Local Mode Behavior Research Articles

Calculation of edge toroidal current density distributions from DIII-D lithium beam measurements using Ampère’s law

The local edge current density j(r) is a parameter of basic importance in understanding the stability of high performance tokamaks, as well as the dynamics of edge localized mode behavior. On DIII-D, the lithium beam polarimetry diagnostic provides precise measurements of the local magnetic field projection along the field of view at 32 radial locations in the plasma edge. Using these measurements, the known spatial calibration and a minimal amount of information about the magnetic field shape from equilibrium reconstructions, Ampères law may be used to provide a straightforward parameterization for the edge toroidal current density in terms of the measured magnetic field and its radial derivative. This approach is relatively insensitive to errors in the reconstruction and is simple to apply.

First stretching overtone of BiH3: an extreme local-mode case for XH3-type molecule?

The first stretching overtone region of short-lived, formerly inaccessible BiH3 near 3405 cm(-1) has been measured by Fourier-transform infrared spectroscopy with a resolution of 0.0066 cm(-1). Only the 2nu1(A1)/nu1+nu3(E) band system has been observed. Rotational analysis, with transitions reaching J'max=14, has revealed almost perfect local-mode behavior for the upper states denoted as (200A1/E) in the local-mode notation. Ratios of vibration-rotation interaction parameters q(eff)/alpha(eff)(BB) and r(eff)/alpha(eff)(BC), and the appropriate rotational constant differences, are in good agreement with theoretical local-mode limit values. A simple stretching vibrational model reproduces the observed vibrational term values well, and the potential parameters obtained are close to true values.

Einstein oscillators in thallium filled antimony skutterudites.

Inelastic neutron scattering measurements on several Tl filled skutterudites (Tl0.5Co3.5Fe0.5Sb12, Tl0.8Co3FeSb12, and Tl0.8Co4Sb11Sn) all show a sharp peak in the vibrational density of states at 57+/-2 K, which is absent in the unfilled skutterudite CoSb3. Heat capacity measurements on Tl0.8Co4Sb11Sn as compared to CoSb3 are consistent with the presence of a localized vibrational mode associated with the "rattling" thallium atoms in this filled skutterudite compound. Both results are well described by a localized Einstein mode model with an Einstein temperature Theta(E) of 53+/-1 K. These data provide perhaps the clearest example of local mode behavior in a concentrated metallic system.

An introduction to the theory of local mode vibrations

A description is given of highly excited rotational and/or vibrational states of molecules in terms of localized vibrations or local modes. It is a didactic paper, making an attempt to unify the ideas and notations of the key publications on the subject in a manner that treats the vibrational and rotational motions equally and that demonstrates the importance of molecular symmetry. Emphasis is put on explaining the intimate relationship between local mode vibrations and the formation of both vibrational and rovibrational energy level clusters. In rovibrational cluster states, a molecule can sustain localized vibrations for very many vibrational periods, even with low vibrational excitation. Local mode behaviour is induced by both vibrational and rotational excitation. An important application of local mode theory is the derivation of relations between the effective rotation-vibration parameters for highly excited vibrational states of a molecule. It is shown here, using the H2 80Se molecule as example, that such relations are valid only for certain forms of the effective rotation-vibration Hamiltonian. Thus caution is required when the results of fittings to spectral data are compared with local mode theory.

Local mode behavior in quasi-1D CDW systems

We analyze numerically the ground-state and spectral properties of the three-quarter filled Peierls–Hubbard Hamiltonian. Various charge- and spin-ordered states are identified. In the strong-coupling regime, we find clear signatures of local lattice distortions accompanied by intrinsic multi-phonon localization. The results are discussed in relation to recent experiments on MX chain [-PtCl-] complexes. In particular we are able to reproduce the observed red shift of the overtone resonance Raman spectrum.

Local mode behavior in the acetylene bending system

The bending eigenfunctions of the acetylene X̃1Σg+ state, as represented by our recently reported effective Hamiltonian [J. Chem. Phys. 109, 121 (1998)], are analyzed up to Evib=15 000 cm−1. A transition from normal to local mode behavior is observed around 8000–10 000 cm−1, such that above these energies, the eigenstates are better described in terms of local mode quantum numbers. The local mode behavior in the bend degrees of freedom of acetylene that is described here is in many ways analogous to the local mode behavior that has been observed in the stretching degrees of freedom of many ABA molecules. However, the local mode behavior in the acetylene bend degrees of freedom, because it involves two two-dimensional rather than two one-dimensional vibrational modes, encompasses a richer range of motions. Specifically, in the “local” limit, the bending eigenfunctions are describable in terms of a continuum of motions ranging from local bend (one hydrogen bending) to counter-rotation (the two hydrogens executing rotations in opposite directions).

The First Si–H Stretching Overtone of H3SiD: Emergence of Local Mode Effects

The FTIR spectrum of H3SiD in the 4100–4500-cm−1region was recorded at Doppler-limited resolution, and four bands were studied. At lower wavenumbers, two strong bands, which in the local mode picture can be assigned to (200,E) (ν0= 4308.5667 cm−1) and (200,A1) (ν0= 4307.8441 cm−1), were analyzed, and at higher wavenumbers, two weaker bands, namely (110,E) at 4378.1950 cm−1and (110,A1) at 4375.9763 cm−1, were analyzed. A total number of ∼1900 lines in the strong dyad and 1000 lines in the weak one were assigned and fitted with standard deviations of the residuals ≈0.0008 cm−1. The strong system (200) is close to local mode behavior, with nox,yCoriolis term needed and only a smallzCoriolis term, and simple arithmetic relations between vibration–rotation parameters are fulfilled as expected. The local mode behavior of the weak system (110) is less pronounced, butzandx,yCoriolis effects are smaller than in the Si–H stretching fundamentals. Comparison of computed and observed spectra provided a good estimate for the ratios of transition moments of the different bands: they are, in absolute value, proportional to 3.5:1.75:1:1 for (200,E), (200,A1), (110,E), and (110,A1), respectively.

Rotational Analysis of thev= 6, 7, and 8 GeH Stretching Overtone Bands of H370GeD

Thev(GeH) = 6, 7, and 8 overtones of monoisotopic H370GeD have been studied by ICLAS with effective optical path lengths between 9 and 40.8 km at a resolution of ca. 0.05 cm−1. Rotational structure was resolved and assigned (in the local mode notation) to the (600), 11649.77 cm−1, (700), 13353.72 cm−1, and (800), 14985.25 cm−1, levels. The observed transitions were fitted to a local mode model with five refined parameters. No Coriolis effects were revealed, and local mode constraints between the off-diagonal and most of the diagonal matrix elements were used. The rms deviation of the fits was ca. 0.04 cm−1, with some obviously perturbed highJandKlevels excluded. When compared with previous studies of the (200) and (300) vibrational levels it is concluded that the (n00) levels of H3GeD essentially reveal local mode behavior forn≥ 3.

High Resolution FTIR Study of the First GeH Stretching Overtone Band of H370GeD

The IR spectrum of monoisotopic H370GeD has been recorded in the region of the first GeH stretching overtone near 4200 cm−1. Three bands have been observed and assigned in the local mode model to (200A1) 4154.139 cm−1, (200E) 4154.366 cm−1, and (110E) 4223.07 cm−1. The low-Ksublevels of the (200A1/E) states are unperturbed. The analysis of the rotational structure, σ(fit) = 4.3 × 10−4cm−1, reveals closeness to local mode behavior although this is less pronounced than for the (300A1/E) levels. Perturbations by unknown dark states affect both the (110E) level and the (210E, 1) level at 6265.56 cm−1that was also analyzed, and Coriolis effects were found to be present here.

Algebraic approach to vibrationally highly excited states of SO 2. Vibrational wavefunctions from spectroscopy

A total of 311 vibrational level energies of SO 2 in the electronic ground state obtained from dispersed fluorescence spectroscopy are fitted to the algebraic Hamiltonian expansion and Dunham-type expansion. A comparison of the results of the numerical fits up to 20407 cm −1 shows that the algebraic approach developed by Iachello, Levine and co-workers is more appropriate than the Dunham-type expansion for describing vibrational level energies in a wide energy range covering the vibrationally highly excited region. It is demonstrated that the vibrational wavefunctions can be constructed directly from the algebraic fit to the experimental data, and that the characteristic bifurcation of the vibrational wavefunctions is identified in the excitation of the symmetric stretching mode. This bifurcation is interpreted as a transition from normal-mode to local-mode behavior on the basis of finding a local-mode doublet representing the vibrational energy flow between the two SO bonds.

SiH stretching frequencies in chlorodisilanes and ab initio calculations of geometry, stretching frequency, vibrational intensity and Mulliken and King effective atomic charges

Infrared frequencies in the νSiH region observed in mixtures of chlorodisilanes are assigned by the joint use of substituent effects, determined earlier in Si 2H 5Cl and 1,1-Si 2H 4Cl 2, and ab initio calculations for 1,2-Si 2H 4Cl 2, 1,1,2-Si 2H 3Cl 3 and SiH 3SiCl 3, which together with 1,1,2,2-Si 2H 2Cl 4 were identified as being present. νSiH frequencies for all the staggered conformers are predicted using harmonic local mode theory. Ab initio geometries were obtained for the above three compounds at the HF 6–31 G ∗ level, and for both conformers of 1,2-Si 2H 4Cl 2 at HF tzvp and MP2 tzvp levels. Alpha or gauche chlorine substitution shortens both SiH and SiCl bonds, the former reflecting νSiH changes. Trans chlorine substitution shortens SiCl bonds slightly, but has no effect on SiH bonds. The local mode behaviour of νSiH vibrations extends to both infrared and Raman intensities. Ab initio-based atomic polar tensors are used to obtain dipole derivatives, dμ dr , for the SiH and SiCl bonds and King effective atomic charges, ξ, for all atoms. The changes in the latter are compared with changes in the Mulliken atomic charges and a close connection is found in the case of gauche chlorine substitution.

FTIR study of the second stretching vibrational overtone system of H3 70GeD: example of an almost asymmetric rotor band

The FTIR spectrum of monoisotopic H3 70GeD around 6100 cm-1 was recorded with a resolution of about 0·012 cm-1. A perpendicular-type band, v 0(E) = 6129·441 cm-1, is observed, which is unperturbed for K′ ⩽ 1>2. Its rotational analysis reveals, in addition to rovibrational r and q resonance effects within the E vibrational state, a strong rovibrational α resonance perturbation by an almost degenerate perturber of A1 symmetry, v 0 = 6129·434 cm-1. Owing to intensity perturbations the parallel component is very weak in spite of a transition moment ratio M(E)/M(A1) of about -2. The rovibrational energy level pattern is indicative of local mode behaviour of the v (GeH) = 3 state, in which Coriolis effects are almost absent and simple arithmetic relations between vibration-rotation parameters fulfilled as expected. This gives rise to an excited state energy level pattern almost consistent with that of an asymmetric rotor.

Diode Laser Spectroscopy of H 232S Around 0.82 μm

The absorption spectrum of H 2S has been investigated in the range 11 930-12 300 cm −1 by means of an externally frequency modulated tunable diode laser and a multipath absorption cell. Approximately 290 lines have been assigned to rovibrational transitions of the 3ν 1 + 2ν 3 and 2ν 1 + 3ν 3 bands which are in strong interaction. The rotational structure of the corresponding excited vibrational states has been satisfactorily reproduced using a Hamiltonian model which takes explicitly into account the strong Coriolis interaction coupling the levels of (302) with those of (203), as well as weaker anharmonic and Coriolis-type interactions between the levels of (302) and (203) and those of (222) and (321). Precise band centers and rotational and coupling constants have been derived and the local mode behavior of the energy levels was clearly observed.

JET relevance to ITER, new trends and initial results

Critical ITER physics requirements and R&D issues are considered and, the relevance and capability of JET in investigating these issues are discussed. In particular, JET gives its highest priority to a coherent programme in support of the design of an ITER divertor operating in a regime consistent with a small scrape-off length. JET intends to perform critical tests of such divertor regimes in D-T plasmas. Initial results from JET after its extensive modifications are presented. These show that the new divertor in JET has good power-handling capability and that carbon blooms, which often plagued the earlier campaign of high performance, have not yet been observed. Good progress in divertor characterization and, in achieving the H and VH modes and full lower hybrid non-inductive current drive has been made. Also, valuable insight into edge localized mode behaviour and their occurrence is being gained.

CH stretching local mode behavior in alkanes: A global analysis of mono- and fully hydrogenated ethanes, propanes, and butanes up to 6 quanta of CH stretching

Existing vibrational data for monohydrogenated C2 to C4 alkanes up to 4 quanta in CH stretching, and data at 6 quanta of excitation in the fully hydrogenated species, are combined in this study, along with CH deformation overtones and CD2 (or CD) stretching fundamentals, to enable a global local mode refinement of CH stretching to be made, to include the effects of both Fermi resonance and interbond coupling effects. Refinement to data over 14 isotopic ethanes, propanes and isobutanes is achieved in terms of consistent CH stretching vibration and anharmonicity parameters and stretch–bend resonance parameters. Data available on n-butanes fully support the findings. CH stretching vibration wave numbers correlate very closely with the structural characteristics in CH3, CH2, and CH groups. The associated CH stretching anharmonicities, however, are found to correlate with the type of CH bond present, primary (−59.6 cm−1), secondary (−62.1 cm−1), or tertiary (−64.5 cm−1), rather than with the individual CH stretching vibration wave numbers, as previously thought. A vibrational dependence of the Fermi resonance parameter is required to reproduce the isolated CH stretching manifolds of CH(CD3)3 and CH(CH3)3 up to 6 quanta in CH stretching.

HIGH RESOLUTION SPECTROSCOPIC STUDY OF THE LOCAL MODE VIBRATIONAL STATES OF SILANE

The stretching vibrational overtone bands (3000), (4000) and (5000) of silane are recorded on a Fourier transform spectrometer with a specially made multipass cell at a resolution of 0.01 cm-1. The spectra show a striking symmetrical top rotational structure, which has been predicted as the limiting case of a spherical top exhibiting local mode behavior, and provides an excellent chance to study the local mode rotational structures in detail. This article reviews the interpretation and analysis of the spectra in both local mode and normal mode pictures. The intramolecular dynamics following initial single bond excitation is also discussed.

Does Quantum Mechanics Select Out Regularity and Local Mode Behaviour in Nonlinearly Coupled Vibrational Systems?

AbstractA two dimensional strongly nonharmonic vibrational system with nonlinear intermode coupling is studied both classically and quantum mechanically. The system was chosen such that there is a low lying transition (in energy) from a region where almost all trajectories move regularly to a region where chaotic dynamics strongly dominates. The corresponding quantum system is far away from the semiclassical limit. The eigenfunctions are calculated with high precision according to a linear variational scheme using conveniently chosen basis functions. It is the aim of this paper to check whether the prediction from semiclassical theory, namely that the measure of classically chaotic trajectories in phase space approaches the measure of irregular states in corresponding energy ranges, holds when the system is not close to the classical limit. It is also the aim to identify individual eigenfunctions with respect to regularity and to differentiate between local and normal vibrational states. It is found that there are quantitative and also qualitative differences between the quantum results and the semiclassical predictions. We found a relatively high amount of regularity in the quantum system for energies where almost all classical trajectories move chaotically. This high regularity is manifested via level spacing statistics as well as by a careful study of the nodal behaviour of the eigenfunctions. Another result was not expected from semiclassical predictions: Some of the wave functions are localized and irregular, a behaviour which was not observed in the corresponding classical system.

ChemInform Abstract: Vibrational Anharmonicity, Fermi Resonance Interactions, and Local Mode Behavior in CH3Cl.

ChemInformVolume 21, Issue 27 Physical Organic Chemistry ChemInform Abstract: Vibrational Anharmonicity, Fermi Resonance Interactions, and Local Mode Behavior in CH3Cl. J. L. DUNCAN, J. L. DUNCAN Dep. Chem., Univ. Aberdeen, Meston Walk, Old Aberdeen AB9 2UE, UKSearch for more papers by this authorM. M. LAW, M. M. LAW Dep. Chem., Univ. Aberdeen, Meston Walk, Old Aberdeen AB9 2UE, UKSearch for more papers by this author J. L. DUNCAN, J. L. DUNCAN Dep. Chem., Univ. Aberdeen, Meston Walk, Old Aberdeen AB9 2UE, UKSearch for more papers by this authorM. M. LAW, M. M. LAW Dep. Chem., Univ. Aberdeen, Meston Walk, Old Aberdeen AB9 2UE, UKSearch for more papers by this author First published: July 3, 1990 https://doi.org/10.1002/chin.199027038AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume21, Issue27July 3, 1990 RelatedInformation

A study of vibrational anharmonicity, fermi resonance interactions, and local mode behavior in CH 3Cl

The infrared spectrum of CH 3Cl has been studied up to 16 500 cm −1 and vibrational assignments made for up to six quanta of excitation in CH stretching. Analysis of a total of 66 vibrational levels has been made in terms of a joint local mode and normal mode model, local with respect to CH stretching vibrations and normal with respect to other vibrations. Fermi resonance interactions with CH 3 deformation overtones must be included in the analysis. Reproduction of the observed vibration levels with a rms error of 2.61 cm −1 is achieved in terms of a 37-parameter model, with the four anharmonicity constants and two Darling-Dennison constants associated with CH 3 group stretchings constrained to be interrelated through local mode relations. The parameters obtained are in excellent accord with those available for the other methyl halides, and with established structural differences between the molecules.

A local mode analysis of the stretching mode spectra of liquid H 2O and D 2O in the temperature range 4 ⪢2- 200 °C

A harmonically coupled non-symmetric (r 1 ≠ r 2) anharmonic oscillator model has been used to compute the stretching mode spectra of liquid H 2O and D 2O. The effect of anharmonicity, intra- and intermolecular coupling on the band shape has been investigated by using only the two stretching coordinates. Molecular interaction are described by the Lippincott-Schroeder potential function for bent hydrogen bonded systems. A quantum local mode analysis of the random molecule configurations is used to compute the eigenstates. Local mode behaviour and oscillator non-similarity produced decoupling for H 2O the latter manifesting itself in the appearance of a high frequency shoulder at 4 °C and at 50 °C. In contrast the normal mode picture of D 2O causes a high frequency splitting at 150 °C and 200 °C beacuse of coupling between similar oscillators.