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The workings of a molecular thermometer: The vibrational excitation of carbon tetrachloride by a solvent
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38.Intramolecular frequencies undergo fluctuations and shifts in a condensed phase, phenomena which the most accurate standard version of classical Landau-Teller theory handles by using the average intramolecular frequencies appropriate to be the particular liquid solution.
38.The and E Raman peaks of have been observed to shift −1 and +5 cm−1, respectively, in going from the gas phase to cyclohexane solution [ R. J. H. Clark and P. D. Mitchell, J. Chem. Soc., Faraday Trans. 2 71, 515 (1975)]. Since solvent shifts of this magnitude would have virtually no effect on the predicted solute-solvent energy transfer rates of this paper, we shall simply assume the vibrational frequencies of are fixed at the gas-phase experimental values. Note, however, that more care is sometimes required for Landau-Teller-predicted IVR rates; solvent-induced fluctuations can cause dramatic errors if the fluctuations allow intramolecular states to become nearly degenerate. See Ref. 34 for a clear discussion of this point.
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48.As we have emphasized in Refs. 7, 10, and 12, while instantaneous-pair (IP) theory is not completely unrelated to the traditional independent-binary-collision (IBC) model for vibrational relaxation, it does have a number of substantial differences from it. Unlike IBC theory, IP theory does not assume that dynamics of dense liquids features discrete, well-defined, two-particle collision events. Instead, it looks upon one liquid configuration at a time, and notes that the dynamic range of solute/solvent forces is so large that the high-frequency components of each configuration’s forces are almost always going to be completely dominated by those from its single most prominent solvent/solute pair. The final result is then an equilibrium average over liquid configurations.
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52.The simulation was initiated by placing 108 Ar atoms in a fcc lattice at a density without the being present. The was then substituted for a cluster of six of the Ar atoms, leaving an Ar density of
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54.Note that this factor is a geometry, and not a degeneracy, factor. Indeed a simple geometric argument suggests that the two results should have almost exactly a ratio of 2: Neglecting the time dependence of the θ angles in Eqs. (2.12) and (2.13) (probably a good approximation, see Ref. 10), and neglecting any anisotropy in the solvent distribution around the solute, we would predict
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56.Our estimate comes from assuming that the ratio of the rate for populating the mode to that for the with 1/2 the geometric factor (Ref. 54) and The resulting exponential-gap-law constant (128 cm−1) is then used to estimate the rates for populating the two modes. We assume that only a single component of each triply degenerate mode contributes and that the and modes have identical geometric prefactors. In a recent paper (Ref. 55) we show that such exponential gap laws can actually be derived from the instantaneous-pair formalism and that it is quite plausible for an exponential gap law to govern the relaxation of all of the modes.
57.Note, however, that Ref. 21 reported results for the and two modes, but not the E mode.
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59.Note that the units of the frequency-domain vibrational frictions reported in Table II should be
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