Lineshape calculations

Quantum calculations of spectral profiles based on Eqn. (3) are known isotropic interaction is commonly assumed. Such quantum calculations account for detailed balance in exact ways and consider not only the free-state to free-state transitions of binary complexes but also the bound-free and bound-bound transitions involving bound van der Waals pairs that are an inseparable part of the CILS spectra. These bound-free and bound-bound components can be quite significant, especially at the lower temperatures and for massive systems [266, 302, 328] see also related work on dimer spectra [262, 263], and the review papers on CILS lineshapes [227, 231, 271]. Lineshape calculations are useful for the detailed comparison of the fundamental theory with spectroscopic measurements. For helium pairs, a close agreement between the fundamental theory and the recent measurements is now observed similarly for the neon pair [45]. 

Lineshape calculations have a reputation of being involved, and the required computer codes are not widely available. It has, therefore, always been thought worthwhile to consider sum formulas (spectral moments) that are mueh more straightforward to compute, especially the elassical expressions, which can be readily corrected to the order for quantum effects. Expressions for the even spectral moments n = 0, 2, 4, and 6 are known. 

We note that it is often possible to approximate exact lineshapes fairly closely if suitable analytical model profiles are selected whose lowest two or three spectral moments are matched to those of the measurement [231], Various suitable model profiles are known, but certain three-parameter models approximate the exact shapes so closely that lineshape calculations may be dispensible for some applications. Other analytical profiles are, however, less than convincing for the purpose [314],... 

Fig. 7. The 13C powder lineshape calculated for the Cp ring hopping between chemically equivalent sites in [A1C14] [AlCp 2]+ using the 13C-shielding tensor determined from ab initio electronic structure calculations.12 The figure illustrates how the lineshape varies with the ring hopping rate k. The orientation of the principal axes of the 13C-shielding tensor determined from the ab initio calculations is shown in the inset.

Figure 7.28 Fano lineshape in H2. The predissociation of the N=2 [R(l) line] and N=1 [R(0) line] levels of the D1ri,ie(u = 5) state by the continuum of B 1is detected by monitoring the Lyman-a emission from one of the fragment atoms. The dots represent the lineshape calculated from the Fano formula [Eq. (7.9.1)] with parameter values Y(N = 2) = 14.5 cm 1,g(N = 2) = -9 r(jV = 1) = 4.8 cm 1,q(N = 1) = —18. These lineshapes should be compared to the symmetric profile of Fig. 7.16 (q = 00). The horizontal dotted line separates the interacting continuum Oi from the noninteracting continua [

Figure 15 (left) Schematic view of a modulated lattice of rods characteristic of a spatially finite bilayer structure, (right) Model lineshape calculations for a powder-averaged diffraction profile resulting from an A-B stacking sequence for (a) monolayer, (b) bilayer, (c) trilayer thick film, (d) illustrates the diffraction profile for an A-B-C trilayer. A triangular, commensurate, close-packed structure was used in each case. The in-plane lattice spacing was the same in all cases. The interplane distance was held fixed between all layers ... 

CHAOHUI YE. SHANGWU DING, AND JINYUAN ZHOU 2.3. Lineshape calculations... 

Figure 1. Comparison of the 4.2 K absorption lineshapes calculated from the Green s function ( solid line ) and the experimental result of Vermeglio and Paillotin ( Biochim. Biophys. Acta 681, 32 (1982), dotted line)...

M.S. Greenfield, A.D. Ronemus, R.L. Void, R.R. Void, P.E. Ellis, T.E. Raidy, Deuterium quadrupole-echo NMR spectroscopy. III. Practical aspects of lineshape calculations for multiaxis rotational processes,. Magn. Reson. 72 (1987) 89—107. 

In order to use the Hamiltonian of Equation (5.27) in lineshape calculations it is necessary to specify its spectral properties, which depend, amongst other things, on the correlation function of B,(f). A simple form of this correlation function is given by... 

Fig. 10.10 Absorption spectral lineshapes calculated as the Fourier transform of the Kubo relaxation function <)> (). (A) (indicated in arbitrary time units) is varied, while a is fixed at 1 reciprocal time unit (B) is fixed at 1 time unit and a is varied as indicated. To use the full Fourier transform (Eq. 10.70), < (r) is treated as an even function of time (Fig. 10.1 lA)...

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