Characteristic vibration

Since the stochastic Langevin force mimics collisions among solvent molecules and the biomolecule (the solute), the characteristic vibrational frequencies of a molecule in vacuum are dampened. In particular, the low-frequency vibrational modes are overdamped, and various correlation functions are smoothed (see Case [35] for a review and further references). The magnitude of such disturbances with respect to Newtonian behavior depends on 7, as can be seen from Fig. 8 showing computed spectral densities of the protein BPTI for three 7 values. Overall, this effect can certainly alter the dynamics of a system, and it remains to study these consequences in connection with biomolecular dynamics. 

Other Inorganics. Inorganic species in solution have been studied very effectively by Raman spectroscopy. Work in this area includes the investigation of coordination compounds (qv) of fluorine (qv) (40), the characterization of low dimensional materials (41) and coordinated ligands (42), and single-crystal studies (43). Several compilations of characteristic vibrational frequencies of main-group elements have been pubflshed to aid in the identification of these species (44,45). 

Transition-metal complexes of the thionylimide anion exhibit characteristic vibrations in the regions 1260-1120, 1090-1010 and 630-515 cm , which are assigned to Oas(NSO), Os(NSO) and <5(NSO), respectively. X-ray structural data for several M-NSO complexes reveal N-S and S-O bond lengths of ca. 1.46 0.04 A indicative of double bond character in both of these bonds. 

Eigenschaftswort, n. adjective epithet. Eigenschwingung, /. proper, natural or characteristic vibration. 

Spectroscopic studies have been carried out on a number of benzo-1,2,3,4-tetrazine 1,3-di-iV-oxides 98 and furazanotetrazine 1,3-di-iV-oxide 99 to investigate their characteristic vibration frequencies and electronic parameters <95MC100>. 

Principles and Characteristics Vibrational spectroscopic techniques such as IR and Raman are exquisitely sensitive to molecular structure. These techniques yield incisive results in studies of pure compounds or for rather simple mixtures but are less powerful in the analysis of complex systems. The IR spectrum of a material can be different depending on the state of the molecule (i.e. solid, liquid or gas). In relation to polymer/additive analysis it is convenient to separate discussions on the utility of FUR for indirect analysis of extracts from direct in situ analysis. 

Similar studies have been conducted on poly(vinyl chloride) (PVC) to assign different IR signatures obtained from different stereo-configurational isomers. The sensitivity of the vC-Cl bond on the stereochemical environment has been utilized using IR spectroscopy. The characteristic vibrations of the vC-Cl bonds are inherently tied in to the configuration as well as the conformation of the... 

Figure 10.3 Carbide hardnesses vs. characteristic vibrational energy densities derived from average force constants (entropic specific heat). After Grimvall and Theissen (1986). The crystal structures are of the NaCi type. The hardness data are fromTeter (1998).

To rationalize the units, g is divided by the lattice parameter, a of each carbide. The final parameter (g /a) = characteristic vibrational energy density has the units of energy per volume (GPa) which is the same as the hardness units. The correlation of this with hardness is shown in Figure 10.3. The correlation is good especially when it is considered that the hardness numbers for carbides scatter as much as 30 percent. 

Diatomic Molecules. Polyatomic Molecules. Characteristic Vibration Frequencies. Factors Affecting Group Frequencies. 

The occurrence of characteristic vibration or group frequencies can be explained in terms of relative masses and of force constants using the classical analogy of weights and springs as depicted in Figure 9.14. 

Even though the Einstein and Debye models are not exact, these simple one-parameter models illustrate the properties of crystals and should give reliable estimates of the volume dependence of the vibrational entropy [15]. The entropy is given by the characteristic vibrational frequency and is thus related to some kind of mean interatomic distance or simpler, the volume of a compound. If the unit cell volume is expanded, the average interatomic distance becomes larger and the... 

Electrons excite characteristic vibrations in the sample, and these can be studied by analyzing the energy loss suffered by the primary electrons (see Chapter 8 on vibrational spectroscopy). 

Measurements of supported catalysts in diffuse reflection and transmission mode are in practice limited to frequencies above those where the support absorbs (below about 1250 cm-1). Infrared Emission Spectroscopy (IRES) offers an alternative in this case. When a material is heated to about 100 °C or higher, it emits a spectrum of infrared radiation in which all the characteristic vibrations appear as clearly recognizable peaks. Although measuring in this mode offers the attractive advantage that low frequencies such as those of metal-oxygen or sulfur-sulfur bonds are easily accessible, the technique has hardly been explored for the purpose of catalyst characterization. An in situ cell for IRES measurements and some experiments on Mo-O-S clusters of interest for hydrodesulfurization catalysts have been described by Weber etal. [11],... 

Two such well studied systems are pyridine chemisorbed on alumina (15) and pyridine chemisorbed on silica-alumina (16). It had been previously shown that alumina contains only sites which adsorb pyridine in a Lewis acid-base fashion whereas silica-alumina has both Lewis and Bronsted acid sites. These two different kinds of sites are distinguishable by the characteristic vibrational bands of pyridine adducts at these sites (see Table I). Photoacoustic and transmission results are compared in Table II. Note that the PA signal strength depends on factors such as sample particle size and volumes of solid sample and transducing... 

The tunnel current which flows from one metal to the other when a potential difference is applied across the junction is mainly due to elastic tunneling. However, if the adsorbed molecules on the junction have a characteristic vibrational mode of energy hv, then an inelastic process can occur when ev hv. 

As mentioned in Section 4.2 earlier in this chapter, infrared spectroscopy was used to provide information about the structural units present in UZM-5. The framework IR spectrum of a UZM-5 sample is shown in Figure 4.18. The characteristic vibrational bands for double four-rings (D4R) and pentasil rings (S5) are present. This provided some valuable information about the types of linkage units present and combined with data from other techniques such as XRD and TEM allowed the structure of UZM-5 to be solved. 

On the other hand however, the cluster-anions P7 and Pii are thermally remarkably stable. In the condensed state (in the crystal as well as in melts), the characteristic vibrations can be observed both in i.r. spectra and in Raman spectra upto temperatures of 900 K (25, 26,27). As an example, the Raman spectra of Ha3P7 in Figure 7 clearly show that the typical cluster-vibrations of the P7 -anion are maintained up to the region of the plastic phase, although the absorption bands become increasingly broader and less distinct with temperature. The lattice vibrations at 50-100 cm " behave completely differently. As expected they disappear at the transition to the plastic phase. Completely unexpected however, they remain sharply resolved up to the critical temperature Tc. This effect can be connected with the presence of two undamped lattice modes (25). 

For further investigations f-BuNC, which is isolobal to CO, was used. With PhLi and t-BuLi, the characteristic vibrational mode of the lithium isonitrile adduct (2135 cm ) was observed at a lower wavenumber than that of the free isonitrile (2179 cm ). Unfortunately, n-BuLi did not undergo complexation. As indicated by the C=N stretching vibrational mode at 1510 cm, only f-BuLi—CN—R reacted further to afford the lithiated Schiff base up to —20°C (equation 2) . ... 

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