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.
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.
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).
Husimi quasiprobability density for Br2 bond wave function with νBrBr = 25.
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.
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.
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.
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.
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.
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.
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.
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.
Parameters for Gaussian fits to Morse potentials.
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.
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