCl( ) reaction in its electronic ground state is studied. The initial state-selected and energy-resolved dynamical attributes such as reaction probability, integral cross section, and thermal rate constant for the Cl-abstraction and H-abstraction pathways are reported. All partial wave contributions of J up to 120 were found to be necessary for the title reaction up to the collision energy of ∼1.0 eV. The dynamical results reveal that the Cl-abstraction is more favored over the H-abstraction for the different rovibrational (v, j) excitations. Due to the existence of an early barrier in the potential energy surface, the cross sections increase with increasing collision energy. The rate constants also monotonously increase with temperature for both channels. Resonances are identified and characterized in terms of eigenfunctions and lifetimes. Nearly 120 well-resolved eigenstates are reported for the LiHCl complex, and they are categorized as van der Waals (vdW), barrier and product states according to the nodal progressions along (R, r, γ). The vdW resonances reveal a local-mode behavior of quasibound type at low energies and extended progressions at high energies. Further, the single-quantized periodic orbit type is also observed in the barrier region, which decays very fast. Finally, the lifetime analysis reveals that the vdW resonances can survive as long as ∼2.2 ps, which is much longer than the lifetime of the resonances in the barrier region.

Resummation of the Rayleigh-Schrödinger perturbation series. Vibrational energy levels of the H2S molecule.

ABSTRACT The Rayleigh – Schrödinger perturbation series possesses the property that can be termed multiple convergence. This property is that using appropriate multivalued approximants it enables the energy levels of several states to be calculated from the coefficient of a series constructed for one state. This multiple convergence property has been previously demonstrated in a number of papers: for linear anharmonic oscillators (Sergeev and Goodson J. Phys. A: Math. Gen. 31 4301 (1998)), for one-dimensional periodic problem (Fernandez and Diaz 2001, Eur. Phys. J. D15 41), for electronic sates of diatomic molecules (Jordan Int. J. Quant. Chem. Symp. 9, 325 (1975); Goodson Mol. Phys. 110, 1681 (2012)) and for vibrational states of formaldehyde (Duchko and Bykov Phys. Scr. 94, 105403, (2019)). In this paper, we examine multiple convergence as applied to the vibrational states of the hydrogen sulphide which exhibits the strong local mode behaviour. We show that property of multiple convergence is connected with the polyad structure of the vibrational energy spectrum and the strength of anharmonic resonance coupling between the states.

Edge localized mode characteristics and divertor heat flux during stationary and transient phase for CFETR hybrid scenario

The study of edge localized mode (ELM) behavior, stationary heat flux and transient heat flux during the ELM crash phase is performed for a China Fusion Engineering Test Reactor (CFETR) 1 GW hybrid mode operation scenario ( = 7.2 m, = 6.5 T, = 13.78 MA). Modeling and simulation start with a scenario obtained by multi-code integrated modeling on the one modeling framework for integrated tasks framework. Linear stability and nonlinear simulations of ELM dynamics are carried out using the BOUT++ six-field reduced magnetohydrodynamic module, which show a much smaller ELM energy loss (ΔELM ~ 0.13%) compared to that of a Type-I ELM. Parametric analysis of the weak linear growth rate and small ELM energy loss characteristics shed light on physics corresponding to a grassy ELM regime for CFETR 1 GW hybrid scenario. The transient heat flux on the divertor target during this small ELM phase is investigated using BOUT++. We found that upstream radial transport in the scrape-off-layer (SOL) induced by small ELMs is weak, which keeps it in the drift-dominated region. However, the heat flux width is still broadened to = 4.64 mm by the increase of separatrix temperature during ELM nonlinear evolution. The impact of transient peak heat load and ELM energy fluence on tungsten melting and net erosion rate of divertor target is evaluated for the first-time using physics-based transport that connects the pedestal with the SOL. Energy fluence caused by a single ELM pulse is below the tungsten melting limit, while tungsten erosion would exceed the material requirements. We conclude that external mitigation methods, such as divertor detachment and advanced divertor geometry are likely needed for the steady state operation of CFETR.

Polyad breaking phenomenon associated with a local-to-normal mode transition and suitability to estimate force constants

ABSTRACTIn a system of two interacting harmonic oscillators a local-to-normal mode transition is manifested as a polyad breaking phenomenon. This phenomenon is associated with the suitability to estimate zeroth-order force constants in the framework of a local mode description. This transition is also exhibited in two interacting Morse oscillators. To study this case, an appropriate parameterisation going from a molecule with local mode behaviour (H2O) to a molecule presenting a normal mode behaviour (CO2) is introduced. Concepts from quantum mechanics like fidelity, entropy and probability density, as well from nonlinear classical mechanics like Poincaré sections are used to detect the transition region. It is found that fidelity and entropy are sensitive complementary properties to detect the local-to-normal transition. Poincaré sections allow the local-to-normal transition to be detected through the appearance of chaos as a consequence of the polyad breaking phenomenon. In addition, two kinds of avoided energy crossings are identified in accordance with the different regions of the spectrum.

Partial detachment of high power discharges in ASDEX Upgrade

Detachment of high power discharges is obtained in ASDEX Upgrade by simultaneous feedback control of core radiation and divertor radiation or thermoelectric currents by the injection of radiating impurities. So far 2/3 of the ITER normalized heat flux Psep/R = 15 MW m−1 has been obtained in ASDEX Upgrade under partially detached conditions with a peak target heat flux well below 10 MW m−2. When the detachment is further pronounced towards lower peak heat flux at the target, substantial changes in edge localized mode (ELM) behaviour, density and radiation distribution occur. The time-averaged peak heat flux at both divertor targets can be reduced below 2 MW m−2, which offers an attractive DEMO divertor scenario with potential for simpler and cheaper technical solutions. Generally, pronounced detachment leads to a pedestal and core density rise by about 20–40%, moderate (<20%) confinement degradation and a reduction of ELM size. For AUG conditions, some operational challenges occur, like the density cut-off limit for X-2 electron cyclotron resonance heating, which is used for central tungsten control.

Experimental and numerical understanding of localized spin wave mode behavior in broadly tunable spatially complex magnetic configurations

Spin wave modes confined in a ferromagnetic film by the spatially inhomogeneous magnetic field generated by a scanned micromagnetic tip of a ferromagnetic resonance force microscope (FMRFM) enable microscopic imaging of the internal fields and spin dynamics in nanoscale magnetic devices. Here we report a detailed study of spin wave modes in a thin ferromagnetic film localized by magnetic field configurations frequently encountered in FMRFM experiments, including geometries in which the probe magnetic moment is both parallel and antiparallel to the applied uniform magnetic field. We demonstrate that characteristics of the localized modes, such as resonance field and confinement radius, can be broadly tuned by controlling the orientation of the applied field relative to the film plane. Micromagnetic simulations accurately reproduce our FMRFM spectra allowing quantitative understanding of the localized modes. Our results reveal a general method of generating tightly confined spin wave modes in various geometries with excellent spatial resolution that significantly facilitates the broad application of FMRFM. This paves the way to imaging of magnetic properties and spin wave dynamics in a variety of contexts for uncovering new physics of nanoscale spin excitations.

H-mode characterization for dominant ECRH and comparison to dominant NBI and ICRF heating at ASDEX Upgrade

The influence of pure electron heating versus combined electron and ion heating on a high collisionality H-mode plasma has been investigated in ASDEX Upgrade. This was done by replacing both neutral beam injection (NBI) and ion cyclotron resonance frequency (ICRF) heating in small steps with electron cyclotron resonance heating (ECRH) while keeping the total heating power constant. The stability of the global plasma parameters and the response of the kinetic profiles on the changed heating mix and torque input is shown. The differences in edge localized mode behaviour between the different heating mixes is reported. The data were analysed with an interpretative transport model and linear gyrokinetic simulations were performed to evaluate the underlying transport mechanism.

A probabilistic model for the identification of confinement regimes and edge localized mode behavior, with implications to scaling laws

Pattern recognition is becoming an important tool in fusion data analysis. However, fusion diagnostic measurements are often affected by considerable statistical uncertainties, rendering the extraction of useful patterns a significant challenge. Therefore, we assume a probabilistic model for the data and perform pattern recognition in the space of probability distributions. We show the considerable advantage of our method for identifying confinement regimes and edge localized mode behavior, and we discuss the potential for scaling laws.

Momentum losses by charge exchange with neutral particles in H-mode discharges at JET

The effect of a neutral density background on the toroidal angular momentum and kinetic energy profiles has been investigated in JET. Under equivalent conditions but with increasing gas fuelling during the flat top phase, it has been observed that both the edge rotation and temperature decrease. The increase in electron density was not sufficient to compensate the rotation and temperature loss such that both energy and momentum confinement times are significantly reduced. The edge localized mode behaviour is observed to be significantly affected by the increased neutral influx. A simple 1.5D fluid model has been used to qualitative capture the neutral transport response within the plasma, followed by a forward model of the passive charge-exchange (CX) emission of carbon to obtain a corrected radial neutral density profile. It has been found that the neutral density is sharply attenuated over the edge region, with similar edge magnitudes in both the non-fuelled (Γ0/ne ∼ 1.2 m s−1) and maximum fuelled case (Γ0/ne ∼ 2.5 m s−1). Discharges with reversed-B operation exhibited even higher normalized neutral fluxes related to first orbit effects and increased wall interactions. Over the full neutral influx range, a decrease in pedestal thermal Mach number from 0.25 to 0.14 was observed. Increased neutral penetration up to the pedestal top (r/a ∼ 0.9) due to multiple CX interactions is obtained from the interpretive model. Under these multiple neutral–ion interactions, the impact on the CX loss of angular momentum is larger compared with the CX energy loss. The drag torque was seen to increase up to 10% of the total applied torque, while energy losses appeared to be smaller. The accuracy of this global approach method is unfortunately limited; however, the estimated momentum sink was found comparable to the torque required to explain the discrepancy between observed global energy and momentum confinement.

Energetic particle driven instability in wall-stabilized high-β plasmas

We have observed a fishbone-like mode in high-β plasmas above the ideal β limit without a conducting wall. The mode frequency chirps down, and its initial value is close to the precession frequency of trapped fast ions produced by perpendicularly injected neutral beams. This mode can often induce the resistive wall mode (RWM). The mode is observed mainly in the high-βN plasma where an ideal kink-ballooning mode (IKBM) and the RWM are marginally stable. Since this mode and the RWM were simultaneously observed, the mode is attributed to the interaction between the trapped fast ions and a marginally stable IKBM stabilized by a conducting wall. Actually, the MARG2D analysis shows that the IKBM is wall-stabilized and has a real frequency of the same order as the observed mode frequency. From these results, the observed mode was named ‘energetic particle driven wall mode (EWM)’. Moreover, the EWM can change the edge localized mode (ELM) behaviour. For example, it was observed that the ELM was synchronized with the EWM. An energy loss due to the EWM-triggered ELM is smaller, and its frequency becomes higher compared with the usual ELM.

Potential energy surfaces in algebraic molecular models using coherent states

The potential energy surfaces provided by the coherent states formalism for the case of interacting one-dimensional oscillators is investigated. The case of two interacting oscillators modelled with Morse potentials are considered in detail. First the traditional treatment is presented in order to identify the need to establish a new transformation between the parameters and the classical variables that allow the full Hamiltonian to be recovered. To this end the connection between the su(2) algebraic model and the usual treatment in configuration space was taken into account. It is shown that the coherent state approach when applied to recover the potential energy surface (PES) from a polyad preserving Hamiltonian is viable only in systems with a local mode behaviour. For molecules with a normal mode behaviour the approach is still valid, but the polyad must be broken in order to recover the PES. Our approach is evaluated through the calculation of the force constants for H2O and CO2, representative examples of local and normal behaviours.

High resolution infrared spectra of the first and second stretching overtone band systems of 123SbD 3

The high resolution infrared spectrum of the mono-isotopic species 123SbD 3 has been studied in the regions of the first and second Sb–D stretching overtones, from 2600 to 2800 cm −1 and from 3900 to 4100 cm −1, respectively. In both regions only two almost degenerate bands of similar intensity have been observed, one parallel and the other perpendicular, corresponding to the low-lying states in the manifolds of the v stretching = 2 and 3 excited vibrational states. These bands have been identified as 2 ν 1( A 1)/ ν 1 + ν 3( E) in the first overtone and 3 ν 1( A 1)/2 ν 1 + ν 3( E) in the second overtone band system. About 1700 transitions with J max ′ = K max ′ = 20 have been assigned to the 2 ν 1( A 1)/ ν 1 + ν 3( E) and about 700 with J max ′ = K max ′ = 21 to the 3 ν 1( A 1)/2 ν1 + ν 3( E) dyad. The transitions assigned to each dyad have been fitted simultaneously since the A 1/ E excited states are affected by strong Coriolis and k-type perturbations treated explicitly in the model. Eventually, the extent to which the parameters resulting from the analyses fulfill the local mode theory requirements has been evaluated. Differently from SbH 3, the deuterated species does not reach true local mode behavior, even in the second overtone.

On the local mode behaviour of the XH2/XD2 and XD/XH fragments with respect to the deuterated species of the near local mode XH3(C3v ) molecule

Effect of isotopic substitution in the near local mode, XH3(C3v ), molecules is considered. On that basis it is shown that the spectroscopic properties of deuterated and/or di-deuterated isotopic species of the XH3(C3v ) molecule with the value of interbond angle close to π/2 are analogous to the spectroscopic properties of its separate fragments: of a three-atomic local mode ‘molecule’ XH2/XD2 and of a diatomic XD/XH ‘molecule’. The phosphine molecule is considered as an illustration.

Local mode behavior in H2Te

A high-resolution spectrum of hydrogen telluride (H(2)Te) was recorded in the 4050-7000 cm(-1) region. Two bands could be observed at 4900 and 5980 cm(-1) and were assigned as the (20(+/-),1) <-- (00(+),0) and (30(+/-),0) <-- (00(+),0) bands, respectively. Rotational transitions of the two bands were assigned for the most abundant H(2) (130)Te and H(2) (128)Te isotopic species. Line position analyses were carried out to investigate a possible local mode behavior. For the first time we found in H(2)Te strong experimental evidence for such a behavior for the higher-lying band as its two upper vibrational states are only 0.027 and 0.032 cm(-1) apart for the H(2) (130)Te and H(2) (128)Te isotopic species, respectively.

Rotational energy cluster formation in XY 3 molecules: Excited vibrational states of BiH 3 and SbH 3

Previous theoretical work on energy cluster formation at high rotational excitation in the vibrational ground state of PH 3 [S.N. Yurchenko, W. Thiel, S. Patchkovskii, P. Jensen, Phys. Chem. Chem. Phys. 7 (2005) 573] is extended to BiH 3 and SbH 3. By means of variational calculations of the rotation–vibration energies based on ab initio potential energy surfaces, we analyze the rotational energy clustering of BiH 3 and SbH 3 at J ⩽ 70 for a number of vibrational states. We show that BiH 3 and SbH 3, with their pronounced local mode behaviour, exhibit cluster formation already at moderate rotational excitation. In addition, owing to its quasi-spherical-top character, BiH 3 undergoes an imperfect bifurcation at high J. This gives rise to an energy cluster type not present in PH 3 and SbH 3. We present a semi-classical approach to the construction of the rotational energy surfaces for vibrationally excited states.

Rotation–vibration energy level clustering in the [formula omitted] ground electronic state of PH 2

We use previously determined potential energy surfaces for the Renner-coupled X ∼ 2 B 1 and A ∼ 2 A 1 electronic states of the phosphino (PH 2) free radical in a calculation of the energies and wavefunctions of highly excited rotational and vibrational energy levels of the X ∼ state. We show how spin–orbit coupling, the Renner effect, rotational excitation, and vibrational excitation affect the clustered energy level patterns that occur. We consider both 4-fold rotational energy level clustering caused by centrifugal distortion, and vibrational energy level pairing caused by local mode behaviour. We also calculate ab initio dipole moment surfaces for the X ∼ and A ∼ states, and the X ∼ – A ∼ transition moment surface, in order to obtain spectral intensities.

Third harmonic EC heating of ELMy H-mode in TCV

Ohmic H-mode discharges in the Tokamak à Configuration Variable (TCV) have recently been heated for the first time by electron cyclotron (EC) waves at the 3rd harmonic (X3) at full power. New edge localized mode (ELM) behaviour has been found, with larger amplitudes at lower frequency than are typical in ohmic H-modes. This new regime required the full available X3-EC Heating (X3-ECH) power to avoid the ELM-free phase, which occurred when less heating power was applied. The energy loss per ELM can be up to 15% of the total stored energy, with values in the range 4–5% being typical of the smaller ELMs usually found in the ohmic H-mode regime. Despite these high-energy losses, the plasma temperature raises significantly in the X3 heated H-modes, doubling the stored energy from its ohmic value. The confinement time decreases when the ECH is applied, but can recover its ohmic H-mode value later in the discharge depending on the EC wave coupling. It is still not possible to provide an unambiguous classification of these ELMs as Type I.

Fenchone, Camphor, 2-Methylenefenchone and 2-Methylenecamphor: A Vibrational Circular Dichroism Study

We report and discuss the infrared (IR) vibrational circular dichroism (VCD) spectra of the enantiomeric pairs of the olefin derivatives of fenchone (1,3,3-trimethyl-2-methylenebicyclo[2.2.1]heptane) and camphor (1,7,7-trimethyl-2-methylenebicyclo[2.2.1]heptane), respectively, together with those of the parent molecules. The VCD spectra were taken in three spectral regions: the mid-IR region, encompassing the fundamental deformation modes, the region of CH-stretching fundamental modes and the NIR-region between 1100 and 1300 nm, which corresponds to the second CH-stretching overtone. The VCD and absorption spectra in the first two regions are analyzed by use of current density functional theory (DFT) calculations. The NIR region is analyzed by a protocol that consists of the use of DFT-based calculations and in assuming local mode behavior: the local mode approach is found appropriate for interpreting the absorption spectra and, for the moment, acceptable for calculating NIR-VCD spectra. The analysis of the first region allows us to track the contribution of the C=O group in the vibrational optical activity of C-C stretching modes; notable differences are indeed found in olefins and ketones. On the contrary, in the other two regions the VCD spectra of olefins and ketones are more similar: in the normal mode region of CH stretching fundamentals the spectra are determined by the mutual orientation of the CH bonds; in the second overtone local mode region olefins and ketones signals show some differences.

Vibrational spectrum of BiH3: Six-dimensional variational calculations on high-level ab initio potential energy surfaces

We report a theoretical study of the ground electronic state of BiH3. The potential energy surface (PES) is obtained from coupled cluster CCSD(T) calculations with a large basis set (289 contracted Gaussian functions). The previously available quartic force field (P4) is extended by adding the dominant quintic and sextic stretching terms to yield improved potential functions in symmetry coordinates (P6) and Morse-type coordinates (M4). Second-order rovibrational perturbation calculations on the P4-PES and full variational calculations on the P6-PES and M4-PES yield almost identical vibrational term values which is rationalized by considering the local mode behavior of BiH3 and the Morse-type character of the M4-PES. The remaining deviations between the computed and observed vibrational term values must thus be caused by imperfections in the CCSD(T) surface. A refinement of this ab initio surface by a restrained fit to experimental data allows an essentially perfect reproduction of the observed vibrational term values. Variational calculations on this refined surface provide predictions for several overtone and combination bands that have not yet been observed.