Local-mode overtone state

Holme and Hutchinson suggest tuning two, or several, lasers to nearly degenerate molecular eigenstates. By adjusting the strength of the field at each frequency, they are able to combine these two molecular eigenstates with arbitrary coefficients, and thereby prepare a desired superposition state. These workers have focused on applications to local mode overtones, where field-free evolution would lead to relaxation into an intramolecular bath. 

The concept of intramolecular vibrational energy redistribution (IVR) can be formulated from both time-dependent and time-independent viewpoints (Li et al., 1992 Sibert et al., 1984a). IVR is often viewed as an explicitly time-dependent phenomenon, in which a nonstationary superposition state, as described above, is initially prepared and evolves in time. Energy flows out of the initially excited zero-order mode, which may be localized in one part of the molecule, to other zero-order modes and, consequently, other parts of the molecule. However, delocalized zero-order modes are also possible. The nonstationary state initially prepared is often referred to as the bright state, as it carries oscillator strength for the spectroscopic transition of interest, and IVR results in the flow of amplitude into the manifold of so-called dark states that are not excited directly. It is of interest to understand what physical interactions couple different zero-order modes, allowing energy to flow between them. A particular type of superposition state that has received considerable study are A/-H local modes (overtones), where M is a heavy atom (Child and Halonen, 1984 Hayward and Henry, 1975 Watson et al., 1981). 

Figure 4. Relative rotational state distributions of OH products from overtone-vibration-induced unimolecular decomposition of HOOH. The solid bars are populations for excitation of the main local mode transition (6v0H) and hatched bars are populations for excitation of the combination transition (6v0H + v ). The quantum number N denotes the rotational OH angular momentum. Figures 4a and 4b show results obtained probing the Q, and R, branches, respectively, of OH. The error bars in Fig. 4(a) show the maximum range of values obtained and are typical of the uncertainties for all states. (Reproduced with permission from Ref. 39.)...

In local-mode sampling an individual local mode such as a CH bond in benzene is excited [28]. This type of trajectory calculation has been performed to determine the population of a local-mode state a) versus time, from which the absorption linewidth of the overtone state may be determined [29]. Good agreement has been found with both experimental and quantum mechanically calculated overtone linewidths for benzene [30] and linear alkanes [31]. 

The survival probability for the n = 3 overtone of benzene has been determined by a time-dependent quantum mechanical calculation based on a 16-mode planar benzene model (5 CH stretch modes are inactive out of the 21 planar modes). All states for these modes are treated in the calculation. The = 3 zero-order overtone state is assumed to be a state with three quanta in one C—H internal coordinate (i.e., a local mode). The quantum survival probability is plotted in figure 4.13. It is similar to the experimental P (t) in that there is a rapid fall-olT at short times, followed by multiple small recurrences. This agreement supports the interpretation that the broad absorption... 

Comprehensive data and assignments of nonfundamental modes were reported [7, 37]. Overtones of the v(CH) modes have been measured on liquid and gaseous Ge(CH3)4 up to 6 v (15818 cm ) and have been assigned on the basis of the local-mode model. This gave localmode CH stretching frequencies of 2990.2 + 0.9 cm for the vapor and 2988 + 4 cm for the liquid. The data are compared for M(CH3)4 compounds (M = C, Si, Ge, Sn) and bandwidths are related to theories of vibrational redistribution from highly excited local-mode states [106]. 

Selective bond breaking has been demonstrated with HOD by first exciting the fourth overtone (local mode) of the OH bond and then photodissociating the molecule via the A X transition. The A <— X transition is red shifted (hot-band absorption) into the 240-270 nm region and the dissociation of the OH bond, relative to the OD bond, is enhanced by a factor of 15. This type of process is referred to as vibrationally mediated photodissociation and can be a very effective approach, provided the initial vibrational excitation remains localized in one chemical bond for a sufficient length of time to allow further excitation and dissociation. In the case of HOD it is clear that randomization of the vibrational energy is slower than the photodissociation step, and this further emphasizes the direct and impulsive nature of dissociation on the A Bi-state PES. 

Actually, the energies of vibrational states of molecules can be described by both models, where the NM model expresses well low vibrational states and the LM model modes that are localized in a particular group of atoms. In most cases, overtones of hydride stretching vibrations, that is, X—(X = C, N or O) are better described by the LM model due to their relatively small couplings to other bonds. 

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