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A study of resonance progressions in the F + HCl → Cl + HF reaction: A lifetime matrix analysis of pre-reactive and post-reactive collision complexes
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10.1063/1.4774057
/content/aip/journal/jcp/138/2/10.1063/1.4774057
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/2/10.1063/1.4774057

Figures

Image of FIG. 1.
FIG. 1.

Adiabatic potential energy surface (PES) for the (a) entrance F + HCl (v = 0); and (b) exit Cl + HF (v′ = 3) channels expressed in the appropriate Jacobi coordinates (R, γ) calculated using the DHTSN-PES of Ref. 36 . Each contour line corresponds to 0.1 kcal/mol. The zero of energy lies at the R → ∞ asymptote for each case.

Image of FIG. 2.
FIG. 2.

The (a) v′ dependence of the cumulative reaction probability of J = 0 F + HCl → Cl + HF (v′); and (b) j′ dependence of the cumulative reaction probability of J = 0 F + HCl → Cl + HF (v′ = 3) as a function of energy. The zero of energy is set to the channel threshold for F + HCl (v = 0, j = 0). The positions of the entrance/exit rotational state thresholds are also given in (a). In (a) results for v′ = 0, 1, 2, and 3 are given by green, pink, blue, and red lines, respectively. In (b) j′ = 5, 6, 7, 8, 9, 10, and 11 are given from the bottom by black, brown, dark blue, light blue, green, pink and red lines.

Image of FIG. 3.
FIG. 3.

The CRP of J = 0–6 F + HCl → Cl + HF reaction calculated at (a) full helicity; (b) blow up of (a); and (c) calculation of J = 2 using limited helicity basis. For visual clarity, the results for J = 2, 3, 4, 5, and 6 are shifted by 1, 2, 3, 4, and 5, respectively. The zero of energy is set at the channel threshold of F + HCl (v = 0, j = 0). Results for J = 0, 1, 2, 3, 4, 5, and 6 are given from the bottom by dotted black, dark blue, pink, red, black, orange and light blue lines in (a) and (b).

Image of FIG. 4.
FIG. 4.

The cumulative elastic probability of J = 0–6 Cl + HF scattering calculated using a full helicity basis is shown in (a) while a narrower energy range expanded view is shown in (b). For visual clarity, the results for each J-value are shifted. The zero of energy is the channel threshold of F + HCl (v = 0, j = 0). The energy range plotted in (a) is 2–4 kcal/mol above the Cl + HF (v′ = 0, j′ = 0) while in (b) it is 3.25–4.00 kcal/mol. Results for J = 0, 1, 2, 3, 4, 5, and 6 are given from the bottom by dotted black, dark blue, pink, red, black, orange and light blue lines in (a) and (b).

Image of FIG. 5.
FIG. 5.

The elastic scattering probability, |S(v′ = 0, j v′ = 0, j′)|2 versus total energy for J = 0 and j′ = 6–11. Each successive curve is displaced upward by 1 for visibility. The energetic threshold for each channel, Cl + HF (v′ = 0, j ), is apparent from the location of the onset of the elastic scattering. The zero of energy is set as the threshold energy of F + HCl (v = 0, j = 0) and the plotted energy corresponds to 2–8 kcal/mol above the Cl + HF (v′ = 0, j′ = 0) threshold. The results for j′ = 6, 7, 8, 9, 10, and 11 are given from the bottom by black, brown, dark blue, light blue, pink and red lines.

Image of FIG. 6.
FIG. 6.

The energy dependence of the largest eigenvalue qmax of the Q-matrix for J = 0 F + HCl reaction. The zero of energy is set as the asymptote energy of F + HCl (v = 0).

Image of FIG. 7.
FIG. 7.

Schematic diagram representing the rotational predissociation model used to assign the progression of resonances seen in F + HCl → Cl + HF.

Image of FIG. 8.
FIG. 8.

Schematic figure of the rotational predissociation picture along the exit channel Jacobi coordinate (R) for Cl + HF (v r ′ = 3). The v R ′ = 2 bound eigenfunction obtained by matrix diagonalization is shown for a number of j′ levels. For the same energy as the ( ) resonance, we plot the bound/continuum wavefunction (obtained from the Numerov method) for the j′−1 channel. For reference, we also show the effective adiabatic potential curves, U j j(R), where results for j′ = 8, 9, 10, 11, and 12 are given in black, green, red, blue, and pink, respectively.

Image of FIG. 9.
FIG. 9.

Cumulative sum of resonance states calculated by the Q-matrix and the rotational predissociation model as a function of total energy from Cl + HF (v′ = 0) for (a) J = 0; and (b) J = 1. The thresholds for the opening of the Cl + HF (v′): v = 1, 2, 3, and F + HCl (v = 0) as well as the position of the adiabatic barrier are also plotted. The zero of energy is set as the asymptote energy of F + HCl (v = 0) and the plotted energy corresponds to 0–40 kcal/mol from the Cl + HF (v′ = 0). The dashed line contains the contribution of all resonances in the model while the dotted line only considers the Δj′ = 1 (short lifetime) resonances.

Tables

Generic image for table
Table I.

Important energetics for the DHTSN-PES: reaction barrier height and van der Waals well depth in kcal/mol with and without harmonic zero point vibrational correction; diatomic B-constants in cm−1.

Generic image for table
Table II.

Threshold energies, En, for the vibrational channels. The primed quantum numbers indicate product channel Cl + HF while the unprimed quantum numbers are the reagent channel F + HCl.

Generic image for table
Table III.

Resonance properties calculated for Cl + HF (v′ = 0) collisions. The resonance energies, in kcal/mol, and lifetimes, in ps, are obtained from the largest eigenvalue of the Q-matrix and the product distribution (partial width ratio Γ i /Γ) is obtained from the square of its eigenvectors. The assignments based on the rotational predissociation model (v R ′,v r ′,j′) as well as the model results, given in parenthesis, are also presented. The results are for the −29.3 to −28.5 kcal/mol range measured with respect to the zero point energy of the F + HCl (v = 0). This corresponds to 3.3–4.1 kcal/mol measured from Cl + HF (v′ = 0) and is the range given in Fig. 4 .

Generic image for table
Table IV.

Same as Table III except that the energy range is for −23.5 to −22.1 kcal/mol from F + HCl (v = 0). Values for j′ = 0–5 are zero so they are ignored in the table.

Generic image for table
Table V.

Resonance characteristics for the J = 0 Q-matrix calculations in the energy range 2.58–3.00 kcal/mol measured from the F + HCl (v = 0, j = 0), corresponding to the range given in Fig. 3 . The energies are given in kcal/mol, while the lifetime is given in ps. The partial widths have been summed over rotational product states to simplify the presentation. The assignment is to either reagent (R) or product (P) van der Waals complexes. To aid visibility, product channel states are underlined.

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2013-01-10
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A study of resonance progressions in the F + HCl → Cl + HF reaction: A lifetime matrix analysis of pre-reactive and post-reactive collision complexes
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/2/10.1063/1.4774057
10.1063/1.4774057
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