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Semiclassical description of vibrational quantum coherence in a three dimensional cluster: A forward-backward initial value representation implementation
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Image of FIG. 1.
FIG. 1.

Schematic depiction of the semiclassical FB IVR method. A classical trajectory starting from initial condition undergoes a momentum jump at time , then it is propagated backward to time 0 terminating at .

Image of FIG. 2.
FIG. 2.

The time-dependent probability distribution for a one-dimensional model of the iodine molecule. The upper panel shows the comparison of FB-IVR result (solid line) with the quantum (DVR) calculation (dotted line) at 196 fs. For reference, the initial probability function (dashed line) is also shown in the upper panel. The lower panel shows the same comparison between FB-IVR and quantum (DVR) results at a longer time 640 fs. All parameters are taken from Ref. 26.

Image of FIG. 3.
FIG. 3.

Time evolution of the probability distribution function of the iodine molecule in three dimensions. The initial distribution (not shown completely) corresponds to the coherent state of the iodine molecule at its electronic ground state. After photoexcitation, the probability distribution evolves on the electronic excited state potential surface. Results are shown for , 88, 176, 265, and 352 fs. The harmonic vibrational period of the excited state is about 276 fs.

Image of FIG. 4.
FIG. 4.

Comparison of the FB IVR result for the probability distribution of iodine at time to that given by the LSC IVR method. The inset shows the results for larger distances.

Image of FIG. 5.
FIG. 5.

Same as Fig. 4 except for longer times.

Image of FIG. 6.
FIG. 6.

Time dependent probability distribution of iodine clustered with one or six argon atoms at time . All results are calculated by using FB-IVR in full three dimensional space for all the atoms. The probability distribution of the free iodine molecule is shown (solid line) for comparison. The dotted line is for the case of one argon atom and the dashed line is the result with six argon atoms. The inset shows the results for larger distances corresponding to dissociated .


Generic image for table
Table I.

Parameters for the Morse potential. [Atomic interactions for excited state of iodine molecule and for I–Ar, used in Eq. (3.6a) (taken from Ref. 36)].


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Semiclassical description of vibrational quantum coherence in a three dimensional I2Arn(n≤6) cluster: A forward-backward initial value representation implementation