Competition between electronic and vibrational predissociation in Ar–I2(B): a molecular dynamics with quantum transitions study

doi:10.1016/S0301-0104(98)00377-2

Chemical Physics

Volume 240, Issues 1–2, 1 January 1999, Pages 229-239

https://doi.org/10.1016/S0301-0104(98)00377-2 Get rights and content

Abstract

A theoretical study of the competition between vibrational and electronic predissociation of the Van der Waals complex Ar⋯I₂(B) using the Molecular Dynamics with Quantum Transitions (MDQT) method of Tully, is presented. The electronic predissociation is modeled by surface hopping from the B to the a state with probabilities given by the Franck–Condon factors between them. The vibration of I₂ is treated quantum mechanically using a Discrete Variable Representation (DVR) while the relative motion of the Ar atom with respect to I₂ is treated classically. The agreement between calculated and measured predissociation rates is very good. Analysis of the results indicate that first order rate equations are not adequate to describe the time dependent signals. This is due to the dependance of the electronic predissociation rates on the vibrational quantum number of the intermediate states of the process.

Introduction

One of the current goals in the field of chemical physics and molecular dynamics is to understand the role of weak intermolecular forces of the Van der Waals type (solvation bonds) in chemical reactivity and relaxation. Van der Waals clusters in which several atoms or molecules are bound to a chromophore provide ideal model systems to investigate photofragmentation and relaxation processes affected by these weak intermolecular interactions 1, 2, 3, 4, 5, 6, 7, bridging the gap between gas phase isolated molecules and molecules solvated in liquids and cryogenic matrices.

The iodine molecule has been studied under a wide range of experimental conditions in compressed gases 8, 9, liquids 10, 11, 12, 13, and matrices 14, 15. The M_n⋯I₂ clusters, where M is a rare gas atom, have been extensively studied in the excitation region of the bound levels of the excited B state, both experimentally 1, 16, 17, 18, 19, 20 and theoretically 2, 21. These studies have provided a wealth of crucial information, not only on the structure of the complexes but also on the dynamics of vibrational and electronic predissociation.

When the Van der Waals molecule M⋯I₂ is excited in the spectral region of the I₂(B←X) transition, the fluorescence excitation spectrum shows broadened features which are attributed to quasibound levels associated to M⋯I₂(B,v′). These resonances decay by two competing intramolecular relaxation processes 1, 2, 20: vibrational predissociation (VP)

$M ⋯ I_{2} (B,v′) → VP M + I_{2} (B,v≤v′)$ and complex-induced electronic predissociation (EP) $M ⋯ I_{2} (B,v′) → EP M + I (^{2} P_{3/2})+ I (^{2} P_{3/2})$

Since channel (1) produces electronically excited I₂ fragments which can fluoresce while channel (2) is dark, measurements of the I₂ fluorescence quantum yield in conjunction with Ar⋯I₂ absorption spectra can provide the relative importance of vibrational predissociation as compared to electronic predissociation [20].

For Ar⋯I₂ the relative importance of vibrational and electronic predissociation depends very much on the vibrational quantum number v′ of the initially excited state 1, 2, 3, 21. For low vibrational levels (v′<15) electronic predissociation prevails, but for highly excited levels (v′>30) vibrational predissociation dominates. In the range 15<v′<30, where the two channels compete, it was found that the electronic predissociation rates oscillate as a function of v′ and these oscillations were similar to those observed in the electric-field-induced quenching of the B state of isolated I₂ [16]. This suggests that the repulsive potential energy surface responsible for the complex-induced electronic predissociation, channel (2), is the same as the one involved in the electric-field-induced predissociation, namely the a(³Π_1g) [16]. This was born out by a Franck–Condon study of Ar⋯I₂ electronic predissociation [22], which demonstrated that the other possible candidate, namely the B′′ state, could not reproduce the observed oscillations in the vibrational predissociation rate. It was also shown that in order to reproduce these oscillations the a state Van der Waals interaction could be chosen to be either 100 cm⁻¹ more attractive or 900 cm⁻¹ more repulsive than B state interaction. In subsequent wave-packet studies 23, 24, it was shown that the a state Ar⋯I₂ interaction had to be attractive, since for a repulsive interaction the oscillations of the lifetime with v desappear. These wave-packet studies further showed that with an attractive a-state Ar⋯I₂ interaction, the Ar atom can be considered as a spectator and the Franck–Condon approximation is valid.

On the other hand, vibrational predissociation of Ar⋯I₂ without the inclusion of the electronic predissociation channel has been studied by Gray and Roncero 25, 26. They concluded that vibrational predissociation in this cluster proceeds via an IVR mechanism in the sparse limit. This should give an erratic behaviour of the linewidth as a function of the initial vibrational level of I₂. However, the experiments 19, 20 indicate that IVR in this system is in the statistical limit, since the linewidth for the first excited Van der Waals level is very similar to the one for the zero-point energy level and this is not what one would expect in the sparse limit. It can be argued that all these calculations were performed for total angular momentum J=0 and that rotational excitation increases the density of levels for IVR as has been shown for the case of Ar⋯Cl₂ [27]. This has been investigated by Goldfield and Gray [28] who found no evidence of a transition to the statistical limit even for J as large as 24.

All the calculations performed up to now on this system have treated vibrational and electronic predissociation independently. Since electronic predissociation will provide a linewidth to each one of the intermediate levels in the IVR process, this contribution could make the system undergo a transition from the sparse to the statistical limit. It is the purpose of this paper to present model calculations to study the effect of the combination of vibrational and electronic predissociation on the Ar⋯I₂ fragmentation dynamics, in order to assess the importance of electronic predissociation on the vibrational energy redistribution prior to fragmentation. Recently [29], we have shown that vibrational predissociation can be described quite satisfactorily by the technique of Molecular Dynamics with Quantum Transitions (MDQT) as developed recently by Tully 30, 31, 32. Hence in this work we study the competition between vibrational predissociation and electronic predissociation using MDQT. Electronic predissociation is modeled by surface hopping from the B to the a state with probabilities given by the Franck–Condon factors between these two states at the energy of the bound levels of the B state. The vibration of I₂ is treated quantum mechanically using a Discrete Variable Representation (DVR) 33, 34, 35 and the relative motion of the Ar atom with respect to I₂ is treated classically.

The paper is organized as follows. In Sections 2 and 3 we present the methodology and the potential parameters, respectively. Section 4 presents the results and the discussion of a simplified kinetic scheme which provides insight into the mechanism of energy redistribution and fragmentation. Finally, Section 5 is devoted to the conclusions.

Section snippets

Methodology

As stated above we have used the Molecular Dynamics with Quantum Transitions (MDQT) method of Tully 30, 31, 32. Briefly, the trajectory for the classical degrees of freedom evolves on a potential energy surface which is defined by a single state of the quantal degree of freedom. Hops from one surface to another are governed by a wavefunction retaining the full coherence between quantum states (that is, the wave function is not reset when a jump occurs for the classical degrees of freedom).

Potential energy surface

The potential energy surface for the excited electronic B state was modeled by a sum of pairwise functions. For the I₂[B(³Π_0⁺u)] potential energy curve, RKR points were taken from the literature [38] and adjusted to a Morse plus a long range interaction according to: $V_{B} (r)= T_{e} +D_{I_{2}} 1− e^{−α_{I_{2}}(r−r_{e})}^{2} r≤r_{s} V_{B} (∞)−C_{6} /r^{6} −C_{8} /r^{8} −C_{10} /r^{10} r>r_{s}$ with D_I₂=ω_e²/4ω_eχ_e and $α_{I_{2}} = 2μω_{e} /ℏ$ , μ being the reduced mass of I₂ taken equal to 63.452 amu. The numerical values for the parameters are given in Table 1. The C₆, C₈, and C₁₀

Results and discussion

In Fig. 1 we present our calculated Vibrational Predissociation Efficiencies (VPE), that is the number of molecules which undergo vibrational predissociation relative to the total number of dissociated molecules, for different initial vibrational quantum number of I₂(B) in the range v=18–24. It is seen that the calculated VPE results are in good agreement with the experiments 1, 17, 20.

In Fig. 2, we represent the probability for electronic predissociation for the relevant vibrational channels (v

Conclusions

The Molecular Dynamics with Quantum Transitions (MDQT) method of Tully 30, 31, 32 has been applied to the study of the competition between vibrational predissociation and electronic predissociation of ArI₂(B,v=15−25). The electronic predissociation hopping probability amplitudes from the initial B state to the final dissociative a channel giving Ar + I + I was modeled through Franck–Condon factors between these two states. The I₂ vibration was treated quantum mechanically using a Discrete

Acknowledgements

This work was partially supported by the spanish Ministerio de Educación y Ciencia under projects PB 94-1130 and PB 97-1041. A collaboration grant from the spanish and french governments, Acción Integrada Picasso no 98155, is gratefully acknowledged. We also thank Sharon Hames-Schiffer for her enlighting comments on the surface hopping methodology.

References (39)

Y. Yan et al.
Chem. Phys. Lett.
(1992)
C. Lienau et al.
Chem. Phys. Lett.
(1994)
O. Roncero et al.
Chem. Phys. Lett.
(1994)
A. Bastida et al.
Chem. Phys. Lett.
(1997)
J.V. Lill et al.
Chem. Phys. Lett.
(1982)
D.H. Levy
Adv. Chem. Phys.
(1981)
J.A. Beswick et al.
Adv. Chem. Phys.
(1981)
K.C. Janda
Adv. Chem. Phys.
(1985)
N. Halberstadt, K.C. Janda, (Eds.), Dynamics of Polyatomic van der Waals complexes, Plenum, New York,...
S.K. Shin et al.
Adv. Photochem.
(1991)

E.R. Bernstein

Annu. Rev. Phys. Chem.

(1995)

R.B. Gerber et al.

Annu. Rev. Phys. Chem.

(1996)

B. Otto et al.

J. Chem. Phys.

(1984)

J.T. Hynes

Annu. Rev. Phys. Chem.

(1985)

A.L. Harris et al.

Annu. Rev. Phys. Chem.

(1988)

N.F. Scherer et al.

J. Chem. Phys.

(1993)

N. Schwentner, M. Chergui, Photochemistry, charge transfer states and laser applications of small molecules in rare gas...

Z. Li et al.

J. Phys. Chem.

(1995)

N. Goldstein et al.

J. Chem. Phys.

(1986)

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Competition between electronic and vibrational predissociation in Ar–I2(B): a molecular dynamics with quantum transitions study

Abstract

Introduction

Section snippets

Methodology

Potential energy surface

Results and discussion

Conclusions

Acknowledgements

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Competition between electronic and vibrational predissociation in Ar–I₂(B): a molecular dynamics with quantum transitions study