Vibrational quasi-continuum

V. S. Letokhov My answer to Prof. Quack is that it is indeed difficult to predict theoretically the effect of intense femtosecond IR pulses on the IVR rate of polyatomic molecules, which is important for the transfer of vibrationally excited molecules from low-lying states to the vibrational quasi-continuum. We are developing the relevant theoretical mechanisms of IR MP E/D of polyatomics since the discovery of this effect for isotopic molecules BC13 and SF6 in 1974-1975.1 hope that it will become more realistic to study experimentally the influence of intense IR pulses on IVR due to the great progress of femtosecond laser technology. 

Transition of Highly Vibrationally Excited CO2 Molecules into the Vibrational Quasi Continuum... 

When the number of quanta exceeds the critical value (5-18) (the so-called Chirikov stochasticity criterion Zaslavskii Chirikov, 1971), the molecular motion becomes quasi random and the modes become mixed in the vibrational quasi continuum. In the general case of polyatomic molecules, the critical excitation level decreases with number N of... 

If temperatures related to different vibrational modes are different, then transition to quasi continuum takes place along the mode characterized by the highest temperature. Let us specify the asymmetric vibrational temperature as a higher one (Lva > fys). Transition to the vibrational quasi continuum then takes place during excitation along the asymmetric mode, and the vibrational quantum number for the symmetric modes can be chosen as fixed on its average value Til ... 

The result of summations in Eqn. (50) is largely determined by the spectrum of the intramolecular subsystem final state. The spectrum can be either discrete or continuous. For instance, in the case of H-atom abstraction from the molecule by the methyl radical the value of the thermal effect of the reaction is such that the energy evolved may be sufficient only to excite the fourth vibration level of the C-H bond of the CH4 molecule. In such small molecules the quasi-continuum region lies much higher [157]. For the symmetric reaction of radical pair transformation in dimethylglyoxime the thermal effect is nought, and the discreteness of the final intramolecular spectrum, in this case, is evident. If, however, as a result of the reaction, highly excited multiatom molecules are formed or dissociation of the excited molecules occurs, the intramolecular subsystem final state spectrum is continuous. 

This two-state quantum beat example is identical to the doorway mediated non-radiative decay problem frequently encountered in polyatomic molecule Intramolecular Vibrational Redistribution (IVR), Inter-System Crossing (ISC), Internal Conversion (IC), and compound anticrossings. There is a single, narrow bright state. It couples to a single, broad, and dark doorway state. The width of the doorway state is determined by the rate of its Fermi Golden Rule decay into a quasi-continuum of dark states. 

When a bright basis-state is embedded in a dense manifold (quasi-continuum) of dark basis-states, a variety of dynamical processes ensue (Bixon and Jortner, 1968 Rhodes, 1983). These include Intramolecular Vibrational Redistribution (IVR), Inter-System Crossing (ISC), and Internal Conversion (IC). At t = 0, the bright basis state, which is not an eigenstate of H, is prepared, k(O) = bright ... 

This kinetic approximation assumes a single vibrational temperature 77 for CO2 molecules and, therefore, is sometimes referred to as quasi equilibrium of vibrational modes. As one can see from (5-20), most of the vibrationally excited molecules can be considered as being in quasi continuum in this case. Vibrational kinetics of polyatomic molecules in quasi continuum was discussed in Chapter 3. The CO2 dissociation rate is limited not by elementary dissociation itself, but via energy transfer from a low to high vibrational excitation level of the molecule in the W-relaxation processes. Such a kinetic situation was referred to in Chapter 3 as the fast reaction limit. The population of highly excited states with vibrational energy E depends in this case on the number of vibrational degrees of freedom 5 and is proportional to the density of the vibrational states p E) a. The... 

Numerically, E (15-20) x quasi continuum actually takes place at very high levels of excitation of the asymmetric vibrational mode, close to the dissociation energy (see Fig. 5-14). Thus, most of the vibrational distribution function relevant to CO2 dissociation in this case, in contrast to the one-temperature approach, is not continuous but discrete. The discrete distribution function /(Va, Vs) over vibrational energies (5-16) can be presented analytically according to Licalter (1975a,b, 1976) in the Treanor form ... 

Most of the symbols in (5-26) are the same as those in expression (5-22) for the dissociation rate coefficient in a one-temperature approximation. Additionally, d = Aty/XasUl is a vibrational quantum number corresponding to the transition to quasi continuum along the asymmetric mode (5-24) f E) is the vibrational energy-dependent ratio of rate coefficients of VT and W relaxation (see Fig. 5-12) y = is the logarithmic sensitivity of the VTAA relaxation ratio to vibrational energy accumulated on the asymmetric mode (see Fig. 5-12) and Xm is the effective CO2 oscillation anharmonicity in quasi continuum (for... 

Continuum. Explain the mechanism for mixing different vibrational modes of CO2 molecules when the oscillation amplitudes are relatively high. Consider the influence of vibrational beating on energy transfer between modes and the transition of a polyatomic molecule to a quasi continuum of vibrational states. Analyze how the critical maximum number of quanta on an individual mode depends on the number of vibrational modes (see (5-18) and below). 

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