Nonrandom excitation

In the previous sections random sampling procedures were described for preparing a classical microcanonical ensemble of states. However, for comparison with experiment and to study the rate of intramolecular vibrational energy redistribution (IVR) [12,27] within a molecule, it is important to sample the states (i.e., phase space) of the molecule nonrandomly. Here, both normal and local mode [28] quasi-classical [2-4] sampling schemes are described for nonrandom excitation. 

In the following parts of this section, the selection of two different types of initial conditions for a unimolecular reactant are described. Selecting a microcanonical ensemble of states is described first. These initial conditions are never realized in an actual experiment, but are important for identifying intrinsic non-RRKM behavior and studying a molecule s intramolecular dynamics. The last procedure described is the selection of initial conditions for the nonrandom excitation of initial states for a molecule, as occurs in actual experiments. 

Here, the nonrandom excitation of C2H4F is described by the dynamics of the F - - C2H4 bimolecular reaction. To simulate chemical activation, proper initial conditions must be chosen for the reactants and for their relative properties. The procedure for choosing initial conditions for the reactant s relative properties is given below in the discussion of bimolecular reactions. The quasi-classical method may be used to select initial conditions for molecular reactants. The energy for a symmetric-top polyatomic molecule in a specific vibrational-rotational state may be approximated by the harmonic oscilla-tor/rigid rotor model... 

The classical trajectory calculations were performed at fixed total energies with both random and nonrandom excitation of HCC. Orthant sampling was used to choose the random initial conditions. 

The effect of nonrandomly exciting HCC was accomplished by simulating the chemical activation reaction H + C=C > H-C-C. Initial conditions were chosen by varying the H + C=C relative translational energy E rel vibrational energy E-y, and C=C rotational... 

General Method. In systems where the chromophore distribution is other than random in an infinite volume, two Important points must be taken into account in the calculation of G (t), regardless of which formalism is used to describe the transport dynamics. First, in performing the spatial average over all configurations of molecules surrounding the initially excited molecule, the appropriate radial distribution function must be employed. This is true for nonrandom distributions in infinite or finite systems. 

Carlo sampling schemes are described for exciting A randomly with a microcanonical ensemble of states and nonrandomly with specific state selection. For pedagogical purposes, selecting a microcanonical ensemble for a normal mode Hamiltonian is described first. 

The search for nonrandom energy flow finally succeeded when Rynbrandt and Rabinovitch (1970, 1971a,b) reacted singlet methylene with hexafluorovinylcyclopro-pane to produce a bi-cyclic excited molecule. 

In the spectra of nonrandomly oriented polymers, the intensity and polarization of the Raman scattered light are dependent on the polarization of the exciting light relative to the orientation of the molecules (35). If the orientation of the molecules is known, comparison of spectra recorded with different polarizations of the exciting light yields useful information about the directionality of the vibrational motions. Conversely, information about molecular orientation can be gained if the directionality of the vibrations is... 

Investigation of the PFR of 2-naphthyl acetate in poly(methyl methacrylate) by means of time-resolved fluorescence has shown that the photoproducts act as long-range quenchers for the starting ester. This confirms singlet excited state involvement and suggests a nonrandom distribution of the generated chromophores [27]. 

If bottlenecks restrict intramolecular vibrational energy redistribution," the unimolecular dissociation is not random and not in accord with equation (4). There is considerable interest in identifying which unimolecular reactions do not obey equation (4). In this section Monte Carlo sampling schemes are described for exciting A randomly with a micro-canonical ensemble of states and nonrandomly with mode selective excitation. For pedagogical purposes, selecting a microcanonical ensemble for a normal mode Hamiltonian is described first. 

The So Si internal conversion step excites So nonrandomly. A microcanonical ensemble of states is not prepared, although So may relax to this ensemble after efficient and complete IVR. Thus, to accurately simulate the intramolecular and unimolecular dynamics of the excited So molecule, it is necessary to choose correct initial conditions for So- The specific vibrational excitations on So have probabilities proportional to Ajj, where i is the initial vibrational level on Si and j is the vibrational level on So. " The term includes a Franck-Condon factor so that only certain types of So mode excitations have high probabilities and therefore the excitation of So may be highly... 

In recent experiments the vibrational manifold of the ground electronic state has been directly excited by either single-step one-photon or multi-step infrared multiphoton absorption. An enor-mour literature exists with respect to the infrared multiphoton experiments. Although very few of these experiments have been designed to reveal dynamical information about unimolecular reactions, some have yielded unimolecular branching ratios and product energy distributions.The manner in which molecules are excited by infrared multiphoton absorption is not clearly understood at this time. For some cases the excitation appears to be nonrandom, while for other cases it seems to be nearly as random as is thermal acti-... 

In Fig. 3 trajectory lifetime distributions are shown for H-CEC-Cl excited nonrandomly at a total energy of 200 kcal/mol. ... 

Apparent non-RRKH behavior has been detected in classical gas bulb" chemical activation and in infrared multiphoton absorption experiments.Thus, by localizing the energy in a molecule it is experimentally possible to promote or diminish a uniraolecular decomposition channel. Experiments in which a molecule is excited nonrandomly and then rate constants are measured as a function of... 

H + C2H1,. following nonrandom H + C2Hi. C2H5 and random excitation. Total energy is 100 kcal/mol. 

Fig. 5. Classical trajectory relative translational energy distributions for C2H5 H -F C2H. at a total energy of 100 kcal/mol. In plots (a)-(c) C2H5 is excited randomly. In plots (d)-(f), it is excited nonrandomly by H + C2HLJ. C2H5. Plots (a) and (d) are for the exit-channel barrier, plots (b) and (e) are for the products, and plots (c) and (f) are for = [E g2.(P oducts) - (barrier) ] <...

Fig. 9. Representation of the HCC molecular phase space and lifetime distributions following random and nonrandom (beam) excitation (50 kcal/mol total energy). Dashed lines are the random lifetime distributions and have identical probability values in both plots. Both time axes have the same scale and a maximum time of 1,5 X s.

In principle, photoactivation allows the selection of a well-defined reactant state. In practice, the quasicontinuous absorption of polyatomic molecules, arising from the high internal state density and the thermal distribution of absorbers over closely packed rovibrational levels, usually frustrate this desirable objective. In single-photon excitation relying on fast internal conversion from an electronically excited state, the distribution is unlikely to be completely random, or to be entirely independent of excitation wavelength, but it is not possible to control the initial nonrandomness. The results of such experiments (see Section 1.4.3) are consistent with rapid energy randomization but no direct tests of the random lifetime assumption have been made. 

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