Chapter 17
The Contribution of Wide-Angle Motions to Collisional Energy Transfer Between Benzene and Argon Downloaded by UNIV OF ARIZONA on January 10, 2013 | http://pubs.acs.org Publication Date: June 10, 1997 | doi: 10.1021/bk-1997-0678.ch017
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V. Bernshtein and I. Oref
Department of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
Trajectory calculations of collisional energy transfer between an excited benzene molecule and an Ar bath atom are reported. Calculations were made for three groups of initial conditions of the excited molecule. a. Fully rotating and vibrating molecule. b. The overall rotations are frozen prior to the start of the collisions. c. The out-of-plane vibrations are frozen prior to the start of the collision. Trajectories that lead to large values of energy transfer, supercollisions, are analyzed individually. It is found that these collisions occur in a narrow cone of angular approach around 90°. That the energy transfer in down collisions is either from rotation to translation or vibration to translation. In up collisions the reverse process takes place. The overall rotations and out-of-plane vibrations are the vehicle by which energy is transferred. The actual energy transfer process is shorter than intramolecular energy redistribution time. Therefore, only a small moiety participates in the actual energy transfer. Measurements of C-Ar and H-Ar van der Waals distances in the energy transferring moiety show that C is the prominent atom in the mechanism of energy transfer.
Collisional energy transfer, CET, plays a major role in reactive and non-reactive gas phase processes (7). In photophysical processes energy transfer at low and high levels of excitation provide an understanding of the preferred routes of vibration to vibration/rotation/translation energy exchange (2). In photochemical and thermal processes, CET is part of the reactive mechanism. It provides the mechanism by which energy is pumped up and down the energy ladder (lb,3). Thus, collisions cool highly excited molecules and excite molecules which are located in the part of the population distribution which is far away from the threshold value for reaction. 'Corresponding author © 1997 American Chemical Society In Highly Excited Molecules; Mullin, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1997.
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The energy transfer probability function from initial energy state Ε to final state E \ P(E,E'), is an elusive quantity which is extremely hard to measure (lb). Most experiments do not give the whole functional form but only the first moment of the distribution (la). In the rarest of cases the second moment can be obtained as well. Recent physical experiments which utilize spectroscopic means give greater insight into the shape of the function but even here, a priori assumptions must be made in order to fit the data to an assumed function (2). This unhappy situation led to the development of many empirical energy transfer models which were used in master equation calculations of unimolecular rate coefficients (lb,4). Without such models the great progress, due mainly to Marcus and Rabinovitch and their co-workers, in understanding unimolecular reactions which was made since the late 1950's would have come to nothing. Lately, quasi-classical trajectory calculations have provided new insights into the collisional process (5). The ability to selectively probe the parameters which govern the energy transfer process provided an important technique by which the principal elements which effect the energy exchange can be studied. The effects of the intermolecular potential, of the mass, internal excitation, temperature, collision duration and internal modes were studied in a systematic way. A n important feature of trajectory calculations is the ability, in principle, to evaluate P(E,E') (6). Regretfully, there is no one to one correspondence between P(E,E') and the trajectory results. The unknown elastic peak is an obstacle and P(E,E') is not fully determined. Exactly as in the physical experiments of energy transfer, also here some a priori assumptions must be made in order to obtain the complete form of Ρ(Ε,Ε'). Nevertheless, trajectory calculations provide an important tool for understanding energy transfer. Quantum and classical calculations show that there is a general agreement between the two types of calculations (5s,7) lending important theoretical support to studying collisional energy transfer by quasiclassical calculations. Previous work has provided information on the nature of the energy exchange process. Calculations of the duration of a collision have indicated that practically all collisions are very fast. The average collision duration is ~ 680 fs at 500 Κ and -230 fs at 1500 Κ (5o). Probing the center-of-mass velocity during the collision show that most collisions are impulsive (5t). There is a fraction of "chattering" collisions in which the bath atom spends between 300 fs to 600 fs near the excited polyatomic molecule. However, the energy transferred does not seem to result from an accumulation of small quantities of energy in succession. Rather, the bath atom hovers over the molecule and the energy transfer event occurs during a short time at the end of the collision. It was also found by quantum mechanical calculation that the out-of-plane modes play a major role in the energy transfer process (5s). The role of the wide angle motions in the energy transfer process was confirmed by trajectory calculations (8). These calculations show that the out-ofplane modes and over all rotations play a major role in the CET of excited benzene colliding with Ar as a bath gas.
In Highly Excited Molecules; Mullin, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1997.
Downloaded by UNIV OF ARIZONA on January 10, 2013 | http://pubs.acs.org Publication Date: June 10, 1997 | doi: 10.1021/bk-1997-0678.ch017
17. BERNSHTEIN & OREF
Contribution of Wide-Angle Motions
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A sub-group within the inelastic collisions is those collisions which transfer very large quantities of energy in one collision, supercollision (9). Previous work on benzene/Ar and toluene/Ar has shown that the large values of ΔΕ encountered in those collisions are due to dynamical effects (5s,8). That is to say, the incoming atom has to be in a perpendicular orientation relative to the molecule and it has to be in phase with an out-of-plane motion or overall rotation. There are basically two types of mechanisms. The first is impulsive and the collision is of a very short duration. In the second, the atom hits the molecule once and transfers energy to it. As a consequence it is slowed down. After a very short time, it is hit by a wide angle motion and departs energy rich. These energy rich collisions were not found to depend on the relative translational energy. Thus, a slow moving atom with the right orientation can obtain a large value ΔΕ in a down-collision. In what follows we probe the dynamics of the collisions and the dependence of CET on orientation especially for supercollisions. We do so by monitoring the angle and the distances between the incoming atom and the atoms in the moiety which defines the collision site. Theory The numerical methods used in the present work are reported in refs. 5o and 5p. The equations of motion were integrated by using a modified public domain program Venus (10). The intermolecular potential was a pairwise Lennard-Jones potential. Its parameters are given in ref. 5s. The intramolecular potential includes all the normal modes contributions, stretching, bending and wagging. The values of the parameters of this potential were obtained from modified valance force field calculations by Draeger (77) and are also given in references 5o and 5p. The initial translational and rotational energies were chosen from the appropriate thermal energy distributions at 300K. The initial impact parameter was chosen randomly between 0 and its maximum value b . The internal energy was 51762 cm" . The beginning and the end of a collision were determined by the Forward and Backward Sensing (FOBS) method (5o,5p). In this method each trajectory is scanned forward and the moment that, for the first time, a change ε is observed in the internal energy of the hot molecule in a period τ is noted. Then, the trajectory is scanned backward and again, when a change ε is detected the time is noted again. These two times bracket the collisional event. The value of ε used in our calculations was 70 cm' and the value of τ was 20 fs. This value was obtained after a careful study in which ε was changed systematically and the value chosen such that a small variation in ε did not change the initial time or duration of the collision (5o,5p). For each trajectory the change in energy was noted as well as its duration as determined by FOBS. The value of the maximum impact parameter bm was determined separately (5o, 5p) A value of 1.1 nm was used in the present calculations. A 1
m
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In Highly Excited Molecules; Mullin, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1997.
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systematic study of post collision distances between Ar and the closest atom of toluene has shown that for distances larger than 0.8 nm, no changes in the values of the integral of ll were observed, therefore, this value was taken as the terminal distance for all trajectories and the end point from which the back sensing of FOBS was initiated. A convergence of and
