The Journal of
Physical Chemistry
0 Copyright, 1984, b y the American Chemical Society
VOLUME 88, NUMBER 22
OCTOBER 25, 1984
LETTERS Collisional Deactlvation of Highly Vibrationally Excited Molecules. Dynamics of the Collision Event Noreen Date, William L. Hase,* Department of Chemistry, Wayne State University, Detroit, Michigan 48202
and Robert G. Gilbert Department of Theoretical Chemistry, Sydney University, New South Wales 2006, Australia (Received: April 30, 1984; In Final Form: September 4, 1984)
Classical trajectories are used to study microscopic details of collisions between argon atoms and highly excited methane molecules. Plots of orbital angular momentum, methane rotational angular momentum, and methane vibrational-rotational energy during the course of a collision reveal strong couplings between the Ar + CHI relative degrees of freedom and the CH4 vibrational-rotational motion.
The collisional deactivation of highly vibrationally excited molecules is important in many different chemical processes. Detailed information about the energy transfer efficiency has been determined from thermal unimolecular reactions in the falloff and second-order pressure regimes and from chemical activation studies of unimolecular reactions.'** In very recent experiments, collisional energy transfer has been studied directly by measuring either infrared fluorescence decay3 or hot UV absorption spectra4 of excited molecules. Much of the research has focused on finding values of ( A E ) , the average energy transferred per collision (including both activation and deactivation). However, there is also significant interest in (1) the form of the energy transfer probability function and how it depends on properties of the
energized molecule and bath molecule and ( 2 ) how ( M )and the energy transfer probability distribution function depend upon temperat~re6~ or, more microscopically, depend upon the energy3s4 and angular momentum of the excited molecule and the relative translational energy of the collision partners. Statistical models proposed to explain the energy transfer probabilities assume energy redistribution between "active" degrees of freedom in a short-lived collision c ~ m p l e x . ' - ~ These ~ ~ ~ * models were successful in interpreting the earliest experimental data in terms of the relative insensitive quantity, the collision efficiency, but are much less successful in interpreting the most recent results which show the ( A E ) values are significantly smaller than expected from such model^.^,^ A recently proposed "biased random walk" theory, based on a stochastic model, seems very promising
(1) D. C. Tardy and B. S. Rabinovitch, Chem. Rev., 77, 369 (1977).
(2) M. Quack and J. Troe, Spec. Period. Rep.: Gas Kinet. Energy Transfer, 2, 175 (1977). (3) M. J. Rossi, J. R. Pladziewicz, and J. R. Barker, J . Chem. Phys., 78, 6695 (1983). (4) H. Hippler, J. Troe, and H. J. Wendelken, J . Chem. Phys., 78, 6709, 6718 (1983).
(5) T. T. Nguyen, K. D. King, and R. G. Gilbert, J . Phys. Chem., 87,494 (1983). . (6) V. V. Krongauz, B. S.Rabinovitch, and E. Linkaityte-Weiss, J. Chem. Phvs.. 78. 5643 (1983). '(7) Y.'N. Lin'and B. S.Rabinovitch, J . Phys. Chem., 74, 3151 (1970). (8) R. C. Bhattacharjee and W. Forst, Chem. Phys., 30, 217 (1978).
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5136 The Journal of Physical Chemistry, Vol. 88, No. 22, 1984
for interpreting energy transfer data.g A limited number of trajectory studies have provided some insight into the dynamics of the energy transfer process,’*13 but more are needed to point the way to appropriate phenomenological models. Development of an accurate model for the energy transfer process will be enhanced if a dynamical picture of the collision event is available. From trajectory calculations of argon-methane collisions we have been able to uncover informative aspects of the dynamics. The results are presented here.
Computational Method The trajectory calculations are performed with the general Monte Carlo classical trajectory computer program MERCURY.I4 The intramolecular potential of the methane molecule in internal coordinates is represented by four Morse functions (0 = 1.863 A-1, D = 112.45 kcal/mol, and ro = 1.086 A) and six harmonic bends If= 0.585 m d y d / r a d 2 and Bo = 109.47O). The Ar-CH4 intermolecular potential is written as a sum of five Lennard-Jones potentials. The Ar-H potential parameters were assumed to be the same as those for Ar-He (e = 19.4 K, u = 3.09 A).15 Those for Ar-C were assumed to be the same as those for Ar-Ne (e = 70 K, u = 3.06 &.I5 The minimum-energy geometry for the Ar-CH4 van der Waals complex is one with Ar symmetrically positioned 3.317 A above a plane formed by three hydrogen atoms. The well depth is 161.03 K. Collisions between an Ar atom and a CH, molecule are simulated for initial conditions in which the CH4 molecule contains 103 kcal/mol of vibrational-rotational energy E , and has a rotational angular momentumj for a temperature of 1000 K. The initial conditions used in this study are representative of those for energy transfer collisions in the thermal unimolecular dissociation of methane.” The impact parameter is 1 A,I6 and the methane molecule is randomly oriented with respect to the impinging Ar atom. The Ar + CHI line-of-centers relative translational energy E,,, is 5.0 kcal/mol. Thus, each trajectory has the same CH4 energy and angular momentum, relative translational energy, and impact parameter. The trajectories differ in the orientation of the methane molecule and the phases of the CH4 vibrational motions. The two constants of motion are the total energy E, a n i the_ tots1 angu1:r momentum J . The latter is the vector sum J f j 1, where j is the CH4 rotational angular momentum and I is the Ar-CH4 orbital angular momentum. To analyze each trajectory, the total energy is partitioned as
+
Et = Evr
+ Ere1 + Vinter + l2/&rr,2
Letters 40
r
1
10 -/ 0.4
I
I
I
0.5
0.6
0.7
0.8
Time Figure 1. Plot of CH4 internal energy in kcal/mol (-), CH4rotational angular momentum in h (---), and Ar-CH, orbital angular momentum in h (-- -) during an Ar + CH, collision. Time is in units of picoseconds. Details of the trajectory initial conditions are described in the text. 40
r 108
1
c 102
II‘ i
n y
I
I
I
I
,
0.4
0.5
0.6
0.7
0.8
IVY
Time Figure 2. Same as Figure 1, but a different trajectory.
(1)
where Vinter is the Ar + CH, intermolecular potential and rre1is the distance between Ar and the CHI center of mass. The remaining terms in eq 1 are defined above. At infinite separation E, equals the sum of E,, and E,,l.
Results and Discussion It is often argued that collision complexes play a role in the relaxation of highly vibrationally excited m o l e ~ u l e s . l ~The ~*~ collision complex represents an intermediate formed by a “sticky” collision, in which there are multiple oscillations in the relative motion of the two colliding species. For the Ar + CH4trajectories studied here there is no evidence for the formation of such a collision complex, since each trajectory is characterized by only one inner turning point in the Ar + CHI relative motion. This (9) R. G Gilbert, J . Chem. Phys., 80, 5501 (1984). (10) D. L. Bunker and S. A. Jayich, Chem. Phys., 13, 129 (1976). (11) A. J. Stace and J. N. Murrell, J . Chem. Phys., 68, 3028 (1978). (12) C. R. Gallucci and G. C. Schatz, J . Phys. Chem., 86,2352 (1982). (13) N. J. Brown and J. A. Miller, J . Chem. Phys., 80, 5568 (1984). (14) W. L. Hase, QCPE, 3, 453 (1983). (15) G. Scoles, Annu. Rev. Phys. Chem., 31, 81 (1980). (16) An impact parameter of 1 8, is an intermediate value, since the largest impact parameter for which energy transfer occurs is approximately 3 8, (ref 17). (17) N Date and W. L. Hase, to be submitted for publication.
10
I
0.4
I
0.5
V
I
0.6
0.7
98 0.8 ~
Time Figure 3. Same as Figure 1, but a different trajectory.
result is found for a relative translational energy as low as 1.OO kcal/ mol. l 7 Plots of Z,j, and E, during the course of a collision reveal details of the collision dynamics. Such plots for ten representative trajectories are shown in Figures 1-9. The argon atom and methane molecule strongly interact for approximately 0.1-0.2 ps. This interaction time is expected to increase for lower relative translational energies. During the interaction there are strong couplings between the Ar + CH4 relative degrees of freedom and the CH4
The Journal of Physical Chemistry, Vol. 88, No. 22, 1984 5137
Letters 50
1lO
1
Ig5 I105
50
E
5
100 x
-I-
b l
b 9
3 20
0,
5
90
2
-r
10
k--'
10
4
0.4
0.6
0.5
I
0.7
80 0.8
01 0.4
I
I
I
0.5
0.6
0.7
0.8
Time Figure 7. Same as Figure 1, but a different trajectory.
Time Figure 4. Same as Figure 1, but a different trajectory. 110
40
S
1
E
5 0)
5
I
10
4
0.4
0.6
0.5
90 0.7
0.8
0.4
Time Figure 5. Same as Figure 1, but a different trajectory. 50
1
I
I
0.6
0.7
0.8
Time Figure 8. Same as Figure 1, but a different trajectory.
r
I ,
I
0.5
r
110
'lo
E
-I1 -
S
0)
El
I
V
I
I
I
I
I
0.4
0.5
0.6
0.7
0.8
=-
Time Figure 6. Same as Figure 1, but a different trajectory. vibrational-rotational motion, which result in energy transfer between the relative motion and the CH4 internal degrees of freedom. This is clearly illustrated by the 1-j modulations and the rapid oscillations in E",. It is particularly interesting to note that changes in E,, during the collision are much larger than the difference between the initial and final values. Is the observed behavior a reasonable qualitative representation of that actually occurring? While these calculations are intended to be illustrative rather than directly applicable to the interpretation of a particular experiment, it is noted that the results are in acceptable agreement with experiment: for example, the average energy transfer for the ten trajectories studied is ca. -1
0/10 0.4
0.5
0.6
0.7
0.8
Time Figure 9. Same as Figure 1, but a different trajectory. kcal/mol, in agreement with the result reported for the average downward energy transfer'* from analysis of thermal falloff data for CH,-Ar under conditions corresponding to those modeled here (note that, for this system, the average downward energy transfer is approximately ( A E ) ) . Bepause the energy exchange seems to take place during close encounters between individual atoms of the substrate and the bath gas atom, it is likely that the overall potential well depth (attractive (18) C . Chiang, J. A. Baker, and G. B. Skinner, J . Phys. Chem., 84,939 (1980).
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J. Phys. Chem. 1984, 88, 5138-5141
force) between the collision partners is not an overriding factor in the energy transferred. This is in general accord with observation1s2where it is often found that the detailed structure of the substrate does not seem to be a strong determinant of the average energy transfer. We feel that these calculations provide insight which can be used for the derivation of an accurate model for describing the collisional deactivation of highly vibrationally excited molecules. Gilbert9 has recently developed a stochastic theory for collisional energy exchange in highly vibrationally excited molecules. The theory is based on a biased random walk model, which postulates the internal energy will undergo rapid fluctuations resembling a random walk during a collision. The basic postulate of this theory is supported by the results of this Ar + CH4 trajectory study. While it was suggested that this biased random walk model would be quantitatively applicable only if the substrate is moderately large (say, with more than 15 internal degrees of freedom), the present calculations indicate that a stochastic treatment in either E or j should be applicable even in substrates as small as CH4, although no doubt much improvement of the simple model of ref 9 would be needed for the quantitative applicability to such small systems. It is expected that the energy transfer depends upon the structure and intramolecular properties of both the excited molecule and the bath gas. Such effects have been found in a classical trajectory study of ion-molecule recombination effic i e n c i e ~ . ~For ~ collisional energy transfer in highly excited molecules intramolecular properties such as low-frequency torsions (19) K. N. Swamy and W. L. Hase, J. Am. Chem. Soc., 106,4071 (1984).
and vibrations may strongly influence the energy transfer efficiency. Studies of the microscopic details of the collision deactivation of molecules which have the above intramolecular properties are currently in progress. At the level of excitation considered in this work the internal motion of the CH4 molecule is chaotic. A chaotic trajectory is characterized by having nondiscrete mechanical frequencies, evidenced by a broadened power spectrum.20 In sharp contrast, a quasi-periodic trajectory exhibits a spectrum of discrete lines which correspond to the fundamental classical frequencies of motion, overtone frequencies, and combination bands. It is interesting to conjecture that the energy and angular momentum fluctuations shown in Figures 1-9 are characteristic of collisional energy transfer of molecules with chaotic motion. In contrast, the deactivation of a molecule with quasi-periodic motion may be significantly more impulsive. We are currently investigating this conjecture by studying the collisional deactivation of the H-C-C model molecule which has both chaotic and quasi-periodic motion above the unimolecular threshold.2' It would be very significant if the form of a measured energy transfer probability distribution function is found to be diagnostic of a highly excited molecule's intramolecular motion, Le., chaotic or quasi-periodic. Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for the support of this research. Registry No. Ar, 7440-37-1; CH4, 74-82-8 (20) D. W, Noid, M. L. Koszykowski, and R. A. Marcus, J. Chem. Phys., 67, 404 (1977). (21) R. J. Wolf and W. L. Hase, J . Chem. Phys., 73, 3779 (1980).
Plcosecond Dynamics of Photochemlcal Electron Transfer in Porphyrin-Quinone Intramolecular Exciplex Systems Noboru Mataga,* Akiya Karen, Tadashi Okada, Department of Chemistry, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan
Shinji Nishitani, Nobuyuki Kurata, Yoshiteru Sakata, and Soichi Misumi The Institute of Scientific and Industrial Research, Osaka University, Mihogaoka, Ibaraki, Osaka 567, Japan (Received: March 13, 1984)
Mechanisms of photochemical electron transfer in porphyrin-quinone photosynthetic model systems have been investigated by means of a microcomputer-controlledpicosecond Nd3+:YAGlaser photolysis system. The rate of photoinduced electron transfer in (0ctaethylporphyrin)-(CH2),-(benzoquinone) (PnQ) showed an inverse exponential dependence on the length of the intervening methylene chains, which suggested the possibility of an intramolecular electron-tunneling mechanism. Furthermore, the picosecond dynamics of photoinduced charge-separation processes in (eti~porphyrin)-(CH,)~-(benzoquin~ne)-(CH~)~-(trichlorobenzoquinone)(P4Q4Q) have been investigated in various solvents and the important role of the existence of Q for the realization of a gharge-separationstate with a much longer lifetime than in PnQ has been demonstrated.
Introduction In connection with mechanisms of photochemical electrontransfer (ET) and charge-separation (CS) processes in biological as well as biomimetic photosynthetic systems, investigations on porphyrin-electron acceptor model systems have been made quite 0022-3654/84/2088-5138$01.50/0
extensively.',2 However, in marked contrast to the photosynthetic reaction center in vivo, where ET from excited singlet (SI) (1) See: Alfano, R. R., Ed. "Biological Events Probed by Ultrafast Laser Spectroscopy"; Academic Press: New York, 1982.
0 1984 American Chemical Society
