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Vibrational relaxation of the CH stretch fundamental in liquid
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Image of FIG. 1.
FIG. 1.

The six geometries for the dimer used for the ab initio computations. Interaction energies for each of them have been computed as a function of the C–C distance. (a) facing , (b) CH facing , (c) linear CH–HC, (d) linear CBr–HC, (e) crisscross, and (f) “locked.”

Image of FIG. 2.
FIG. 2.

Interaction energy for the six geometries. The ab initio values are shown as points whereas the curves are obtained through the model potential. (a) facing (+), CH facing (×), and linear CH–HC (∗). (b) Linear CBr–HC (+), crisscross (×), and locked (∗).

Image of FIG. 3.
FIG. 3.

Comparison of interaction energy using the adjusted and unadjusted potentials for two geometries. CH facing : adjusted (---), unadjusted (–––); crisscross: unadjusted (---), adjusted (⋯).

Image of FIG. 4.
FIG. 4.

Plot of energies of available acceptor states. Only those states that have no quanta of CH stretch excitation have been shown. The only exception is the CH stretch fundamental itself, shown with the long dotted line. (a) States in the range sorted by the change in number of quanta from . Only states that have three quanta or less in the low frequency umbrella and CBr bend modes are shown. (b) Set of candidates chosen for the Landau-Teller calculation.

Image of FIG. 5.
FIG. 5.

Plots of , the Fourier transform of the normalized correlation function, for (⋯), (- - -), and (—).

Image of FIG. 6.
FIG. 6.

Plots of rate of population transfer between and computed as a function of frequency. The plots differ in the terms in of Eq. (2) that are retained. Linear (-∙-∙-), up to quadratic (- - -), up to cubic (—), and up to quadratic (⋯).

Image of FIG. 7.
FIG. 7.

Intramolecular couplings between basis functions in the Van Vleck representation. All functions are of symmetry. The label is for a basis function with two quanta in mode 4 and one quantum in mode 5.

Image of FIG. 8.
FIG. 8.

Plots of population of the CH stretch, , obtained from two-state time-dependent calculations involving and for different values of the scale factor . The rates of decay, obtained with exponential fits to these plots, are given in Table VII.

Image of FIG. 9.
FIG. 9.

Plots of population of the CH stretch, , obtained from two-state time-dependent calculations involving and the near-resonant state. The dashed line is for a calculation with diagonal couplings set to zero for both states. The solid and dotted lines have the included, the latter of which employs a linear combination of the above two eigenfunctions to represent the CH stretch state (see Sec. IV C).


Generic image for table
Table I.

Energies (in ) of some states obtained from gas phase calculations (Ref. 33) of along with experimental condensed phase values (Ref. 10). Note that the experimental energies of and , as provided in Ref. 10, are estimates using the , , and frequencies. Hence no symmetry labels are implied for these two numbers.

Generic image for table
Table II.

Higher order solute-solvent coupling terms used in Eq. (2). The here are in curvilinear normal coordinates (Ref. 33). As noted in Sec. IV, the quartic terms are not included in obtaining the final results.

Generic image for table
Table III.

Optimized unadjusted parameters for the model potential. The and values have units of . is fixed at 20°. Adjusted parameters are obtained by applying Eq. (11) with to those in this table.

Generic image for table
Table IV.

Rotational decay times with the adjusted model potential at different temperatures. The experimental values are from the work of Seifert and Kadarisman (Ref. 13).

Generic image for table
Table V.

Landau-Teller time scales for CH stretch population decay to various states. Only those states are listed for which the is less than . No quantum correction factor has been applied. The states are also distinguished by the value for their leading basis function (Ref. 33). Negative values indicate that the state is below .

Generic image for table
Table VI.

Comparison of time scales of decay from to each of , , and using eigenfunctions determined in three basis sets. All numbers are in picoseconds. and refer to three- and four-function basis sets described in the text. The column subheadings “All” and “Diag” refer to whether the include all couplings between basis functions [Eq. (12)] or only select diagonal ones [Eq. (13)].

Generic image for table
Table VII.

Time scales of CH stretch decay to the state using the time-dependent approach for different values of the scale factor . The time scales were obtained from single exponential fits to the of Fig. 8 in the range of in each case.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Vibrational relaxation of the CH stretch fundamental in liquid CHBr3