Frequency shifts, vibrational spectra

The crystallographic study of the potassium salt is complicated by disorder but in CsOs03N Os=N is 1.676 A and Os=0 1.739-1.741 A. Assignments of the vibrational spectrum of Os03N is assisted by isotopic substitution the higher frequency absorption is shifted significantly on 15N substitution whereas the band just below 900 cm-1 is scarcely affected (Table 1.7) conversely the latter band is shifted by some 50 cm-1 on replacing l60 by l80 [56], Nitrido salts are discussed later (section 1.12.2). 

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. 

It should be noted that there is a considerable difference between rotational structure narrowing caused by pressure and that caused by motional averaging of an adiabatically broadened spectrum [158, 159]. In the limiting case of fast motion, both of them are described by perturbation theory, thus, both widths in Eq. (3.16) and Eq (3.17) are expressed as a product of the frequency dispersion and the correlation time. However, the dispersion of the rotational structure (3.7) defined by intramolecular interaction is independent of the medium density, while the dispersion of the vibrational frequency shift (5 12) in (3.21) is linear in gas density. In principle, correlation times of the frequency modulation are also different. In the first case, it is the free rotation time te that is reduced as the medium density increases, and in the second case, it is the time of collision tc p/ v) that remains unchanged. As the density increases, the rotational contribution to the width decreases due to the reduction of t , while the vibrational contribution increases due to the dispersion growth. In nitrogen, they are of comparable magnitude after the initial (static) spectrum has become ten times narrower. At 77 K the rotational relaxation contribution is no less than 20% of the observed Q-branch width. If the rest of the contribution is entirely determined by... 

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. 

The entropy difference A5tot between the HS and the LS states of an iron(II) SCO complex is the driving force for thermally induced spin transition [97], About one quarter of AStot is due to the multiplicity of the HS state, whereas the remaining three quarters are due to a shift of vibrational frequencies upon SCO. The part that arises from the spin multiplicity can easily be calculated. However, the vibrational contribution AS ib is less readily accessible, either experimentally or theoretically, because the vibrational spectrum of a SCO complex, such as [Fe(phen)2(NCS)2] (with 147 normal modes for the free molecule) is rather complex. Therefore, a reasonably complete assignment of modes can be achieved only by a combination of complementary spectroscopic techniques in conjunction with appropriate calculations. 

A small fraction of the molecules are in vibrationally excited states. Raman scattering from vibrationally excited molecules leaves the molecule in the ground state. The scattered photon appears at higher energy, as shown in Figure lb. This anti-Stokes-shifted Raman spectrum is always weaker than the Stokes-shifted spectrum, but at room temperature it is strong enough to be useful for vibrational frequencies less than about 1500 cm 1. The Stokes and anti-Stokes spectra contain the same frequency information. 

The vibrational spectrum of methylguanine-methylcytosine (GC) complex consists of 99 normal modes frequencies. Differently from the AT base pair, in the GC complex the normal modes of the two bases are coupled together, thus an analysis of the shift relatively to the isolated bases is extremely complicated. This stronger coupling can possibly he ascribed to the presence of three h-bonds, rather than two as in AT. However, we tentatively discuss some significant shifts. 

Crystallinity In crystallization of polymers, the polymer forms crystalline and amorphous regions [2,4,25]. The formation of crystalline regions is accompanied by an increase in new vibrational modes caused by their crystal lattice interactions [2]. The IR spectrum of a given polymer differs by various absorption bands, depending on whether it is in the amorphous or crystalline state [2]. The IR spectrum exhibits regularity bands, splitting, and frequency shifts. Other absorption bands are not affected by crystallization and remain the same in both cases. Crystalline and amorphous bands can be used in the determination of the degree of crystallinity independent bands are useful for the determination of sample thickness [2],... 

The complexity of the physical properties of liquid water is largely determined by the presence of a three-dimensional hydrogen bond (HB) network [1]. The HB s undergo continuous transformations that occur on ultrafast timescales. The molecular vibrations are especially sensitive to the presence of the HB network. For example, the spectrum of the OH-stretch vibrational mode is substantially broadened and shifted towards lower frequencies if the OH-group is involved in the HB. Therefore, the microscopic structure and the dynamics of water are expected to manifest themselves in the IR vibrational spectrum, and, therefore, can be studied by methods of ultrafast infrared spectroscopy. It has been shown in a number of ultrafast spectroscopic experiments and computer simulations that dephasing dynamics of the OH-stretch vibrations of water molecules in the liquid phase occurs on sub-picosecond timescales [2-14],... 

Kaupert, Heydtmann and Thiel"2 calculated the vibrational spectrum of monohalo-genated 1 at the HF level using the 6-31 G(d) basis set and effective core potentials with DZ + P basis sets for Cl, Br and I. Reduction from Z)3h to Cs symmetry leads to considerable coupling between modes (exceptions C—H stretching and CH2-deformation modes) of 1. Vibrational frequencies that are influenced by the halogen substituent are shifted to lower values with increasing mass of the halogen. 

For most purposes only the Stokes-shifted Raman spectrum, which results from molecules in the ground electronic and vibrational states being excited, is measured and reported. Anti-Stokes spectra arise from molecules in vibrational excited states returning to the ground state. The relative intensities of the Stokes and anti-Stokes bands are proportional to the relative populations of the ground and excited vibrational states. These proportions are temperature-dependent and follow a Boltzmann distribution. At room temperature, the anti-Stokes Stokes intensity ratio decreases by a factor of 10 with each 480 cm-1 from the exciting frequency. Because of the weakness of the anti-Stokes spectrum (except at low frequency shift), the most important use of this spectmm is for optical temperature measurement (qv) using the Boltzmann distribution function. 

As seen above, IR spectroscopy is most commonly used to identify functional groups and bonding patterns in molecules from the higher energy portion of the spectrum (1200-4000 cm ) where absorptions are primarily due to bondstretching vibrations. Some information on atom connectivity in the molecule can also be deduced from the frequency shifts caused by structural factors. In general, however, it is not possible to completely deduce the structure of a molecule by examination of its IR spectrum. However, IR spectroscopy is a powerful complement to NMR spectroscopy for structure determination. 

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