Vibrational eigenstates obtaining

As an example of the application of time propagating the quantum vibrational wavefunction and also as a practical means of obtaining selected vibrational eigenstates, we briefly take a look at the energy screening method [420]. 

If we use an ns probe pulse, we can tune its wavelength resonant to one particular vibronic transition. In this case, the LIF signal reflects the population of a single vibrational level involved in the WP. By scanning the wavelength of the probe pulse, we can observe the population distribution of the eigenstates involved in the WP. The peak intensities of the LIF signal are influenced by the Franck-Condon factors and the probe laser intensities, so that the relevant corrections are necessary to obtain the population distribution. 

Aside from solitons, there is a continuous spectrum of torsional modes, or rotons. These excitations are the eigenstates of the linearized Hamiltonian. To obtain their spectrum, one replaces the last term in (7.68) with a harmonic potential. This approximation implies that the vibrational amplitude of a rotor must be small enough compared with the large amplitude motion of a rotor participating in a soliton. The frequencies of rotons obey the dispersion equation ... 

Fig. 11 Illustration of the excited state relaxation derived from experimental results obtained for poly(dA).poly(dT) by steady-state absorption and fluorescence spectroscopy, fluorescence upconversion and based on the modeling of the Franck-Condon excited states of (dA)io(dT)io. In red (full line) experimental absorption spectrum yellow circles arranged at thirty steps represent the eigenstates, each circle being associated with a different helix conformation and chromophore vibrations.

As previously discussed, if two or more excited eigenstates can combine in absorption with a common ground-state level, then these eigenstates can be excited so as to form a coherent superposition state. The superposition state, in turn, can give rise to quantum beat-modulated fluorescence decays. All this, of course, lies at the heart of the theory of vibrational coherence effects. However, it also implies that the same experimental conditions under which vibrational coherence effects are observed should allow for the observation of rotational coherence effects. That is, since more than one rotational level in the manifold of an excited vibronic state can combine in absorption with a single ground-state ro-vibrational level, then in a picosecond-resolved fluorescence experiment rotational quantum beats should obtain. 

The most commonly used experimental techniques probe molecules in the frequency domain rather than in the time domain. As emphasized recently (1) the increased level of detail provided by frequency-domain methods produces a more complete picture of the vibrational energy redistribution process, invalidating frequently made claims that time domain techniques, being more direct, are somehow superior. The molecular eigenstate spectra provided by high-resolution experiments currently provide the most complete picture of molecular dynamics. Of course, the frequency-domain and time-domain viewpoints are complementary and we frequently obtain enhanced understanding by considering both viewpoints. 

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