Local mode frequency

As an introduction to the theory as it relates to these defect complexes, we point out that the most conspicuous experimental feature of a light impurity such as hydrogen is its high local-mode frequency (Cardona, 1983). Therefore, it is essential that the computational scheme produce total energies with respect to atomic coordinates and, in particular, vibrational frequencies, so that contact with experiment can be established. With total-energy capabilities, equilibrium geometries and migration and reorientation barriers can be predicted as well. 

The most commonly accepted model for the hydrogen-acceptor pairs locates H at the BC site (see Fig. 4). This model was originally proposed for the H—B complex on the basis of satisfied bonds to explain the increased resistivity (Pankove et al., 1983), SIMS profiles (Johnson, 1985), and a hydrogen local-mode frequency consistent with a perturbed hydrogen-silicon bond (Pankove et al., 1985 Johnson, 1985 Du et al., 1985). The acceptor deactivation by atomic hydrogen was subsequently observed for Al, Ga, and In acceptors in silicon (Pankove et al., 1984). Hydrogen local-mode vibrations were identified as well for the H—Al and H—Ga complexes (Stavola et al., 1987). The boron vibrational frequency for the H—B pair was first identified by Stutzmann (1987) and Herrero and Stutzmann (1988a). 

Buchanan EG, James WH, Choi SH, Guo L, Gellman SH, Muller CW, Zwier TS (2012) Single-conformation infrared spectra of model peptides in the amide 1 and amide 11 regions experiment-based determination of local mode frequencies and inter-mode coupling. J Chem Phys 137 094301... 

Apart from inversions, there is another way to determine whether or not there is mixing in the Sun. Any spherically symmetric, localized sharp feature or discontinuity in the Sun s internal structure leaves a definite signature on the solar p-mode frequencies. Gough (1990) showed that changes of this type contribute a characteristic oscillatory component to the frequencies z/ / of those modes which penetrate below the localized perturbation. The amplitude of the oscillations increases with increasing severity of the discontinuity, and the wavelength of the oscillation is essentially the acoustic depth of the sharp-feature. Solar modes... 

FREQUENCIES OF THE HYDROGEN LOCAL MODES OF VIBRATION AT 5 K OBSERVED IN BULK III-V MATERIALS. WHEN OBSERVED, THE CORRELATION WITH A DOPANT IS INDICATED. 

FREQUENCIES OF THE LOCAL MODES OF VIBRATION OBSERVED AFTER PROTON OR DEUTERON IMPLANTATION OF III-V COMPOUNDS. THE MEASUREMENT TEMPERATURE AND THE TYPE OF ATOM TO WHICH H (OR d) IS BONDED ARE INDICATED. 

FREQUENCIES OF THE LOCAL MODES OF VIBRATION AT 5 K OF HYDROGEN SATURATING A DANGLING BOND IN A VACANCY IN VARIOUS SEMICONDUCTORS. 

In addition to the effects of motional narrowing, vibrational line shapes for the OH stretch region of water are complicated by intramolecular and intermolecular vibrational coupling. This is because (in a zeroth-order local-mode picture) all OH stretch transition frequencies in the liquid are degenerate, and so the effects of any... 

Herein we present calculations [6] for liquid H20 that are similar in spirit but different in detail from those of Buch [71, 110] and Torii [97]. The MD simulations are of the SPC/E model [135]. Local-mode anharmonic frequencies are generated from our most recent map developed for the H0D/D20 system [98], as are our transition dipoles. The relatively small intramolecular coupling fluctuates with molecular environment, and is determined by a separate map parameterized from ab initio calculations on clusters. The form of the intermolecular couplings is transition dipole, which is tested and parameterized from additional ab initio calculations. The effects of motional narrowing are taken into account approximately with the TAA [99]. 

Child, M. S., and Halonen, L. O. (1984), Overtone Frequencies and Intensities in the Local Mode Picture, Adv. Chem. Phys. 57, 1. 

Besides the peaks of the local proton modes typical for hydrogen bond, a sharp peak at 28 meV was observed in KDP [34] and attracted much attention [34,38,39]. This peak exists in DKDP at somewhat higher frequency its intensity decreases in both crystals and its width decreases upon the transition from the FE to the PE phase, without any softening of its frequency [38]. Hence, it is concluded that this mode is connected with the phase transition dynamics, i.e., coupled to the polarization fluctuations. This mode is not the tunneling mode or any local mode of proton or deuteron, but rather some collective optical mode of the lattice that involves substantial proton or deuteron displacement. It has been suggested [38] that this mode corresponds to the mode that has a peak at about 200 cm (25 meV) in Raman scattering and infrared reflectivity spectra, and that it is coupled to the soft mode and usually... 

In addition, for solid samples or peptides in nonaqueous solvents, the amide II (primarily in-plane NH deformation mixed with C—N stretch, -1500-1530 cm-1) and the amide A (NH stretch, -3300 cm-1 but quite broad) bands are also useful added diagnostics of secondary structure 5,15-17 Due to their relatively broader profiles and complicated by their somewhat weaker intensities, the frequency shifts of these two bands with change in secondary structure are less dramatic than for the amide I yet for oriented samples their polarization properties remain useful 18 Additionally, the amide A and amide II bands are highly sensitive to deuteration effects. Thus, they can be diagnostic of the degree of exchange for a peptide and consequently act as a measure of protected or buried residues as compared to those fully exposed to solvent 9,19,20 Amide A measurements are not useful in aqueous solution due to overlap with very intense water transitions, but amide II measurements can usefully be measured under such conditions 5,19,20 The amide III (opposite-phase NH deformation plus C—N stretch combination) is very weak in the IR and is mixed with other local modes, but has nonetheless been the focus of a few protein-based studies 5,21-26 Finally, other amide modes (IV-VII) have been identified at lower frequencies, but have been the subject of relatively few studies in peptides 5-8,18,27,28 ... 

To answer Prof. Marcus s question, we may therefore conclude that the natural motions of the system are the short-time periodic orbits. Those that arise from the symmetric-stretch bifurcations depend on the frequency ratio local modes in the 1 1 case, 7-shaped orbits at the 3 2 instability, horseshoes at the 2 1 resonances, and so on. 

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