Spectral density adiabatic approximation

On the other hand, the undamped autocorrelation function (17) we have obtained within the standard approach avoiding the adiabatic approximation must lead after Fourier transform to spectral densities involving very puzzling Dirac delta peaks given by... 

Figure 5. Illustration of the equivalence between the spectral densities obtained within the adiabatic approximation and those resulting from the effective Hamiltonian procedure, using the wave operator. Common parameters a0 = 0.4, co0 = 3000cm-1, C0Oo = 150cm-1, y = 30cm-1, and T = 300 K.

We shall compare later the spectral density /sf ex and the adiabatic one If [given later by Eq. (103)] that supposes implicitly the exchange approximation. We may expect no difference between their lineshape in cases for which the adiabatic approximation is valid. 

Figure 8. Comparison between the adiabatic spectral density and the standard one (with or without the exchange approximation), (a) and (c) display the spectral density Isf from Eq. (81), using dashed lines, (b) and (d) display the spectral density /sf ex from Eq. (88), within the exchange approximation, using dashed lines. Comparison is made with the adiabatic spectral density If (thin plain lines) obtained from (96). Spectra (a) and (b) are computed with Oo = 1.2, whereas spectra (c) and (d) are computed with a0 = 0.6. Common parameters A = 120cm-1, (n0 = 3000cm-1, C05 = 1440 cm-1, co00 = 150 cm-1, y0 = y5 = 60 cm-1, and T = 300 K.

We kept the same structure in Figs. 8(a) and 8(b), but the spectra were computed for a greater value a0 = 1.2. As may be seen, some differences between the adiabatic and nonadiabatic spectral densities appear in all cases, whether applying the exchange approximation or not. Within the exchange approximation, Fig. 8(b), these discrepancies may be safely attributed to the... 

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). 

These conclusions must be considered keeping in mind that the general theoretical spectral density used for the computations, in the absence of the fast mode damping, reduces [8] to the Boulil et al. spectral density and, in the absence of the slow mode damping, reduces to that obtained by Rosch and Ratner one must also rember that these two last spectral densities, in the absence of both dampings [8], reduce to the Franck-Condon progression involving Dirac delta peaks that are the result of the fundamental work of Marechal and Witkowski. Besides, the adiabatic approximation at the basis of the Marechal... 

On the contrary, the semiclassical approach in the problem of the optical absorption is restricted to a great extent and the adequate description of the phonon-assisted optical bands with a complicated structure caused by the dynamic JTE cannot be done in the framework of this approach [13]. An expressive example is represented by the two-humped absorption band of A —> E <8> e transition. The dip of absorption curve for A —> E <8> e transition to zero has no physical meaning because of the invalidity of the semiclassical approximation for this spectral range due to essentially quantum nature of the density of the vibronic states in the conical intersection of the adiabatic surface. This result is peculiar for the resonance (optical) phenomena in JT systems full discussion of the condition of the applicability of the adiabatic approximation is given in Ref. [13]. 

P. Blaise, O. Henri-Rousseau. Spectral density of medium strength H-bonds. Direct damping and intrinsic anharmonicity of the slow mode. Beyond adiabatic approximation. Chem Phys 256 85-106, 2000. 

The quantum theory of spectral collapse presented in Chapter 4 aims at even lower gas densities where the Stark or Zeeman multiplets of atomic spectra as well as the rotational structure of all the branches of absorption or Raman spectra are well resolved. The evolution of basic ideas of line broadening and interference (spectral exchange) is reviewed. Adiabatic and non-adiabatic spectral broadening are described in the frame of binary non-Markovian theory and compared with the impact approximation. The conditions for spectral collapse and subsequent narrowing of the spectra are analysed for the simplest examples, which model typical situations in atomic and molecular spectroscopy. Special attention is paid to collapse of the isotropic Raman spectrum. Quantum theory, based on first principles, attempts to predict the. /-dependence of the widths of the rotational component as well as the envelope of the unresolved and then collapsed spectrum (Fig. 0.4). 

---