Frequency, characteristic

In general, each nomial mode in a molecule has its own frequency, which is detemiined in the nonnal mode analysis [24]- Flowever, this is subject to the constraints imposed by molecular synmietry [18, 25, 26]. For example, in the methane molecule CFI, four of the nonnal modes can essentially be designated as nonnal stretch modes, i.e. consisting primarily of collective motions built from the four C-FI bond displacements. The molecule has tetrahedral synmietry, and this constrains the stretch nonnal mode frequencies. One mode is the totally symmetric stretch, with its own characteristic frequency. The other tliree stretch nonnal modes are all constrained by synmietry to have the same frequency, and are refened to as being triply-degenerate. 

Ultrafast TRCD has also been measured in chemical systems by incoriDorating a PEM into the probe beam optics of a picosecond laser pump-probe absorjDtion apparatus [35]. The PEM resonant frequency is very low (1 kHz) in these experiments, compared with the characteristic frequencies of ultrafast processes and so does not interfere with the detection of ultrafast CD changes. 

D. Lin-Vien, N.B. Colthup, W.G. Fately, J. G. Grasselli, Infrared and Raman Characteristic Frequencies of Organic Molecules, Academic Press, New York, 1991. 

M. E. Elyashberg, Infrared spectra interpretation by the characteristic frequency approach, in The Encyclopedia of Computational Chemistry,... 

Molecular vibrations are the basis of infrared (IR) spectroscopy Certain groups of atoms vibrate at characteristic frequencies and these frequencies can be used to detect the pres ence of these groups in a molecule... 

Conceptually, the problem of going from the time domain spectra in Figures 3.7(a)-3.9(a) to the frequency domain spectra in Figures 3.7(b)-3.9(b) is straightforward, at least in these cases because we knew the result before we started. Nevertheless, we can still visualize the breaking down of any time domain spectrum, however complex and irregular in appearance, into its component waves, each with its characteristic frequency and amplitude. Although we can visualize it, the process of Fourier transformation which actually carries it out is a mathematically complex operation. The mathematical principles will be discussed only briefly here. 

The primary characteristic frequency of an ordinary gas is the rate of coUision f = V/X = ttVnD, where V is the mean particle velocity, and V = [SkT for particles of mass m. Among the special frequencies associated with plasmas, the most notable is the plasma frequency ... 

Radiometry. Radiometry is the measurement of radiant electromagnetic energy (17,18,134), considered herein to be the direct detection and spectroscopic analysis of ambient thermal emission, as distinguished from techniques in which the sample is actively probed. At any temperature above absolute zero, some molecules are in thermally populated excited levels, and transitions from these to the ground state radiate energy at characteristic frequencies. Erom Wien s displacement law, T = 2898 //m-K, the emission maximum at 300 K is near 10 fim in the mid-ir. This radiation occurs at just the energies of molecular rovibrational transitions, so thermal emission carries much the same information as an ir absorption spectmm. Detection of the emissions of remote thermal sources is the ultimate passive and noninvasive technique, requiring not even an optical probe of the sampled volume. 

Ap Frictional pressure drop Pa CO Characteristic frequency or reciprocal time scale of flow 1/s... 

Since the calculation of multidimensional PES is a very difficult task, in most cases the choice of the internal PES coordinates is based on models, which take into account the information about the structure, barrier height and characteristic frequencies of the reaction complex and... 

At low frequencies when power losses are low these values are also low but they increase when such frequencies are reached that the dipoles cannot keep in phase. After passing through a peak at some characteristic frequency they fall in value as the frequency further increases. This is because at such high frequencies there is no time for substantial dipole movement and so the power losses are reduced. Because of the dependence of the dipole movement on the internal viscosity, the power factor like the dielectric constant, is strongly dependent on temperature. 

Spectrometers are designed to measure the absorption of electromagnetic radiation by a sample. Basically, a spectrometer consists of a source of radiation, a compartment containing the sfflnple through which the radiation passes, and a detector. The frequency of radiation is continuously varied, and its intensity at the detector is compar ed with that at the source. When the frequency is reached at which the sample absorbs radiation, the detector senses a decrease in intensity. The relation between frequency and absorption is plotted as a spectrum, which consists of a series of peaks at characteristic frequencies. Its interpretation can furnish structural information. Each type of spectroscopy developed independently of the others, and so the data format is different for each one. An NMR spectrum looks different from an IR spectrum, and both look different from a UV-VIS spectrum. 

Section 13.20 IR spectroscopy probes molecular- structure by examining transitions between vibrational energy levels using electromagnetic radiation in the 625-4000-cm range. The presence or absence of a peak at a characteristic frequency tells us whether a certain functional group is present. Table 13.4 lists IR absorption frequencies for common structural units. 

Ultrasonic absorption is a so-called stationary method in which a periodic forcing function is used. The forcing function in this case is a sound wave of known frequency. Such a wave propagating through a medium creates a periodically varying pressure difference. (It may also produce a periodic temperature difference.) Now suppose that the system contains a chemical equilibrium that can respond to pressure differences [as a consequence of Eq. (4-28)]. If the sound wave frequency is much lower than I/t, the characteristic frequency of the chemical relaxation (t is the... 

Molecules vibrate at characteristic frequencies, which depend both on the difficulty of the motion (the so-called force constant) and on the masses of the atoms involved. The more difficult the motion and the lighter the atomic masses, the higher the vibrational frequency. For a diatomic molecule the vibrational frequency is proportional to ... 

Parameters of IR spectra (in solutions, films, or KBr) of acetylenylpyrazoles are close to those in the arylacetylene series. The values of the characteristic frequencies of the stretching vibrations of a disubstituted triple bond are in the... 

The splitting of both groups (visible and UV regions) is related to a vibrational structure of electron transitions (characteristic frequencies being... 

The IR spectra of isoxazole derivatives have been extensively investigated. " The most exhaustive and precise data, including both the characteristic frequencies and intensities, were reported by Katritzky and Boulton " for isoxazole and its homologs, aryl- and alkoxy-isoxazoles, acids, and some other derivatives. 

Calling ui = 1/A the characteristic frequency of the quantum CA, the general conservation law that holds for QCA-I systems may then be written as... 

Metal oxidizers contribute their energy in the form of spectral emission at characteristic frequencies. The human eye has the greatest sensitivity to the Na emission. For this reason, Mg-Na nitrate flares are selected as the best intensity light source... 

Pulsed deuteron NMR is described, which has recently been developed to become a powerftd tool for studying molectdar order and dynamics in solid polymers. In drawn fibres the complete orientational distribution function for the polymer chains can be determined from the analysis of deuteron NMR line shapes. By analyzing the line shapes of 2H absorption spectra and spectra obtained via solid echo and spin alignment, respectively, both type and timescale of rotational motions can be determined over an extraordinary wide range of characteristic frequencies, approximately 10 MHz to 1 Hz. In addition, motional heterogeneities can be detected and the resulting distribution of correlation times can directly be determined. 

Except in simple cases, it is very difficult to predict the infrared absorption spectrum of a polyatomic molecule, because each of the modes has its characteristic absorption frequency rather than just the single frequency of a diatomic molecule. However, certain groups, such as a benzene ring or a carbonyl group, have characteristic frequencies, and their presence can often be detected in a spectrum. Thus, an infrared spectrum can be used to identify the species present in a sample by looking for the characteristic absorption bands associated with various groups. An example and its analysis is shown in Fig. 3. 

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