Lineshape effects

High-spin dendrimers, like 5 (G = 1), are ideal probes for such a study since they are ESR active and this spectroscopy has the same time scale as such a dynamic process. In fact, the anisotropic components of some ESR parameters, such as those responsible for the fine structures of a high-spin molecule, are averaged out under molecular tumbling leading to noticeably lineshape effects. 

R lineshape effects are observed for distances up to 300-350 pm. Both the R2TR and the R T approaches utilize low-power RF amplitudes to generate new and adjustable resonance conditions. The idea of generating such new R conditions by applying additional RF irradiation has been outlined earlier, in an approach where short cycles of high-power RF pulses, together with... 

Temperature dependent lineshape effects studied discussion of internal pseudo-rotation. ... 

Lineshape effects due to relaxation over the energy barrier may be significant down to low temperature because of the blocking of the smallest particles if the volume distribution is not narrow. Deviations from the ideal width, shape, and position of the lines will also occur if the assumption of fast diffusion is not accurate. The fluctuations around the easy direction have been found faster than about 10 -10 " s for... 

Advantages. The experiment can be carried out with a conventional fast-spuming MAS probe so that it is straightforward to implement. For recording the satellite transition lineshapes it offers better signal-to-noise and is less susceptible to deadtime effects than static measurements. As the effects differ for each value, a single satellite transition experiment is effectively the same as carrying out multiple field experiments on the central transition. 

Binsch G 1969 A unified theory of exchange effects on nuclear magnetic resonance lineshapes J. Am. Chem. Soc. 91 1304-9... 

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 approach to the evaluation of vibrational spectra described above is based on classical simulations for which quantum corrections are possible. The incorporation of quantum effects directly in simulations of large molecular systems is one of the most challenging areas in theoretical chemistry today. The development of quantum simulation methods is particularly important in the area of molecular spectroscopy for which quantum effects can be important and where the goal is to use simulations to help understand the structural and dynamical origins of changes in spectral lineshapes with environmental variables such as the temperature. The direct evaluation of quantum time- correlation functions for anharmonic systems is extremely difficult. Our initial approach to the evaluation of finite temperature anharmonic effects on vibrational lineshapes is derived from the fact that the moments of the vibrational lineshape spectrum can be expressed as functions of expectation values of positional and momentum operators. These expectation values can be evaluated using extremely efficient quantum Monte-Carlo techniques. The main points are summarized below. 

In the stochastic theory of lineshape developed by Blume [31], the spectral lines are calculated under the influence of a time-dependent Hamiltonian. The method has been successfully applied to a variety of dynamic effects in Mossbauer spectra. We consider here an adaptation due to Blume and Tjon [32, 33] for a Hamiltonian fluctuating between two states with axially symmetric electric field gradients (efg s), the orientation of which is parallel or perpendicular to each other. The present formulation is applicable for states with the same... 

A theoretical investigation of the use of NMR lineshape second moments in determining elastomer chain configurations has been undertaken. Monte Carlo chains have been generated by computer using a modified rotational isomeric state (RIS) theory in which parameters have been included which simulate bulk uniaxial deformation. The behavior of the model for a hypothetical poly(methylene) system and for a real poly(p-fluorostyrene) system has been examined. Excluded volume effects are described. Initial experimental approaches are discussed. 

As a consequence of the wide frequency range over which Fermi resonances may be effective, let us conclude that, in practical situations, several Fermi couplings may be involved in a spectrum, which must lead to puzzling spectral lineshapes. 

In the full quantum mechanical approach [8], one uses Eq. (22) and considers both the slow and fast mode obeying quantum mechanics. Then, one obtains within the adiabatic approximation the starting equations involving effective Hamiltonians characterizing the slow mode that are at the basis of all principal quantum approaches of the spectral density of weak H bonds [7,24,25,32,33,58, 61,87,91]. It has been shown recently [57] that, for weak H bonds and within direct damping, the theoretical lineshape avoiding the adiabatic approximation, obtained directly from Hamiltonian (22), is the same as that obtained from the RR spectral density (involving adiabatic approximation). 

The two quantum mechanisms lead to a broadening of the lineshapes obeying approximately a coth1/2(cvf/7 j law, so that the temperature effect is... 

How then, can one recover some quantity that scales with the local charge on the metal atoms if their valence electrons are inherently delocalized Beyond the asymmetric lineshape of the metal 2p3/2 peak, there is also a distinct satellite structure seen in the spectra for CoP and elemental Co. From reflection electron energy loss spectroscopy (REELS), we have determined that this satellite structure originates from plasmon loss events (instead of a two-core-hole final state effect as previously thought [67,68]) in which exiting photoelectrons lose some of their energy to valence electrons of atoms near the surface of the solid [58]. The intensity of these satellite peaks (relative to the main peak) is weaker in CoP than in elemental Co. This implies that the Co atoms have fewer valence electrons in CoP than in elemental Co, that is, they are definitely cationic, notwithstanding the lack of a BE shift. For the other compounds in the MP (M = Cr, Mn, Fe) series, the satellite structure is probably too weak to be observed, but solid solutions Coi -xMxl> and CoAs i yPv do show this feature (vide infra) [60,61]. 

As in the parent binary phosphides MV, the metal 2p3 p XPS spectra for the mixed-metal phosphides M XM XV exhibit asymmetric lineshapes originating from final state effects [34] involving the metal-metal bonding network. Virtually no changes in BE are observed relative to the binary phosphides MV or the elemental metals... 

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