Transition frequency shift

The origin of the rotational structure of the isotropic Q-branch (Av = 0, Aj = 0) is connected with the dependence of the vibrational transition frequency shift on rotational quantum number j [121, 126]... 

Porsev, S.G., Koshelev, K.V, Tupitsyn, I.I., Kozlov, M.G., Reimers, D., and Levshakov, S.A., Transition frequency shifts with fine structure constant variation for Fe II Breit and core-valence correlation correction, Phys. Rev. A, 76, 052507, 2007, arXiv 0708.1662. 

Ultrasonic Flow Meters. Ultrasonic flow meters can be divided into three broad groups passive or turbulent noise flow meters, Doppler or frequency-shift flow meters, and transit time flow meters. 

Molecules vibrate at fundamental frequencies that are usually in the mid-infrared. Some overtone and combination transitions occur at shorter wavelengths. Because infrared photons have enough energy to excite rotational motions also, the ir spectmm of a gas consists of rovibrational bands in which each vibrational transition is accompanied by numerous simultaneous rotational transitions. In condensed phases the rotational stmcture is suppressed, but the vibrational frequencies remain highly specific, and information on the molecular environment can often be deduced from hnewidths, frequency shifts, and additional spectral stmcture owing to phonon (thermal acoustic mode) and lattice effects. 

Here te, tc are the correlation times of rotational and vibrational frequency shifts. The isotropic scattering spectrum corresponding to Eq. (3.15) is the Lorentzian line of width Acoi/2 = w0 + ydp- Its maximum is shifted from the vibrational transition frequency by the quantity coq due to the collapse of rotational structure and by the quantity A due to the displacement of the vibrational levels in a medium. 

Rhombohedral Se was found as a high-pressure allotrope of sulfur above 9-10 GPa by several groups [58, 137, 150, 184, 186, 188, 191]. The pressure dependence of frequencies [137, 150, 184] as well as the kinetics of the transition from p-S to Ss [186] have been investigated systematically by Raman spectroscopy. The pressure dependent frequency shifts of chemically prepared Ss and of high-pressure Ss have been found to be identical [137, 150]. 

According to the quantum transition state theory [108], and ignoring damping, at a temperature T h(S) /Inks — a/ i )To/2n, the wall motion will typically be classically activated. This temperature lies within the plateau in thermal conductivity [19]. This estimate will be lowered if damping, which becomes considerable also at these temperatures, is included in the treatment. Indeed, as shown later in this section, interaction with phonons results in the usual phenomena of frequency shift and level broadening in an internal resonance. Also, activated motion necessarily implies that the system is multilevel. While a complete characterization of all the states does not seem realistic at present, we can extract at least the spectrum of their important subset, namely, those that correspond to the vibrational excitations of the mosaic, whose spectraFspatial density will turn out to be sufficiently high to account for the existence of the boson peak. 

A transition linearly coupled to the phonon field gradient will experience, from the perturbation theory perspective, a frequency shift and a drag force owing to phonon emission/absorption. Here we resort to the simplest way to model these effects by assuming that our degree of freedom behaves like a localized boson with frequency (s>i. The corresponding Hamiltonian reads... 

Figure 12.12 Kinetics of the (2 x 2) —3CO - ( /l9 xvT9)R23.4° — 13CO phase transition on a Pt( 111) electrode in a CO-saturated 0.1M H2SO4 electrolyte, observed via SFG of atop CO. The frequency shift data in (b) and (e) indicate that a new potential is estabhshed on the electrode within 0.2 s. The forward transformation is much slower than the reverse. There are minimal differences between the first and second cycles, indicating minimal change in electrolyte composition during kinetic measurements.

When propylene chemisorbs to form this symmetric allylic species, the double-bond frequency occurs at 1545 cm-1, a value 107 cm-1 lower than that found for gaseous propylene hence, by the usual criteria, the propylene is 7r-bonded to the surface. For such a surface ir-allyl there should be gross similarities to known ir-allyl complexes of transition metals. Data for allyl complexes of manganese carbonyls (SI) show that for the cr-allyl species the double-bond frequency occurs at about 1620 cm-1 formation of the x-allyl species causes a much larger double-bond frequency shift to 1505 cm-1. The shift observed for adsorbed propylene is far too large to involve a simple o--complex, but is somewhat less than that observed for transition metal r-allyls. Since simple -complexes show a correlation of bond strength to double-bond frequency shift, it seems reasonable to suppose that the smaller shift observed for surface x-allyls implies a weaker bonding than that found for transition metal complexes. 

In summary, NMR techniques based upon chemical shifts and dipolar or scalar couplings of spin-1/2 nuclei can provide structural information about bonding environments in semiconductor alloys, and more specifically the extent to which substitutions are completely random, partially or fully-ordered, or even bimodal. Semiconductor alloys containing magnetic ions, typically transition metal ions, have also been studied by spin-1/2 NMR here the often-large frequency shifts are due to the electron hyperfine interaction, and so examples of such studies will be discussed in Sect. 3.5. For alloys containing only quadrupolar nuclei as NMR probes, such as many of the III-V compounds, the nuclear quadrupole interaction will play an important and often dominant role, and can be used to investigate alloy disorder (Sect. 3.8). 

In the imido systems the n n transition is shifted to lower energy (518 nm) and markedly decreases in intensity. On the other hand, upon substitution of the anionic trans-ligands by acetonitrile the n->-n transition is found at 450 nm, shifting to 525 nm upon protonation. Moreover, the metal-N(nitrido) stretching frequency increases to 1016 cm From a chemical viewpoint it is important that the nitrido-nitrile complex can be... 

In general, though, Raman spectroscopy is concerned with vibrational transitions (in a manner akin to infrared spectroscopy), since shifts of these Raman bands can be related to molecular structure and geometry. Because the energies of Raman frequency shifts are associated with transitions between different rotational and vibrational quantum states, Raman frequencies are equivalent to infrared frequencies within the molecule causing the scattering. 

In transition metal complexes, proton hfs are normally < 20 MHz so that the corresponding second order contributions, which amount to < 10 kHz, may usually be neglected. For nitrogen ligands, however, the second order corrections produce frequency shifts up to 200 kHz. Since hf interactions of central ions can amount to several hundred megacycles, the terms in AE become very important for a correct description of the ENDOR spectra. 

If two magnetically nonequivalent nuclei I and K are present in the spin system, the transition frequency of nucleus I is shifted by an additional second order term48 55)... 

The hfs and quadrupole tensors of one of the nitrogen ligands have been determined with ENDOR by Calvo et al.63). The 14N-ENDOR transition frequencies observed between 11 and 23 MHz were found to depend significantly on the nuclear quantum number mCu of the EPR observer line. These shifts are due to Cu-N crossterms (Sect. 3.2) and amount to more than 1 MHz for certain orientations of B0. ENDOR resonances of... 

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