banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Cartesian coupled coherent states simulations: Ne n Br2 dissociation as a test case
Rent this article for


Image of FIG. 1.
FIG. 1.

Schematic of Br2Ne showing the momenta contributions to the momenta of the atoms from the Morse potentials. The numbers below the atom names are the indices used to reference the atoms. Show x, y, and z axes.

Image of FIG. 2.
FIG. 2.

Typical distribution of points in the Br–Br phase space for the different sampling methods for νBrBr = 25. Panel (a) shows the points chosen using the WFNMC selection process, note the increased density around q = 3 · 75 Å, p = 0 u Å fs−1. The points in panel (b) were chosen using the EW selection method: open squares are chosen with σ = 1 and the solid circles with σ = 5. Panel (c) shows a set of points chosen with the SRT method. The solid black lines indicate the energy contour for the 25th energy level.

Image of FIG. 3.
FIG. 3.

Panel (a) compares the mean initial wave function densities obtained for different sampling methods. The plotted densities are each the mean of the densities from ten basis sets each with 250 basis functions. For clarity, the density has been multiplied by 2 for r < 3.6 Å. Panel (b) shows the result of averaging the SRT wave function using Eq. (31) before calculating density profile. The average is calculated over the same set of initial wave functions as is the mean density profile for the SRT sampling in panel (a).

Image of FIG. 4.
FIG. 4.

Husimi quasiprobability density for Br2 bond wave function with νBrBr = 25.

Image of FIG. 5.
FIG. 5.

Mean projections of initial Br2 wave functions for ν = 25 with 250 basis functions onto the true wave functions of the vibrational levels for ν = 25 + δν.

Image of FIG. 6.
FIG. 6.

Time evolution of the cluster survival probability for ν = 25. Squares: Average over ten WFNMC samplings each with 250 basis functions. Dashed line: average fit with τ = 26 · 5 ± 1 · 5 ps. Circles: Average of ten SRT sampling each with 400 basis functions. Dotted line: average fit parameters τ = 25 ± 2 ps. Solid line: previous classical simulations. The inset magnifies the initial 30 ps of the decay curve and shows that the initial plateau present in the classical calculations is corrected by our approach.

Image of FIG. 7.
FIG. 7.

Dissociation rates for different vibrational levels averaged over ten simulations each with 400 basis functions chosen using SRT sampling of the Br–Br mode and WFMC sampling of the Br–Ne mode. Squares: ν = 21. Circles: νBrBr = 22; up triangles: νBrBr = 25; down triangles: νBrBr = 27; and diamonds: νBrBr = 28.

Image of FIG. 8.
FIG. 8.

Comparison of the time evolution of the survival properties determined using classical, semiclassical, and quantum methods. Circles: quantum CCS on the averaged PES; dotted line: classical simulations on the averaged PES; squares: classical simulations on the unaveraged PES; triangles: classical simulations on the unaveraged PES but with the Br2 ZPE added to the Br2 energy; solid line: classical simulations from our previous work.

Image of FIG. 9.
FIG. 9.

Panel (a): Mean probability density for the Br2 mode after 150 ps. The system was prepared with νBrBr = 25, the probability density for the true wave function is shown by the gray line. The dark green line shows the probability density for νBrBr = 24. Panel (b): Mean projection of final wave function onto true wave functions for νBrBr = 25 + δν. The mode is clearly at δν = −1 as is found experimentally.

Image of FIG. 10.
FIG. 10.

Demonstration that nondissociated basis functions remain coupled throughout the simulation. The coupling reduces with time as the other basis functions dissociate. Red line, left-hand axis, basis function probability. Blue and green lines, right-hand axis, the two Br–Ne separations.

Image of FIG. 11.
FIG. 11.

Multistage decay of tetra-atomic (top) and penta-atomic (bottom) clusters. The lines that descend from the top left show the probability of finding clusters with at least a certain number of bromine atoms. Thus the three lines in the penta-atomic plot show, from left to right, the probability of finding a cluster with three neon atoms, the probability of finding clusters with two or three neon atoms, and finally the probability of finding clusters with one, two, or three neon atoms. The bumps at the bottom show the probability of finding clusters with exactly two neons (left) and exactly one neon (right). The lines on the tetra-atomic plot are defined similarly.


Generic image for table
Table I.

Parameters for the Morse potentials. The Br–Br and Br–Ne interaction parameters are from Ref. 4 while the Ne–Ne interaction parameters are from Ref. 24.

Generic image for table
Table II.

Parameters for Gaussian fits to Morse potentials.

Generic image for table
Table III.

Shape parameters.

Generic image for table
Table IV.

Comparison of lifetimes in picoseconds for different initial Br2 vibrational excitations and with experimental and classical dynamics results. γ(ω0) denotes calculations done with the shape parameters given in Table III that are derived from the ground state vibrational frequencies of the potentials. γ(ν) denotes that the shape parameters depend on the vibrational excitation of the Br2 as described in the main text. The heading “decay” denotes the appearance lifetimes calculated by fitting the dissociation as described in the text. The experimental and quantum lifetimes are for appearance (left column) and disappearance (right column) measurements. The values in brackets are for the appearance of Br2 with a change in the vibrational excitation of Δν = −2 rather than Δν = −1. The experimental, quantum, and classical results are from Refs. 2 and 5, and 7 , respectively.


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Cartesian coupled coherent states simulations: NenBr2 dissociation as a test case