J. Phys. Chem. 1992,96, 1523-1525 triplet product is an alternative. These results considerably extend the scope of our knowledge of systems which give CIDEP in a sense opposite to the usual situation. It is probable that a number of radical pairs have J > 0 in contrast to the usual case. The unusual pairs include ea; with phenoxyl, phenylthiyl, p-benzosemiquinone ion, C03’-, and TMPD+ as well as anion radicals of benzoic, p-methoxybenzoic, and p-toluic acids with phenoxyl or phenylthiyl. As was noted previously for several of the examples,3 reaction in each of these pairs is highly exothermic. It appears that reaction to form an excited state is possible even though it is not necessary to invoke formation of a triplet state. Adrian’ has given a possible explanation of how reaction of ion pairs (D+-A-) might give a triplet-state product. He points out that the ion pair state will be mixed with an excited state (D*-A) and, with a particular ordering of the states’ energies, the triplet state will be lowered more than the singlet. A very similar situation could pertain here. Possible energy levels are given in Figure 4. On the left are levels for the product, for example phenoxide ion, with excited states as given. On the right are levels for the nearly separated radical pair e,,-/phenoxyl. With the levels as given, mixing between the radical pair states and those of the same multiplicity for phenoxide will lower the triplet state of the ion pair more than the singlet (because of the proximity in energy) so that J > 0 during the reencounter. Although reaction to form the ground state will be slowed by the large energy release, it still can occur so the F pairs are triplets.
1523
Perturbation of the energy levels in this way will only be significant when the reaction is strongly exothermic so the triplet state of the product is close in energy to the separated radicals. In addition, this effect will be enhanced with increased overlap of the wave functions as is expected for the diffuse structure of e, - The anion radical of benzoic acid will be somewhat similar. y h e electron in this case is in a shallow trap (bound weakly to the benzoate) because the reduction potential is only slightly less negative than for ea; (-2.77 V22). The striking change to normal behavior for the anion radical of p-acetylbenzoate with phenoxyl or phenylthiyl may be the result of a decrease in magnitude of the reduction potential which decreases the energy of the pair as well as changes in the nature of the orbital of the anion radical. A more systematic and more quantitative study of, for example, the polarizations for various substituted anion radicals together with predictions of the exact energy levels for the excited states of the product will be needed to better define this effect.
Acknowledgment. The work described herein was supported by the Office of Basic Energy Sciences of the Department of Energy. This is Contribution No. NDRL-3425 from the Notre Dame Radiation Laboratory. We thank Drs. D. M. Chipman and I. Carmichael for helpful discussions. (22) Hart, E. J.; Anbar, M. The Hydrated Electron; Wiley-Interscience: New York, 1970; p 63.
The Cage Effect and Energetic and Steric Requirements of Elementary Bimolecular Reactions in Condensed Phases M. Ben-Nun and R. D. Levine* The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University, Jerusalem 91 904, Israel, and Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, California 90024-1569 (Received: October 31, 1991; In Final Form: December 30, 1991)
Caging in atom-diatom exchange reactions in rare gases was found predominantly at such high densities that the rare gas atoms themselves become caged. Even when the reactants undergo repeated collisions within the cage, reaction will not occur unless the steric and kinematic requirements for barrier crossing are satisfied. These requirements can be understood in terms of the potential energy surface of the isolated reactants.
The “cage effect” whereby the first solvation shell leads to repeated collisions is central to our thinking about reactions in condensed phases.’” Molecular dynamics simulations of activated bimolecular reactions in rare gas solvents4-’ have thus far failed to discem a cage effect. The results of such simulations were that initiating classical trajectories at the peak of the activation barrier resulted in a rapid separation into the product (or reactants) region. During this separation the energy transfer to the solvent was considerable, but it occurred typically only a t the foothills of the chemical barrier. Beyond the initial moderation of the nascent hot products, the energy transfer to or from the solvent is quite limited.* The constraints imposed by the environment are often sufficient to detain the reactants in the region of the onset of (1) North, A. M. The Collision Theory of Chemical Reactions in Liquid; Methuen: London, 1964. (2) Adelman, S . A. Ado. Chem. Phys. 1983, 53.61. (3) Schroeder, J.; Troe, J. Annu. Rev. Phys. Chem. 1987, 38, 163. (4) Bergsma, J. P.; Reimers, J. R.; Wilson, K. R.; Hynes, J. T. J . Chem. Phys. 1986,85, 5625. ( 5 ) Benjamin, I.; Gertner, B. J.; Tang, N. J.; Wilson, K. R.J. Am. Chem.
SOC.1990, 112, 524.
(6) Li, Y . S.;Wilson, K. R. J . Chem. Phys. 1990, 93, 8821. (7)
Benjamin, I.; Liu, A.; Wilson, K. R.; Levine, R. D. J . Phys. Chem.
1990, 94, 3937.
( 8 ) Charutz, D. M.; Levine, R. D. Chem. Phys. 1991, 152, 31.
chemical forces. But the large fluctuations9 necessary to induce a remounting of the barrier are too rare on the time scale of diffusing out into the bulk. There is thus no cage effect in the sense of a solvent-induced recrossing of the barrier by collision products which have previously separated to the foothills of their chemical interaction. Of course, if the bare gas-phase potential contains a well (as for nucleophilic substitution reactionsIbl2), then the reactants will fail to immediately separate. This complex formation will occur also for a collision in the gas phase. It is not a solvent-induced change in the dynamics from direct in the gas phase to a multiple collision event in the solvent. In this Letter we report that at much higher densitiesI3 we do see a clear-cut cage effect. The pair of reactants spend long times within the foothills of their chemical interaction and repeatedly attempt to scale the bamer. There is a gradual yet quite noticeable change in the dynamics of the collision as the pressure is in(9) Wilson, K. R.; Levine, R. D. Chem. Phys. Lett. 1988, 152, 435. (10) Bergsma, J. P.;Gertner, B. J.; Wilson, K. R.; Hynes, J. T. J. Chem. Phys. 1987, 86, 1356. (11) Gertner, B. J.; Whitnell, R. M.;Wilson, K. R.; Hynes, J. T. J . Am. Chem. SOC.1991, 113, 74. (12) Patron, F.; Adelman, S . A. Chem. Phys. 1991, 152, 121. (13) Zha, C. S.; Boehler, R.; Young, D. A.; Ross,M.J . Chem. Phys. 1986, 85. 1034.
0022-365419212096- 1523$03.00/0 0 1992 American Chemical Societv
1524 The Journal of Physical Chemistry, Vol. 96, No. 4, 1992
0 -100
-
Letters
1 -50
0 Timelfs
50
0 i -100 -50 0 50 100 Time/fs
100
Figure 1. ‘Old” and “new” bond distances versus time, computed for 0 OH H using the potential energy surface of ref 15. The reactants are surrounded by 100 Ar atoms, at a density of p = 1.19 interacting with a pairwise Lennard-Jones (6,12) potential ( u = 3.41 A). The solventsolute potential is a sum of atom-atom potentials, as in other simulations in rare gas solvents. The initial conditions (at t = 0) for the trajectory are drawn from a thermal ensemble at 300 K. At this density, which is just below freezing, the products are somewhat detained at the foothills of their chemical interaction but there is no rescaling of the barrier; cf. Figure 2.
+ H2
+
creased.I4 Remarkably, in terms of the density, the onset of caging is fairly abrupt. Examination of the radial pair distribution function has failed, thus far, to show any very obvious structural changes at such densities where extensive caging sets in. We have seen the onset of caging in about the same range of density for a number of different chemical reactions. This suggests that it may reflect some property of the solvent itself. Examination of the trajectories of the rate gas atoms shows that caging of the reactants sets in at the same density that self-caging becomes important. This is the density where, on longer time scales, the liquid becomes glasslike. On the other hand, we wish to emphasize that over the duration of barrier crossing there is no dynamical distinction in the behavior of the solvent. This suggests that studies of reaction dynamics in rare gas glasses can provide useful insights into the dynamical role of the environment on reactions in solution. The meaningful distinction between a glasslike and a liquid state is only evident on time scales which are longer than those probed by direct bimolecular reactions. The repeated geminate “collisions” induced by the solvent cage are less chemically important than the traditional would suggest. The reason is that many approaches of the reactants result in failure to react because the barrier is not crossed. These nonreactive collisions will be shown below to reflect the steric and kinematic requirements of the reaction. Thus, while the solvent cage repeatedly sends the reactants toward one another with enough total energy to scale the barrier, often the reaction fails to take place. We have observed this to be the case for a number of reactions in an Ar solvent. We here report explicit results for the 0 + H2 -,OH + H reaction and its inverse rather than for the “standard” C1+ C12exchange in order to avoid any suggestion that a favorable mass ratio assists in caging the solute. The potential energy surface for the gas-phase collision is of the LEPS functional form with parameters of Johnson and Winter.15 The dynamics in the gas phase have been studied previously.I6 The Ar-Ar and Ar atom potentials are Lennard-Jones (6,12) functions using literature parameter^.^,^ Figure 1 is a typical output of a trajectory computation at a high Ar density p* = pu3 = 1-19at 300 K. (This is the density at the onset of freezing at 300 K for pure Ar at eq~i1ibrium.l~) Shown are the bond distances versus time for a reactive 0 + H2 -,OH H collision. The origin of time is when the reactants are at the top of the barrier. The results shown are typical for this and lower densities in that there is no real caging. The escaping H atom is being strongly moderated by the solvent (at
+
(14) Troe, J . J . Phys. Chem. 1986, 90, 357. (15) Johnson, B. R.;Winter, N. W. J . Chem. Phys. 1977, 66, 4116. (16) Alfasi, Z. B.; Baer, M. Chem. Phys. 1981, 63, 275. Broida, M.; Persky, A. J. Chem. Phys. 1984.80, 3687.
i
0 ” ’ -100
,
’
-50
’
’
0 Timelfs
i
50
100
Figure 2. Same as Figure 1 but at the higher density of 1.68. Also shown, as a dashed line, is the 0-H-H angle a. (a, top) A reactive 0 + H2 OH + H encounter. Note the failure to react when the angle (Y is not near 180’. (b, bottom) A nonreactive OH H encounter. Note the failure of the incoming H atom to displace the bound H atom.
-
+
positive times), but it continues to move further away a t longer times. At lower densities and/or for heavier atoms, the ‘old” bond length is typically monotonically increasing with time for t > 0. The results shown in Figure 1 are to be contrasted with those at a very high density, p* = 1.68, shown in the two panels of Figure 2. Caging is very evident as the reactants fail to move apart. Despite the repeated close approaches seen in Figure 2, there is only one successful barrier crossing in panel a and none in panel b. Why do the reactants approach to well within the range of their mutual chemical force and fail to react? As an aid in the interpretation, we also show in Figure 2 the H-H-0bond angle a versus time. Clearly, the reactants manage to get to the point where the H2 bond distance (equilibrium value 0.74 A) is below the OH bond distance (equilibrium value 0.97 A) only for nearly collinear collisions. Examination of the LEPS potential energy function15 shows that the cone of acceptance for reaction” is quite narrow for 0 H2or for the reverse OH H reaction. When the bond-bond angle a (cf. Figure 2) is 150°, the barrier height for reaction exceeds its value (4.2 kcal mol-’) for a collinear approach by over 1 kcal mol-’. Most repeated geminate collisions do not have the right orientation for reaction. Note that, consistent with earlier work7 it is the cone of acceptance for the bare gas-phase potential that determines the steric requirements in solution. For a noncollinear approach in a real experiment one must also consider the possibility of surface crossing to the higher lying O(lD) H, surface. * Another manifestation of the role of the gas-phase potential energy surface is provided by the second panel of Figure 2. Shown therein is an OH + H collision. An H atom received a particularly high impulse from the cage and is moving quite fast (note the slope) nearly collinearly toward HO. It gets very near yet fails t o react. As is evident in Figure 1 of ref 15, a fast H atom moving toward a vibrationally cold HO will rebound from the inner hard core and fail to react. Such events are very common in the ensemble of trajectories that we have run. Note that this is also
+
+
+
(1 7) Levine, R. D.; Bernstein, R. B. Molecular Reaction Dynamics and Chemical Reactiuity; Oxford University Press: New York, 1989. (18) Rudich, Y . ;Lifson, S.;Naaman, R. J . Am. Chem. Soc. 1991, 113,
7077.
J . Phys. Chem. 1992, 96. 1525-1527
0 -/ -L.I
0
L&_
1 2 -
100
L
I
-
L
200 300 Timelfs
-
._-L
400
500
Figure 3. Variance of the distribution of Ar-Ar interatomic distances (in units of d)versus time for three densities at 300 K. As evident from Figures 1 and 2, the barrier crossing time is shorter than 100 fs.
a mass effect.Ig The relative distance of H to the OH center of mass becomes essentially the "new" OH bond distance. It therefore fails to impart too much momentum to the "old" OH bond distance and hence fails to displace it. To probe the state of the rare gas environment, we have examined both individual Ar atom trajectoric id ensemble averages. Caging of the (small sized) reactants vciurs only at such densities that solvent atoms are also caged so that diffusion is considerably slowed down. But diffusion is a longer time scale (19) Schechter, I.; Levine, R. D.; Gordon, R. G.J . Phys. Chem. 1991,95, 8201.
1525
phenomenon, and on the time scale of barrier crossing there is no discernible differences in the dynamic response of the solvent. We illustrate this point in Figure 3 which shows the variance of inter Ar atom distances versus time. Most previous simulations in liquid Ar at 300 K were carried out at p* = 0.83 when no caging is evident. If the time axis of Figure 3 is scaled by an order of magnitude, so that it runs to 5 ps, then the behavior at p = 0.83 will be seen to be diffusive ((9) a t ) . On the time scales of interest to us, the behavior of the solvent at p = 1.68 is not qualitatively different from that at p = 0.83. In conclusion, we found that even at very high densities where caging does take place, the response of the rare gas environment is still slow on the time scale of a direct bimolecular reaction. This can possibly be used to simplify the experimental study of the dynamics of such reactions which are typically over in a vibrational period. The motion from the reactants valley over the barrier and to the products valley exhibits the same dynamics in either a fluid or a glass environment. Differences due to the changes in the solvent dynamics as the density is increased are manifested only at longer times. A detailed discussion of this separation of time scales, with the short time dynamics being governed essentially by the potential energy of the isolated reactants, is being prepared for publication.
Acknowledgment. We thank Professors W. M. Gelbart, D. Kivelson, R.Lynden-Bell, M. F. Nicol, M. Ross,and K. R.Wilson for useful discussions and comments. This work was supported by the US.-Israel Binational Science Foundation, BSF, Jerusalem, Israel.
Near-Infrared Absorption Spectra of C,, Radical Cations and Anions Prepared Simultaneously in Solid Argon Zbigniew Gasyna, Lester Andrews,* and Paul N. Schatz* Department of Chemistry, University of Virginia, Charlottesuille, Virginia 22901 (Received: November 13, 1991)
The codeposition of Ca vapor with excess argon and argon resonance radiation has produced strong new absorptions at 973 and 1068 nm in solid argon at 11 f 1 K. A similar experiment with CC14 added to serve as an electron trap reduced the yield of the 1068-nm band with little effect on the 973-nm absorption. The 973-nm band is assigned to Cm*+produced by photoionization and the 1068-nm band to C60*- formed by electron capture. These identifications are in excellent agreement with glassy matrix, solution, and photoelectron spectra.
The laboratory synthesis of Cmand other carbon cages known as fullerenes has spawned a host of studies on this highly symmetrical soccerball-shaped molecule. The reader is referred to a comprehensive recent review by Kroto, Allaf, and Balm' and to sources for rapid and continuing literature updatesa2 Since the discovery3 in 1985 of the stability of c60, attributed to a truncated icosahedral cage structure, a host of studies have confirmed the I,, symmetry of the molecule and established its precise geometry. The low ionization energy (7.6 eV) and high electron affinity (2.6 eV)49Smake electron-transfer properties unusually interesting (1) Kroto, H. W.; Allaf, A. W.; Balm, S . P. Chem. Reu. 1991, 91, 1213. (2) Two good methods of keeping abreast of this rapidly moving field are ( I ) the Bucky News Service, send e-mail message to
[email protected]. u p e n n d u ; and (2) a complete and continuing bibliography from R. E. Smalley, e-mail to
[email protected]. (3) Kroto, H. W.; Heath, J. R.; OBrien, S. C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162. (4) Lichtenberger, D. L.; Nebesny, K. W.; Ray, C. D.; Huffman, D. R.; Lamb, L. D. Chem. Phys. Lett. 1991, 176, 203.
for Cs0 and facilitate the preparation and study of the molecular cation and anion. Accordingly, Shida and co-workers have obtained electronic absorption spectra of Cm radical anions and cations following radiolysis in different glassy matrices a t 77 K using proven technology developed at Kyotoa6 EPR spectra of these species in different solutions have also been reported.'-I0 Very recently, the near-infrared absorption spectrum of Cm*-has also been observed following controlled-potential coulometry.I0 ( 5 ) Yang, S. H.; Pettiette, C. L.; Conceicao, J.; Cheshnovsky, 0.;Smalley, R. E. Chem. Phys. Lezr. 1987, 139, 233. (6) Kato, T.; Kodama, T.; Shida, T.;Nakagawa, T.; Matsui, Y.; Suzuki, S.; Shiromaru, H.; Yamauchi, K.; Achiba, Y. Chem. Phys. Lett. 1991, 180, 446. (7) Kukolich, S. G.;Huffman, D. R. Chem. Phys. Lett. 1991, 182, 263. (8) Krusic, P. J.; Morton, J. R.; Preston, K. F.J . Am. Chem. Soc. 1991, 11., 3. 6274. .~ (9) Keizer, P. N.; Morton, J. R.; Preston, K. F.; Sugden, A. K. J . Phys. Chem. 1991, 95, 7117. (10) Greaney, M. A.; Gorun, S. M. J . Phys. Chem. 1991, 95,7142. Kato. T.; Kodama, T.; Oyama, M.; Okazaki, S.; Shida, T.Chem. Phys. Lerr. 1991, 186, 35.
0022-365419212096-1525%03.00/0 0 1992 American Chemical Society
