Spectral density Fermi resonance

The Spectral Density of Pure Fermi Resonance Beyond the Exchange Approximation... 

The eigenvalues o>(r and the four sets of scalar products may be computed by full diagonalization of the Hamiltonian Hgi. Then, the spectral density of a medium-strength H bond involving a Fermi resonance is... 

Figure 10. Pure Fermi coupling within or beyond the exchange approximation. Left column spectra were obtained from expression (110) of the spectral density /sf (m, V. = 0) ex (a) Resonant case A — 0. A — 60 cm-1 (b) nonresonant case A — 120cm 1 with A — 60 cm-1 (dotted line),...

Figure 13. Hydrogen bond involving a Fermi resonance relative influence of the damping parameters. Spectral densities 7sf(co) computed from Eq. (81). Common parameters a0 = 1, A = 160cm-1, co0 = 3000cm-1, co00 = 150cm-1, 2t05 = 2790cm-1, and T = 300K.

At last, in his model, the ACF playing the role of [GD iv(Vj] in Eq. (309), is extracted from the two other models playing the role of [G rmi(f)] and [O0(t)IP]T. They give a numerical expression, which after Fourier transform, is assumed to give the peeled-off spectral density, that is, the SD of the H-bonded centrosymmetric cyclic dimer that would be observed if the Fermi resonances were missing. 

Figure 24. Effects of temperature and isotopic substitution on the spectral densities of crystalline adipic acid in the absence of Fermi resonance. Comparison between theoiy (Eq. (279)) (thick Line) and experiment [101] (grayed spectra). Left column calculations using the breaking of the IR selection rule (r)° = 0). Right column same calculations but without the breaking of the IR selection rule (r 0 = 0).

Figure 27. Spectral densities of crystalline glutaric acid theory without Fermi resonances. Experiment Thick line to [112] Theoretical, grayed spectra.

Figure 29. Spectral densities of crystalline naphtoic acid with four Fermi resonances are acting. Experiment grayed spectra [113].

The supercritical CO2 absorption bands change in intensity as a function of density but the band shape does not change - at least not at the 8 cm spectral resolution typically used for this application. As a result, it is a simple matter to subtract the supercritical carbon dioxide absorption spectrum from an FT-IR data file collected during an SFC/FT-IR experiment. The subtraction factor is adjusted to exactly compensate for the Fermi resonance absorption. The resulting spectrum will then contain only absorption bands due to other components, if any, entrained in the supercritical fluid. The regions from 3800-3500 cm and from 2500-2200 cm appear as gaps in the spectrum because the supercritical carbon dioxide absorbs all the available infrared radiation in these regions. 

The spectral features in the data shown in Figures 172 and 173 resemble those expected for a density-wave state, for example, as in (TMTSF)2PF6 where an SDW gap is formed at around 100 cm" in the direction perpendicular to the chains [1212]. With this interpretation, the resonance at 70 cm Vould be identified with the pinned collective mode. The spectral weight within the 70 cm resonance corresponds to a small fraction (approximately 10%) of the oscillator strength, which was redistributed from below 2A to above 2A. Alternatively, since the gap spans only a part of the Fermi surface, the results reported here can be interpreted in the context of the correlation-induced semimetallic state proposed by Vescoli et al. [1213]. 

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