Lineshapes broadening

The r-point transition energies shift to lower energies with increasing temperature. The energy shift is accompanied by a continuous lineshape broadening, and is caused mainly by the increase in electron-phonon interaction. 

IvX(co) represents an absorption lineshape broadened by Jg(x), whereas 7V/1(oj) represents an emission lineshape broadened by J x). 

Fig. 18. Time dependent frequency shifts from CARS spectra of (a) 1 xm thick downstream anthracene gauge, and (b) dye probe in 3 xm thick nanoscattering or nanoporous PMMA. The incident 4.2 GPa shock front is attenuated to 3.7 GPa and 2.7 GPa by the scattering and porous samples. After the shock is over (about t = 6 ns), the dye probe shows a persistent residual redshift associated with heat generated by shock compression. In the porous sample, this redshift is larger and it develops more slowly, over 3 ns, which is the time constant for pore collapse. The extra heat generated by pore collapse results in CARS lineshape broadening (inset). Reproduced from ref. [120].

Gerhart and Hooper(S). Uniaxial stress applied to the crystal produced 1 SSNMR lineshape broadening one component of the gradient-elastic tensor was determined ... 

Marsh and Casabella induced elastic strain upon single crystals of NaCl and NaBr by plying static pressure (up to 6.9 MPa) and noted, as expected, that the C1 and Br NMR lineshapes broadened and became less intense. The authors determined that the purely ionic model of vK was inadequate to describe the changing field gradients at the chlorine and bromine nuclei with respect to changing pressure. It was concluded that ion orbital overlap between nearest and NNN atoms was a satisfactory model to rationalize their observations and that pure covalent effects did not need to be included. The effects of static elastic strain on chlorine SSNMR spectra were observed to determine the gradient-elastic tensors for LiCl and RbCl by Flackeloer and Kanert. ... 

When the dipolar splitting is significant relative to linewidths in the continuous wave (CW) EPR spectra, the analysis of the lineshape broadening can be used to determine the magnitude of the dipolar interaction. A qualitative indication of spin-spin interaction can be obtained by measuring the relative amplitudes of characteristic peaks in a nitroxyl spectrum (the ratio d,/d) (51). 

The energy spectrum of the resonance states will be quasi-discrete it consists of a series of broadened levels with Lorentzian lineshapes whose full-width at half-maximum T is related to the lifetime by F = Fn. The resonances are said to be isolated if the widths of their levels are small compared with the distances (spacings) between them, that is... 

This angular dependence is different from the first-order perturbations so that the conventional teclmique of removing linebroadening in solids, MAS (see below), caimot completely remove this interaction at the same time as removing the first-order broadening. Flence, the resolution of MAS spectra from quadnipolar nuclei is usually worse than for spin-2 nuclei and often characteristic lineshapes are observed. If this is the case, it is... 

Figure B2.4.3 shows an example of this in the aldehyde proton spectnim of N-labelled fonnamide. Some lines in the spectnim remain sharp, while others broaden and coalesce. There is no frmdamental difference between the lineshapes in figures B2.4.1 and figures B2.4.3—only a difference in the size of the matrices involved. First, the uncoupled case will be discussed, then the extension to coupled spin systems.

Therefore, the absorjDtion line is massively inlromogeneously broadened at low temperature. An inliomogeneous lineshape can be used to detennine the static or quasistatic frequency spread of oscillators due to a distribution of environments, but it provides no dynamical infonnation whatsoever [94, 95]. As T is increased to 300 K, the absorjDtion linewidth decreases and increases. At 300 K, the lineshape is nearly homogeneously broadened and dominated by vibrational dephasing, because fast dephasing wipes out effects of inliomogeneous environments, a well known phenomenon tenned motional narrowing [951. 

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. 

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

In molecularly rigid systems, the direct (through-space) dipole-dipole interaction between nuclear spins I = fe is normally the dominant source of broadening of the NMR lineshape. For a pair of similar nuclear spins i and j in a magnetic field Hq the dipolar splitting in their spectrum is given by... 

Hagen, W.R. 1981. Dislocation strain broadening as a source of anisotropic linewidth and asymmetrical lineshape in the electron paramagnetic resonance spectrum of metal-loproteins and related systems. Journal of Magnetic Resonance 44 447-469. 

As we have found in the above section, the damping of the slow mode when it is nearly alone produces (within the Boulil et al. model) a collapse of the fine structure of the lineshapes. That is in contradiction with the RY semiclassical model which predicts a broadening of the lineshape. Of course, because the quantum model is more fundamental, the semiclassical model must be questioned. However, it is well known that the RY semiclassical model of indirect relaxation has the merit to predict lineshapes that may transform progressively,... 

Now, return to Fig. 14. The right and left bottom damped lineshapes (dealing respectively with quantum direct damping and semiclassical indirect relaxation) are looking similar. That shows that for some reasonable anharmonic coupling parameters and at room temperature, an increase in the damping produces approximately the same broadened features in the RY semiclassical model of indirect relaxation and in the RR quantum model of direct relaxation. Thus, one may ask if the RR quantum model of direct relaxation could lead to the same kind of prediction as the RY semiclassical model of indirect relaxation. 

Figure 15 gives the superposition of RR (full line) and RY (dotted plot) spectral densities at 300 K. For the RR spectral density, the anharmonic coupling parameter and the direct damping parameter were taken as unity (a0 = 1, y0 = ffioo), in order to get a broadened lineshape involving reasonable half-width (a = 1 was used systematically, for instance, in Ref. 72). For the RY spectral density, the corresponding parameters were chosen aD = 1.29, y00 = 0.85angular frequency shift (the RY model fails to obtain the low-frequency shift predicted by the RR model) and a suitable adjustment in the intensities that are irrelevant in the RR and RY models. 

Width of the lineshapes. The lineshapes are broadened approximately in the same way for the two situations where either the fast mode of, the slow one is damped. 

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