Resonance absorption frequency

The Hammett relation, og(hyjko)= pa, has been applied for many years to substituent eifects on reaction kinetics in solution, and has been particularly successful for reactions of benzene compounds. Attempts have also been made to apply Hammett correlations to other phenomena such as infrared (T. L. Brown, 1960), ultraviolet (Jaffe and Orchin, 1962a) and nuclear magnetic resonance absorption frequencies (Bothner-By and Glick, 1956). 

Equation (2.35), known as the Lorenz-Lorentz relation, provides a method of calculating the molecular polarisability from a macroscopic, observable quantity, the refractive index. We must make the proviso that we stay away from any resonant absorption frequency, where the refractive index is anomalously high. If the refractive index refers to optical frequencies, the polarisability a will be purely electronic in origin. In practice, electronic polarisabilities derived in this way are remarkably insensitive to temperature and pressure, even for highly condensed phases in which intermolecular forces must be large. This is illustrated for the particular case of xenon in Table 2.1. 

Such behaviour is outstanding since, as seen before for pure materials, a change of thickness causes not only a shift in the resonance absorption frequency, but also a decrease of the attentuation in reflectance to less than —20 dB. Our results demonstrate that the microstructure of mixtures strongly influences the magnitude and frequency dependence of e. The... 

When we extract (Mqc E ) from the first root and (Mqc + Ei) from the second, we obtain by a Taylor expansion the power series for the resonant absorption frequency... 

When the absorbing molecules with the resonant absorption frequency coq are placed inside the laser resonator, the standing laser wave of frequency co coq burns two Bennet holes into the population distribution Ni (Vz) (Fig. 9.2b and Sect. 2.2), which, according to (9.3), appear at the velocity components... 

In the limiting case of Mossbauer nucleus a>no < I when the resonance absorption frequency in the... 

Molecular vibration absorption is the vibrational transition from the ground state to an excited state. From Equation 2.4, the resonance absorption frequency for the transition to the nth excited state can be expressed by... 

Construct an explanation for why C—O has a much lower (slower) resonant absorption frequency... 

The original method employed was to scan eitiier the frequency of the exciting oscillator or to scan the applied magnetic field until resonant absorption occiined. Flowever, compared to simultaneous excitation of a wide range of frequencies by a short RF pulse, the scanned approach is a very time-inefficient way of recording the spectrum. Flence, with the advent of computers that could be dedicated to spectrometers and efficient Fourier transfomi (FT) algoritluns, pulsed FT NMR became the nomial mode of operation. 

Application of an oscillating magnetic field at the resonance frequency induces transitions in both directions between the two levels of the spin system. The rate of the induced transitions depends on the MW power which is proportional to the square of oi = (the amplitude of the oscillating magnetic field) (see equation (bl.15.7)) and also depends on the number of spins in each level. Since the probabilities of upward ( P) a)) and downward ( a) p)) transitions are equal, resonance absorption can only be detected when there is a population difference between the two spin levels. This is the case at thennal equilibrium where there is a slight excess of spins in the energetically lower p)-state. The relative population of the two-level system in thennal equilibrium is given by the Boltzmaim distribution... 

Yokagawa Electric Works has developed a thermometer based on the nuclear quadmpole resonance of potassium chlorate, usable over the range from —184 to 125°C. This thermometer makes use of the fundamental properties of the absorption frequency of the Cl nucleus, and its caUbration is itself a constant of nature. 

The farther into the uv and the narrower the distribution of the resonant electron frequencies, the smaller the effect of dispersion in the visible region. The Pb(II) ion exhibits absorption in the near-uv, and addition of Pb(II) to a glass increases both n and dispersion. However, the use of Ba(II) and La(III) increases n without increasing dispersion. Fluorophosphates, having absorption bands located well into the uv, are examples of glasses with high AbbH numbers and low refractive indexes. 

The role of IR spectroscopy in the early penicillin structure studies has been described (B-49MI51103) and the results of more recent work have been summarized (B-72MI51101). The most noteworthy aspect of a penicillin IR spectrum is the stretching frequency of the /3-lactam carbonyl, which comes at approximately 1780 cm" This is in contrast to a linear tertiary amide which absorbs at approximately 1650 cm and a /3-lactam which is not fused to another ring (e.g. benzyldethiopenicillin), which absorbs at approximately 1740 cm (the exact absorption frequency will, of course, depend upon the specific compound and technique of spectrum determination). The /3-lactam carbonyl absorptions of penicillin sulfoxides and sulfones occur at approximately 1805 and 1810 cm respectively. The high absorption frequency of the penicillin /3-lactam carbonyl is interpreted in terms of the increased double bond character of that bond as a consequence of decreased amide resonance, as discussed in the X-ray crystallographic section. Other aspects of the penicillin IR spectrum, e.g. the side chain amide absorptions at approximately 1680 and 1510 cm and the carboxylate absorption at approximately 1610 cm are as expected. 

In the earlier treatment we reached the conclusion that resonance absorption occurs at the Larmor precessional frequency, a conclusion implying that the absorption line has infinitesimal width. Actually NMR absorption bands have finite widths for several reasons, one of which is spin-lattice relaxation. According to the Heisenberg uncertainty principle, which can be stated... 

Moderately slow exchange. The state lifetime is 2t we ask how the absorption band is affected as this becomes smaller. The uncertainty principle argument given earlier is applicable here lifetime broadening will occur as the state lifetime decreases. Thus, we expect resonance absorption at (or near) frequencies Va nnd Vb but the bands will be broader than in the very slow exchange limit. Equation (4-68) is applicable in this regime. 

Figure 15-6. (a) Phoioiuduccd absorption-detected magnetic resonance (ADMR) spectrum of MEH-PPV. HF and FF represents tire half field and full field powder pattern for the triplet (S=l) resonance, respectively, (b) ADMR spectrum ol MEH-PPV/CW, composite film. Both spectra were measured at probe energy 1.35 eV, T=4 K and 3 GHz resonant microwave frequency (reproduced by permission of the American Physical Society from Ref. 1191). 

It would appear that measurement of the integrated absorption coefficient should furnish an ideal method of quantitative analysis. In practice, however, the absolute measurement of the absorption coefficients of atomic spectral lines is extremely difficult. The natural line width of an atomic spectral line is about 10 5 nm, but owing to the influence of Doppler and pressure effects, the line is broadened to about 0.002 nm at flame temperatures of2000-3000 K. To measure the absorption coefficient of a line thus broadened would require a spectrometer with a resolving power of 500000. This difficulty was overcome by Walsh,41 who used a source of sharp emission lines with a much smaller half width than the absorption line, and the radiation frequency of which is centred on the absorption frequency. In this way, the absorption coefficient at the centre of the line, Kmax, may be measured. If the profile of the absorption line is assumed to be due only to Doppler broadening, then there is a relationship between Kmax and N0. Thus the only requirement of the spectrometer is that it shall be capable of isolating the required resonance line from all other lines emitted by the source. 

The infrared absorption frequencies of frans-3-substituted methyl acrylates gave a significant correlation with eq. (2). The value of p obtained is 75, which indicates predominance of the resonance effect. Three sets of nmr chemical shifts also were studied. All three sets gave significant correlation with eq. (2). The values of p obtained in two of the three sets were 70 and 78. Again, the resonance effect appears to predominate. 

The intensity of the absorption of microwave energy is a measure the abundance of that isotope. The potency of the NMR spectroscopy is not only its ability to quantify the concentration of an isotope, but to check the enviromnent into which an isotope is embedded. This is possible because the magnetic resonance and thus the absorption frequency prove to be sensitive to the spins of neighboring atoms and to structural features of the probe. Therefore, NMR spectroscopy is more a tool for scientific structural analyses than for daily food (colorant) inspection. For a detailed study of the NMR techniques used in food science we recommend books by Macomber and Pochapsky. - ... 

In the case of resonance absorption of synchrotron radiation by an Fe nucleus in a polycrystalline sample, the frequency dependence of the electric field of the forward scattered radiation, R(oj), takes a Lorentzian lineshape. In order to gain information about the time dependence of the transmitted radiation, the expression for R(oj) has to be Fourier-transformed into R(t) [6]. 

The method of paramagnetic resonance absorption makes use of the precession of the spinning impaired electron when it is placed in a magnetic field. This precession gives rise to absorption of radiation in the microwave region. The frequency at which the absorption takes place is given by the expression... 

Let the effective loss coefficient now include, in addition to intrinsic loss, a contribution due to absorption (and scattering) by the analyte contained in the evanescent fraction/of the WGM y = yx +/xa. The effect of the analyte on the resonant (single-frequency) drop signal D0a, when analyte absorption is a small fraction of the total loss, can be written in terms of an approximate effective absorption path length Leff as defined below ... 

In addition to the above prescriptions, many other quantities such as solution phase ionization potentials (IPs) [15], nuclear magnetic resonance (NMR) chemical shifts and IR absorption frequencies [16-18], charge decompositions [19], lowest unoccupied molecular orbital (LUMO) energies [20-23], IPs [24], redox potentials [25], high-performance liquid chromatography (HPLC) [26], solid-state syntheses [27], Ke values [28], isoelectrophilic windows [29], and the harmonic oscillator models of the aromaticity (HOMA) index [30], have been proposed in the literature to understand the electrophilic and nucleophilic characteristics of chemical systems. 

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