Linewidths

It is of interest to detennine when the linewidth F( ) associated with the RRKM rate constant lc(E) equals the average distance p( ) between the reactant energy levels. From equation (A3.12.54) F( ) = Dk( ) and from the RRKM rate constant expression equation (A3.12.15) p(Ef = hl% K( )/M( - q). Equating these two... 

Time-dependent quantum mechanical calcnlations have also been perfomied to study the HCO resonance states [90,91]. The resonance energies, linewidths and quantum number assigmnents detemiined from these calcnlations are in excellent agreement with the experimental results. 

High-resolution spectroscopy used to observe hyperfme structure in the spectra of atoms or rotational stnicture in electronic spectra of gaseous molecules connnonly must contend with the widths of the spectral lines and how that compares with the separations between lines. Tln-ee contributions to the linewidth will be mentioned here tlie natural line width due to tlie finite lifetime of the excited state, collisional broadening of lines, and the Doppler effect. 

The most ftmdamental limitation on sharpness of spectral lines is the so-called natural linewidth. Because an... 

Light sources can either be broadband, such as a Globar, a Nemst glower, an incandescent wire or mercury arc lamp or they can be tunable, such as a laser or optical parametric oscillator (OPO). In the fomier case, a monocln-omator is needed to achieve spectral resolution. In the case of a tunable light source, the spectral resolution is detemiined by the linewidth of the source itself In either case, the spectral coverage of the light source imposes limits on the vibrational frequencies that can be measured. Of course, limitations on the dispersing element and detector also affect the overall spectral response of the spectrometer. 

Due to the rather stringent requirements placed on the monochromator, a double or triple monocln-omator is typically employed. Because the vibrational frequencies are only several hundred to several thousand cm and the linewidths are only tens of cm it is necessary to use a monochromator with reasonably high resolution. In addition to linewidth issues, it is necessary to suppress the very intense Rayleigh scattering. If a high resolution spectrum is not needed, however, then it is possible to use narrow-band interference filters to block the excitation line, and a low resolution monocln-omator to collect the spectrum. In fact, this is the approach taken with Fourier transfonn Raman spectrometers. 

For the highest resolution and sensitivity, laser-based spectrometers must be used. These have tire advantage that the resolution depends on the linewidth of the laser, rather than the monocln-omator. Furthennore, at any given moment, all of the power is at the frequency of mterest, rather than being spread out over the whole IR... 

Cheville R A and Grioschkowsky D 1999 Far-infrared foreign and self-broadened rotational linewidths of high temperature water vapor J. Opt. See. Am. B 16 317-22... 

It is occasionally desirable to retain a small proportion of molecular orientation, in order to quantitate the dipolar interactions present, whilst minimizing their contribution to the linewidth. Partial orientation may be achieved by using a nematic solvent. In large, magnetically anisotropic molecules it may occur naturally at the highest magnetic fields. 

The absolute measurement of areas is not usually usefiil, because tlie sensitivity of the spectrometer depends on factors such as temperature, pulse length, amplifier settings and the exact tuning of the coil used to detect resonance. Peak intensities are also less usefiil, because linewidths vary, and because the resonance from a given chemical type of atom will often be split into a pattern called a multiplet. However, the relative overall areas of the peaks or multiplets still obey the simple rule given above, if appropriate conditions are met. Most samples have several chemically distinct types of (for example) hydrogen atoms within the molecules under study, so that a simple inspection of the number of peaks/multiplets and of their relative areas can help to identify the molecules, even in cases where no usefid infonnation is available from shifts or couplings. 

The principal dilTerence from liquid-state NMR is that the interactions which are averaged by molecular motion on the NMR timescale in liquids lead, because of their anisotropic nature, to much wider lines in solids. Extra infonnation is, in principle, available but is often masked by the lower resolution. Thus, many of the teclmiques developed for liquid-state NMR are not currently feasible in the solid state. Furthemiore, the increased linewidth and the methods used to achieve high resolution put more demands on the spectrometer. Nevertheless, the field of solid-state NMR is advancing rapidly, with a steady stream of new experiments forthcoming. 

The sinc fiinction describes the best possible case, with often a much stronger frequency dependence of power output delivered at the probe-head. (It should be noted here that other excitation schemes are possible such as adiabatic passage [9] and stochastic excitation [fO] but these are only infrequently applied.) The excitation/recording of the NMR signal is further complicated as the pulse is then fed into the probe circuit which itself has a frequency response. As a result, a broad line will not only experience non-unifonn irradiation but also the intensity detected per spin at different frequency offsets will depend on this probe response, which depends on the quality factor (0. The quality factor is a measure of the sharpness of the resonance of the probe circuit and one definition is the resonance frequency/haltwidth of the resonance response of the circuit (also = a L/R where L is the inductance and R is the probe resistance). Flence, the width of the frequency response decreases as Q increases so that, typically, for a 2 of 100, the haltwidth of the frequency response at 100 MFIz is about 1 MFIz. Flence, direct FT-piilse observation of broad spectral lines becomes impractical with pulse teclmiques for linewidths greater than 200 kFIz. For a great majority of... 

The interpretation of MAS experiments on nuclei with spin / > Fin non-cubic enviromnents is more complex than for / = Fiuiclei since the effect of the quadnipolar interaction is to spread the i <-> (i - 1) transition over a frequency range (2m. - 1)Vq. This usually means that for non-integer nuclei only the - transition is observed since, to first order in tire quadnipolar interaction, it is unaffected. Flowever, usually second-order effects are important and the angular dependence of the - ytransition has both P2(cos 0) andP Ccos 9) terms, only the first of which is cancelled by MAS. As a result, the line is narrowed by only a factor of 3.6, and it is necessary to spin faster than the residual linewidth Avq where... 

Physical background. MAS will narrow the inliomogeneously broadened satellite transitions to give a series of sharp sidebands whose intensity envelopes closely follow the static powder pattern so that the quadnipole interaction can be deduced. The work of Samoson [25] gave real impetus to satellite transition spectroscopy by showing that both the second-order quadnipolar linewidths and isotropic shifts are fiinctions of / and Some combinations of / and produce smaller second-order quadnipolar effects on the satellite lines than... 

A result of tlie relaxation processes is a shortened lifetime of the spin states giving rise to a broadening of the EPR line, which for most magnetic resonance lines dominated by homogeneous linewidth can be written as... 

The negative sign in equation (b 1.15.26) implies that, unlike the case for electron spins, states with larger magnetic quantum number have smaller energy for g O. In contrast to the g-value in EPR experiments, g is an inlierent property of the nucleus. NMR resonances are not easily detected in paramagnetic systems because of sensitivity problems and increased linewidths caused by the presence of unpaired electron spins. 

After the signal emerges from the lock-m amplifier it still contains a considerable amount of noise. Most of the noise contributions to the signal can be eliminated by passing the signal tlirough a low-pass filter. The filter tune constant is a measure of the cutoff frequency of the filter. If accurate linewidth and g-factor... 

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