Line-broadening

Due to the contribution of various broadening mechanisms, the linewidths typically observed in atomic spectrometry are significantly broader than the natural width of a spectroscopic line which can be theoretically derived. The natural width of a spectral line is a consequence of the limited lifetime r of an excited state. Using Heisenberg s uncertainty relation, the corresponding half-width expressed as frequency is  

From this equation, a typical half-width of ca. 10 pm is obtained for most spectroscopic lines. 

The first important line broadening mechanism is Doppler line broadening. It results from the movement that emitting species make towards or away from the point of observation. The contribution to line broadening is  

Pressure or Lorentz broadening is the second important factor for line broadening. It is a result of the interaction of the emitting species and other, non-emitting particles. Its contribution to line broadening is  

Other factors contributing to hne broadening are isotopic effects and hyperfine structure (as a result of the interaction between radiating and non-radiating atoms of the same species) and Stark broadening which are due to the interaction with electric fields. 

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Of great interest to physical chemists and chemical physicists are the broadening mechanisms of Raman lines in the condensed phase. Characterization of tliese mechanisms provides infomiation about the microscopic dynamical behaviour of material. The line broadening is due to the interaction between the Raman active chromophore and its environment. 

The cross-correlation effects between the DD and CSA interactions also influence the transverse relaxation and lead to the phenomenon known as differential line broadening in a doublet [40], cf Figure Bl.13.8. There is a recent experiment, designed for protein studies, that I wish to mention at tire end of this section. It has been proposed by Pervushin etal [4T], is called TROSY (transverse relaxation optimized spectroscopy) and... 

Figure Bl.14.7. Chemical shift imaging sequence [23], Bothx- andj -dimensions are phase encoded. Since line-broadening due to acquiring the echo in the presence of a magnetic field gradient is avoided, chemical shift infonnation is retained in tire echo.

Even for a single radical tire spectral resolution can be enlianced for disordered solid samples if the inliomogeneous linewidth is dominated by iimesolved hyperfme interactions. Whereas the hyperfme line broadening is not field dependent, tire anisotropic g-matrix contribution scales linearly with the external field. Thus, if the magnetic field is large enough, i.e. when the condition... 

Once the basic work has been done, the observed spectrum can be calculated in several different ways. If the problem is solved in tlie time domain, then the solution provides a list of transitions. Each transition is defined by four quantities the mtegrated intensity, the frequency at which it appears, the linewidth (or decay rate in the time domain) and the phase. From this list of parameters, either a spectrum or a time-domain FID can be calculated easily. The spectrum has the advantage that it can be directly compared to the experimental result. An FID can be subjected to some sort of apodization before Fourier transfomiation to the spectrum this allows additional line broadening to be added to the spectrum independent of the sumilation. 

Kiroz J G, van der Pei]l G J Q and van der Elsken J 1978 Determination of potential energy surfaoes of Ar-HCI and Kr-HCI from rotational line-broadening data J. Chem. Phys. 69 4606-16... 

Vacha M, Liu Y, Nakatsuka FI and Tani T 1997 Inhomogeneous and single molecule line broadening of terryiene in a series of crystalline n-alkanes J. Phys. Chem 106 8324-31... 

Figure C2.17.10. Optical absorjDtion spectra of nanocrystalline CdSe. The spectra of several different samples in the visible and near-UV are measured at low temperature, to minimize the effects of line broadening from lattice vibrations. In these samples, grown as described in [84], the lowest exciton state shifts dramatically to higher energy with decreasing particle size. Higher-lying exciton states are also visible in several of these spectra. For reference, the band gap of bulk CdSe is 1.85 eV.

The Time Dependent Processes Seetion uses time-dependent perturbation theory, eombined with the elassieal eleetrie and magnetie fields that arise due to the interaetion of photons with the nuelei and eleetrons of a moleeule, to derive expressions for the rates of transitions among atomie or moleeular eleetronie, vibrational, and rotational states indueed by photon absorption or emission. Sourees of line broadening and time eorrelation funetion treatments of absorption lineshapes are briefly introdueed. Finally, transitions indueed by eollisions rather than by eleetromagnetie fields are briefly treated to provide an introduetion to the subjeet of theoretieal ehemieal dynamies. 

Each vibrational peak within an electronic transition can also display rotational structure (depending on the spacing of the rotational lines, the resolution of the spectrometer, and the presence or absence of substantial line broadening effects such as... 

In experimental measurements, sueh sharp 5-funetion peaks are, of eourse, not observed. Even when very narrow band width laser light sourees are used (i.e., for whieh g(co) is an extremely narrowly peaked funetion), speetral lines are found to possess finite widths. Let us now diseuss several sourees of line broadening, some of whieh will relate to deviations from the "unhindered" rotational motion model introdueed above. 

Experimental confirmation of the metal-nitrogen coordination of thiazole complexes was recently given by Pannell et al. (472), who studied the Cr(0), Mo(0), and W(0) pentacarbonyl complexes of thiazole (Th)M(CO)5. The infrared spectra are quite similar to those of the pyridine analogs the H-NMR resonance associated with 2- and 4-protons are sharper and possess fine structure, in contrast to the broad, featureless resonances of free thiazole ligands. This is expected since removal of electron density from nitrogen upon coordination reduces the N quad-rupole coupling constant that is responsible for the line broadening of the a protons. 

Equation (2.27) illustrates what is called the natural line broadening. Since each atom or molecule behaves identically in this respect it is an example of homogeneous line broadening, which results in a characteristic lorentzian line shape. 

Natural line broadening is usually very small compared with other causes of broadening. However, not only is it of considerable theoretical importance but also, in the ingenious technique of Lamb dip spectroscopy (see Section 2.3.5.2), observations may be made of spectra in which all other sources of broadening are removed. 

When collisions occur between gas phase atoms or molecules there is an exchange of energy, which leads effectively to a broadening of energy levels. If t is the mean time between collisions and each collision results in a transition between two states there is a line broadening Av of the transition, where... 

With improvements in Instrument sensitivity and the use of techniques such as enhancement by polarization transfer (INEPT), it can be expected that natural abundance N NMR spectra will become increasingly Important in heterocyclic chemistry. The chemical shifts given in Table 10 illustrate the large dispersion available in N NMR, without the line broadening associated with N NMR spectra. 

Carbon Dioxide The contribution to the emissivity of a gas containing CO9 depends on gas temperature Tc, on the CO9 partial pressure-beam length product p L and, to a much lesser extent, on the total pressure P. Constants for use in evaluating at a total pressure of 101.3 kPa (1 atm) are given in Table 5-8 (more on this later). The gas absorptivity Ot equals the emissivity when the absorbing gas and the emitter are at the same temperature. When the emitter surface temperature is Ti, Ot is (Tc/Ti)° times , evaluated using Table 5-8 at T instead of Tc and at p LTi/Tc instead of Line broadening, due to... 

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