3P167
Analysis on the Signs of Resonances in the F+HCl→HF(v’=3)+Cl Reaction（IAMS/University of Colorado）○Kaito Takahashi, Michael Hayes, Rex T. Skodje＜Introduction＞
The F+HCl(v,j)→HF(v’,j’)+Cl reaction is a prototypical hydrogen exchange reaction, and belongs to theheavy-light-heavy reaction type which is studied with great interest in molecular dynamics. In thistype of reactions, the light atom vibration between the two heavy atoms mediates the formation ofmeta-stable resonance states. In addition, due to the large exothermic nature of this reaction, the HF
molecule results in a highly vibrationally excited state. Therefore, it is expected that these dynamicalresonances may appear for this system. However, theoretical analyses on these resonances using
theoretical potential energy surfaces have not been performed.
＜Calculation Method＞
For this system, Deskevich et al. have recently calculated an ab initio potential energy surface1 using thefull valence MRCI+Q method by taking the complete basis extrapolation using aug-cc-pVnZ basis,
where n=2-4 (MOLPRO program2). Hayes et al. performed detailed dynamics calculation using thissurface3 (ABC program4) and reported the cumulative reaction probability for the J=0 channel.
＜Results＞
In the figure on the left, we present the calculated
cumulative reaction probability (black line) versus thecollision energy. In addition to the interesting step feature
seen at around 5, 6, and 7 kcal / mol, one is able torecognize the sharp peak structures signifying theexistence of resonances. It is expected that theseresonances will play a vital role in determining the rate in
low collision energies, therefore it is very important toassign these resonances. Furthermore, it can be seen that in the region between 4 to 5 kcal / mol, thepeak features disappear. It is of ones interest to understand the origin of this disappearance.
With intent to assign these resonance states, we decomposed the cumulative reaction probability into thecontribution from final state vibrational levels. It can easily be noticed that the main contribution for
the resonance is coming from the HCl(v=0)+F→HF(v’=3)+Cl channel, with small features comingfrom the v’=2 channel (at the energies that we are looking at, the channels for HCl(v>1) are closed).
＜Theory & Discussion＞
A three atom reaction for J=0 is expressed using the following Hamiltonian,H =−∂2h2 ∂2 h2 ˆ2−−
j + V ( R, r , γ ) ,2 µ A, BC ∂R 2 2 µ BC ∂r 2 2 I
h2

where R, r , γ are reactant or product Jacobi coordinates. The three reactant (product) Jacobi
coordinates for the present reaction describe the slow Cl F translational motion (R), the fast HCl (HF)
stretching vibration (r), and the HCl (HF) rotation or ClHF bend (γ). Assuming that the fast variable r
conserves quantum number (or classical action), we performed the adiabatic separation of this freedom
from the other two freedoms; thus, by solving the one-dimensional vibrational equation for a given Rand γ, we obtain the adiabatic two-dimensional
Hamiltonian (vr labels the vibrational state)

H vr = −v=0 reactant Jacobi Coordinate
Adiabatic PES

v’=3 product Jacobi Coordinate
Adiabatic PES∂2h2 ˆ2−
j + V vr ( R, γ ) ,22µ A, BC ∂R2Ih2

Since our discussion will be concentrated on theHCl(v=0)+F→HF(v’=3) +Cl channel the respective adiabatic potential energy surface is given in thefigure on the left of the equation. One will easily notice the existence of wells on the adiabatic
potential energy surface allowing for the dynamical resonance trappings.
In the figure on the left, we present the separation of the v’=3
cumulative reaction probability contribution into their j’ statecontributions. One of the key points to notice is that theresonance features for a certain energy regime is given froma reaction to a certain j’ state in the v’=3 product state.
Furthermore, the resulting product states are highly excitedrotational states, therefore we assume that the rotationalmotion may be adiabatically separated from the muchslower translational motion (R). Thereby giving us a simplified one-dimensional (1-D) Hamiltonian ofH vr j ' = −∂2+ V vr j ' ( R )22 µ A, BC ∂Rh2

H vr j ' v R v r j ' = E vvRr j ' v R v r j 'Each resonance state may be assigned using vR, the quantum
number of the 1-D vibrational state on the adiabatic potential
curve labeled by vr and j’(left figure). In the table below,
we compare the eigenvalue for a given j’ vR state with thepeak positions in the cumulative reaction probability, and one will notice that these peaks are easily
assigned, energetically, using this simple model.
peak Productresonance resonance Evvr j 'R
j' quanta vR quanta (kcal / mol) (kcal / mol) j' state
78
2.89
2.88
68
11
3.95
3.91
7
10
4
5.33
5.34
911
1
6.02
6.08
10
112
6.21
6.22
10
11
3
6.36
6.36
10
122
7.48
7.4411The lowering of one quanta in the j’ state seen in going fromthe resonance state to the product state. This is analogous to thepredissociation of van dar Waals complexes. In the figure on
the left, we present a simple visualization of this. For a special
collision energy, the FHCl molecule gets trapped in the j’potential curve, in a state labeled with a quantum number vR(the resonance). Then, this bound state (for R) couples with thecontinuum state (for R) of the j’-1 potential curve causing forthe dissociation (e.g. pink to blue, blue to red).
＜Conclusion＞
Using a simple adiabatic model, the resonance peak structures seen in cumulative reaction probability
were assigned using the j’ and vR quantum numbers for the γ and R product Jacobi coordinates. Thesestates mainly couple with the ∆j’= -1 continuum states. We are presently performing wave packet
calculations to calculate the life time of these resonances to obtain an understanding on thedisappearance seen between 4 to 5 kcal / mol.
＜Reference＞
1:Deskevich et al. to be published. 2:www.molpro.net. 3:Hayes et al. to be published. 4:Manolopouolos
et al. Comput. Phys. Commun. 2000, 133, 128. 5:R. T. Skodje, Annu. Rev. Phys. Chem. 1993, 44, 145.
＜Acknowledgement＞
We thank Mike Deskevich and David Nesbitt for providing us the potential energy surface