Decomposed lineshapes

Eigure 6.37 shows the XPS S2p line measured ex situ for a TTF[Ni(dmit)2]2 thin him. The experimental lineshape can be satisfactorily decomposed into three contribuhons. The most intense line, with a binding energy of 163.5 eV, corresponds to C-S-C bonds, and the 161.8 and 165.3 eV lines to C-S-Ni and C=S bonds, respechvely. In the nominal formula TTE[Ni(dmit)2]2 there are 12 C-S-C, 8 C-S-Ni and4 C=S bonds, which results in a ratio 3 2 1. From the ht, the intensity... 

By computer-fitting the observed spectrum was decomposed to a sum of Lorentzian lineshapes, and then the fractions of the a-helix and p-sheet forms for PLA and PLIL were determined. The PLA/PLIL blend sample with a mixture ratio of 50/50 (wt/wt%) corresponds to the molar mixture ratio... 

Chemical shift spectra of PTFE obtained at 259° are shown in Figure 1. These lineshapes, for three different samples of varying crystallinity, may be seen to be a linear combination of two lineshapes one is characteristic of an axially symmetric powder pattern and the other of an isotropic chemical shift tensor. At this temperature these two lineshapes differ greatly and may be numerically decomposed. 

In Figure 2, these lineshapes are decomposed into the isotropic lineshape and the axially symmetric powder pattern lineshape. This same procedure was used for eight samples. 

Figure B2.4.4. The two-site equally populated exchange lineshape (figure B2.4.1) decomposed into two individual transitions. The bottom spectrum (a) is the situation before coalescence two symmetrically out-of-phase lines. In slow exchange, these become the signals of the two sites. The top spectrum (b) is after coalescence the lineshape is made up of two central lines, one positive and one negative. In fast exchange, the negative line broadens and loses intensity, to leave a single positive line at the average chemical shift.

A new approach to caloilating the lineshape of spin systems has been proposed which invokes Wei- orman Lie algebra. A Hamiltonian is decomposed in terms of the generators of a Lie algebra and the evolution of the generators is then calculated. This method is useful when the time dependence of the Hamiltonian is not cyclic. Analytical solutions can be obtained in certain cases. 

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