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Errors stated here and elsewhere are ±1 standard deviation
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Errors stated here and elsewhere are ±1 standard deviation.
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0042652954
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note
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The vibrational energy in thermal equilibration was calculated using the well known statistical formula hν/(exp(hν/kT)-1), for each individual mode of frequency ν, at the equivalent temperature derived from the Arrhenius law. In general, statistical rate constants are predicted within the more sophisticated framework of Rice-Ramsperger-Kassel-Marcus (RRKM) theory, which is reviewed in Ref. 25. In the present system, however, the absence of a recombination barrier leads to an ill-defined transition state. High level variational RRKM calculations to account for this difficulty are underway, as are quantum mechanical simulations. Both will be published in due course.
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note
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The anisotropy r(t) calculated according to Eq. (1) and plotted in Fig. 2(b) is the convoluted anisotropy. Thus, it exhibits a slower decay than the ∼60 fs obtained by the described fitting routine (Ref. 29) which yields the deconvoluted decay time-constant.
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30
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0041651028
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note
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In a one-photon excitation of an isotropic molecular ensemble, the maximum attainable anisotropy is 0.4, as derived in Ref. 26. Following the same derivation, a 5-photon process exhibits a maximum value of 0.77, while the value for 6-photon excitation is 0.8. The decay time constant is a complicated function of the varying moments of inertia and rotational energy distributions of the diazomethane and nascent carbene fragments along the reaction coordinate. A numerical model based on inertial (i.e., collisionless) free rotor decorrelation of thermally distributed methylene and diazomethane accounted reasonably well for the data, but due to uncertainties in the dissociation geometry and rotational energetics, as well as loss of precision from the convolution of a short decay with a relatively long pump-probe pulsewidth, we hesitate to ascribe significance to the decay time itself. The inferences drawn above from the anisotropy data depend only on the sign of the anisotropy, not the decay rate.
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