J. Phys. Chem. 1989, 93, 2319-2328
A'n,
electronic state but belong to some new, previously uncharacterized state(s) of Cj. The observed lifetimes imply an oscillator strength of the new band system(s) off 5 0.001, demonstrating that the new band system is not electric dipole allowed. Rotationally resolved studies show that the transition intensity- is borrowed from the highly 0.92) V-N XIBg+ system, which has been allowed observed in the vacuum ultraviolet. A comparison of these results with ab initio studies leads u t t o conclude that the observed bands X'Zg+ transition (a lag 4ag tranbelong to either the sition) or the IA, X kZ transition (a l a g l a , transition), or both. An abrupt cutoff in spectral features below 33 027 cm-' and the lack of regularity in the spectrum near this limit lead us to believe that below this limit there is insufficient energy to ionize the C3 molecule. This allows us to estimate the ionization potential of C3 as 12.0 eV, which is in any case an upper bound. Finally, we note that laser vaporization of a mixture of pulverized I2C and I3C, held together by Halocarbon wax, leads to
-
u=
'n
+
+
+
+
+
2319
isotopically mixed C3 species. This demonstrates that C3 is not produced solely by evaporation of C3 molecules directly from the laser-heated surface, since such a process would produce only I2C3 and I3C3. Complete atomization of the gas-phase species is also probably not occurring, since the isotopic distribution of the C3 species does not follow a binomial distribution. It appears that C3 is formed by more than one mechanism in the laser-vaporization process. Acknowledgment. We are grateful to Prof. Lon B. Knight, Jr., for the gift of the I3C samples used in this work and to Prof. William H. Breckenridge for the use of the intracavity etalon employed in the high-resolution studies. We thank Dr. Eric Rohlfing for helpful discussions and for communicating the results of his experiments prior to publication. We also gratefully acknowledge research support from the National Science Foundation, under Grant No. CHE-85-21050. Registry No. C3, 12075-35-3; I3C, 14762-74-4; N1,7727-37-9.
Isotope Effects in the Photodissociation Dynamics of the H,'
Molecular Ion
M. Berblinger, Ch. Schlier,* Fakulrat f u r Physik der Uniuersitat, D- 7800 Freiburg, Federal Republic of Germany
and Eli Pollak Chemical Physics Department, Weizmann Institute of Science, Rehovot 76100. Israel (Received: July 22, 1988)
The unimolecular decay of HD2+and H2D+after IR excitation, as observed by Carrington and Kennedy, is discussed. Since the incorporation of zero-point energies in the classical trajectory tunneling (CTT) method employed in our earlier work on H3+ is difficult, we develop a sudden (with respect to bending angle) transition-state theory (TST). Good agreement is found between a classical version of sudden TST (Le., without zero-point energies) and CTT. We then apply the quantum version of sudden TST to HD2+and H2D+,and compute the decay rate and the average translational energy release as a function of total energy E , total angular momentum J, and channel (H+ or D'). We find that, if one fixes the lifetime range to the experimental window, the contributions of both isotopic channels depend critically on zero-point energy, come from almost nonoverlapping J ranges, and produce different translational energy distributions. These results are in agreement with the experimental findings (different spectra for H+ and D+, predominance of H+ over D+ in the dissociation of HD2+).
I. Introduction The extensive measurement of the photodissociation spectrum of the H3+molecular ion by Carrington and Kennedy's2 has been a rich source for theoretical analysis of very slow unimolecular decomposition. In their experimental study, Carrington and Kennedy discovered new and intriguing properties of the H3+ molecular ion. They found that there exist thousands of very long-lived (-nanoseconds to microseconds) resonance states of H3+, whose energy far exceeds (by up to 4000 cm-I) the dissociation energy into H+ H2. They showed that it is possible to associate with each resonant state a well-defined translational energy release. In a systematic study, with the electrostatic analyzer for the H+ product centered at zero kinetic energy release, they measured 27 000 laser lines. When they coarse-grained the 2000 strongest lines with a window of a few wavenumbers they found a very simple structure: four lines separated by about 53 cm-I. These remarkable results brought about a flurry of theoretical activity.j-I2 We showed that the trapping mechanism leading
+
(1) Carrington, A,; Kennedy, R. A. J . Chem. Phys. 1984, 81, 91. (2) Carrington, A. J. Chem. Sor., Faraday Trans. 2 1986, 2, 1089. (3) Child, M. S. J . Phys. Chem. 1986, 90, 3595. Pfeiffer, R.; Child, M. S. Mol. Phys. 1987, 60, 1367. (4) Badenhoop, J. K.; Schatz, G. C.; Eaker, C. W. J. Chem. Phys. 1987, 87, 5317. ( 5 ) Miller, S.; Tennyson, J. Chem. Phys. Lett. 1988, 145, 117.
to long-lived states may be understood in terms of total angular momentum (J) barriers, which can confine the classical motion behind the barrier for infinite time at energies above the dissociation energy.6~~ A classical Monte Carlo estimate of the number of resonance states7 showed that there exist lo5resonance states, more than enough for the multitude of experimental lines. Unimolecular dissociation rates are determined by tunneling through the J barriers. The tunneling rates were estimated with a classical trajectory tunneling method,1° which also provided estimates of product translational energy (ET)distributions. We found that the narrow experimental lifetime window implies a very strong correlation between the total angular momentum of the resonance state and ET. Because of the exponential dependence of tunneling on energy the small lifetime window translates into a small energy window relative to the top of the J barrier. Since the barrier height increases noticeably with J , one can almost uniquely convert ET into J.
-
(6) Pollak, E. J . Chem. Phys. 1987, 86, 1645. (7) Berblinger, M.; Pollak, E.; Schlier, Ch. J. Chem. Phys. 1988,88, 5643. (8) Schlier, Ch.; Vix, U. Chem. Phys. 1987, 113, 211. Schlier, Ch. Mol. Phys. 1987, 62, 1009. (9) Gomez Llorente, J. M.; Pollak, E. Chem. Phys. Lett. 1987, 138, 175. (10) Gomez Llorente, J. M.; Pollak, E. Chem. Phys. 1988, 120, 37. (11) Gomez Llorente, J. M.; Pollak, E. J . Chem. Phys. 1988, 89, 1195. (12) Berblinger, M.; Gomez Llorente, J. M.; Pollak, E.; Schlier, Ch. Chem. Phys. Lett. 1988, 146, 353.
0022-365418912093-2319$01.50/0 0 1989 American Chemical Societv
2320 The Journal of Physical Chemistry, Vol. 93, No. 6 , 1989
Berblinger et al. TABLE I: Properties of J Barriers [Le., Barriers of the Minimal Effective Potential UJ*(R)] for Some Isotopomers of H3" and Their Different Decay Channels" J, h R, a. r, a. Ebrcm-' Qslab/i, cm-'
Figure 1. Barrier region of the minimal effective potentials CJJmin for the dissociation of H2D+ into D+ (at left) and H+ (at right). The total angular momentum J equals 20, 25, 30, 35, 40 (from below). (a, top) Classical picture; energies are referenced to the classical dissociation energy. (b, bottom) Quantum-mechanical picture; energies are referenced to the zero-point energy of HD, and the different zero-point energy of H2 has been taken into account.
An explanation for the simplicity found in the experimental coarse-grained spectrum has also been recently put forth." We found good agreement between the experimental frequencies and splittings, and vibration and rotation frequencies of the "horseshoe" periodic orbit. This orbit has C, symmetry, the central H+ moving perpendicular to the two other hydrogen atoms and oscillating between them. The vibrational frequency (971 cm-*) corresponds to this oscillatory motion, while the rotational frequency corresponds to the rotation of the pair of H atoms, such that J is along the symmetry axis. A detailed investigation of the properties of this orbit for H3+ has been presented in ref 7 and 11; horseshoe orbits for the other isotopomers will be published in a separate paper.13 At present, only very little, nevertheless meaningful, experimental information is available on the photodissociation of the isotopic species HD2+and HzD+. Carrington and Kennedy found long-lived resonances also for these systems. Most interestingly, for HD2+they found that the spectrum leading to the formation of D+ has no lines in common with the spectrum leading to the formation of H+. They concluded that different resonance states must lead to the two channels. This result is reminiscent of observations of long-lived CH4+ ions and their isotopic counterparts. Ottinger found14 that long-lived CHD3+ dissociates to give only H+ and no D+. Klots analyzed this15 and proposed that one observes only H + because of the lower zero-point energy involved in the formation of H+ relative to D+. We will show immediately that Klots's interpretation of the methane ion dissociation holds to a certain extent also for H3+. In a preliminary report12 we showed that the phenomenon observed by Carrington and Kennedy can be understood in terms of the J barriers and zero-point energies. In Figure l a we plot (13) Berblinger, M.; Schlier, Ch., work in progress. (14) Ottinger, Ch. 2.Noturforsch. 1965, ZOa, 1232 (15) Klots, C. E. Chem. Phys. L e f t . 1971, 10, 422.
10 20 30 35 40 45 50
13.215 8.905 6.161 5.737 5.421 5.156 4.919
1.401 1.401 1.410 1.419 1.431 1.448 1.470
39.3 273.6 1 179.6 1974.5 3007.6 4300.9 5881.7
23.9 59.7 267.3 377.5 476.5 562.5 629.9
IO 20 30 35 40 45 50
14.780 11.412 8.286 6.946 6.354 5.988 5.712
1.401 1.401 1.402 1.404 1.408 1.413 1.420
16.3 98.9 333.4 587.3 959.7 1443.7 2041.5
10.7 27.1 47.3 97.4 160.3 218.3 272.3
10 20 30 35 40 45 50
13.666 9.791 6.563 6.052 5.709 5.441 5.214
1.401 1.401 1.407 1.413 1.422 1.433 1.448
30.9 202.7 820.3 1400.1 2158.5 3105.0 4252.5
19.2 48.4 175.5 270.9 357.5 436.4 506.8
10 20 30 35 40 45 50
14.881 11.498 8.339 7.115 6.558 6.206 5.938
1.401 1.401 1.402 1.405 1.409 1.415 1.422
18.0 108.6 367.0 642.1 1036.8 1545.1 2169.6
11.7 29.7 53.4 109.5 175.1 235.5 291.8
10 20 30 35 40 45 50
13.850 9.986 6.806 6.298 5.957 5.692 5.469
1.401 1.401 1.407 1.413 1.422 1.434 1.449
32.3 210.5 839.3 1424.1 2 186.9 3136.9 4286.1
20.2 50.6 180.9 278.4 367.0 447.9 520.0
10 20 30 35 40 45 50
14.139 10.494 6.949 6.276 5.877 5.578 5.331
1.401 1.401 1.404 1.408 1.415 1.423 1.434
23.5 149.1 575.3 1016.9 1611.4 2364.9 3289.2
14.9 37.9 11 1.2 196.5 273.9 345.0 409.2
H2.H"
"The masses for H and D have been taken as 1.0080 and 2.0150u, respectively. Barrier energies E, are measured from the classical dissociation energy. r is the (relaxed) diatomic distance at the barrier. The stabilization frequency firtab follows from the curvature k at the barrier top as fi = ( k / p ) ' / ' , where p is the reduced mass. Qsbb is imaginary, meaning that the motion is unstable. Note that the conformation of all barriers is collinear. the J barriers for the H+ and D+ channels of HzD+ relative to the classical dissociation energy. The corresponding figure for HD2+was shown as Figure l a in ref 12. Relevant numerical data are given in Table I. Note that for any J the barrier leading to D+ H2 is lower than the one leading to H+ DH. This is easily understood in terms of the larger reduced mass ~ D + . Hfor ~ the D+ + H2 motion compared to pH+.HD. Since the height of the J barrier is inversely proportional to p z (for a -C/R" potential), the barriers of the D+ channel are lower. For long-lived states whose energy is necessarily at or below the barrier energies in both channels, this immediately implies that classically only the D+ channel will be open, although the tunneling of D+ is, of course, less probable than that of H+. The real world, however, is quantum mechanical, so one cannot ignore zero-point energies. The zero-point energy of HD is lower than that of H2, implying that for J = 0 at energies below the threshold for formation of H2 only the H+ channel is open. Increasing J will then lead to a crossover value of J , J,, such that for J < J , mostly H+ is formed, while for J > J , it is mostly D+.
+
+
The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 2321
Photodissociation Dynamics of H3+ This is shown in Figure 1b, where we plot the J barriers relative to the zero-point energy of HD, and add the relevant zero-point energy difference for the other channel. Such a plot demonstrates clearly the crossover from the H + channel at low J to the D+ channel at high J . This is the qualitative explanation for the different resonances leading to the different products. Note that for short-lived ( < 1 ps) states this discussion does not apply. At energies above both barriers, both products may be formed, and the selectivity in the photodissociation disappears. The purpose of this paper is to provide a detailed analysis of the dynamics of photodissociation of HD2+ and H2D+. As is evident from Figure 1, a classical theory that does not incorporate zero-point energy effects is useless. In section I1 we describe a sudden transition-state theory, which will be used to estimate lifetimes and product-state distributions. Since TST is easily formulated with and without zero-point-energy corrections, we first compare (for the HD2+ system) the classical sudden TST with tunneling corrections but without zero-point energies to the more exact classical trajectory tunneling method. The good agreement helps to assure us that the quantal sudden TST which includes zero-point energy should give a reasonable approximation to the exact quantal rates. In section I11 we describe this quantal version and provide detailed results for the photodissociation of HD2+ and HzD+. A discussion follows in section IV. 11. Classical Sudden Transition-StateTheory for
Unimolecular Dissociation At a fixed energy E and total angular momentum J , the transition-state theory estimate for the unimolecular dissociation rate k,(E) is given by the well-known expression where pJ(E) is the microcanonical density of resonance states and N,*(E) is the cumulative dissociation probability. In this section we describe in some detail the estimate for N,*(E); the density of states is evaluated by using the classical Monte Carlo method described in ref 7 . Implicit in all the results presented in this paper is the assumption that a purely classical estimate of pXE) is an excellent approximation for the “true” quantal result. This assumption deserves some comment. Most comparisons of classical and quantal densities of states, which can be found in the literature on unimolecular decay, are based in addition on some approximate harmonic or anharmonic extrapolation scheme.I6*” This is not the case in our computations. We obtain converged exact classical densities of states. If one believes semiclassical dynamics, then for the integrated number of states in any energy interval the largest possible mistake in the purely classical estimate is one state. It is well-known that the classical density of states if the zeroth-order approximation to the smoothed quantal density.ls The classical approximation in the energy interval from E to E AE is good provided that there are “a few” quantum states in the interval. In other words, if, e.g., the classical density of states is 1 per cm-I, it will be a good estimate for the quantum density convoluted with a smoothing function of a few cm-l half-width. This observation has been verified for model systems of 2 degrees of freedom, where comparisons of exact quantal and classical densities of states have been made.I6-I8 Since we are looking at high-energy systems with densities of states which are usually greater than 1 per cm-’ we can assume that the quantum density, smoothed over an energy width of, say, 5 cm-I, will be reasonably well approximated by our classical result. One of the main advantages of TST is that the evaluation of N,f(E) is done with a local theory. The barrier to uni,molecular
+
(16) Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; Wiley Interscience: London, 1972. Note that the classical density of states is called on p 128 “semiclassical after Marcus-Rice”. (17) Forst, W. Theory of Unimolecular Reactions; Academic: New York, 1973. (1 8) Berry, M. V. In Chaotic Behauiour of Deterministic Systems; Iooss, G . , Hellemann, R. H., Stora, R., Eds.; North-Holland: Amsterdam, 1983; p 173 and references therein.
decomposition (for the J range considered here) is located at large values of R (the distance from A to the center of mass of BC), where the potential is almost spherically symmetrical. This implies that in this region the orbital angular momentum I is for all practical purposes conserved. As is well-known, TST is a variational theory, and one should vary the transition state to minimize the flux. The approximate separability then implies that the location of the transition state should be determined via the orbital angular momentum 1 rather than with total J . In the following, the BC coordinate is denoted by r, and the bend angle between R and r is y. The classical I-dependent barrier is defined as
.
c
V / ( R , y )= min r
I
V(r,R,y)
+-
The y-dependent transition state V/*(R*,y)is located at the maximum of Vl(R,y);the appropriate value of r is denoted as r*. Having defined the barrier, we can use the sudden (with respect to the bend angle y) transition-state theory with tunneling corrections described in ref 19 to estimate the cumulative dissociation probability atfixed J . In this section, all variables will be treated classically. The vibration of the diatom at the transition state is assumed to be anharmonic but with the same constants as the asymptotic diatom. At a given total energy E, classical vibrational action n, and rotational action j , the translational energy is E T ( n j ) = E - (nu, - n2w,xe/h) -
jz
2mrt2
(2.3)
Here, we, and wewe are the usual (asymptotic) vibrational constants of the diatom BC viewed as a Morse oscillator, r* is taken as the asymptotic diatomic equilibrium distance, and m is the diatomic reduced mass ( m = mBmC/mBC).Note that eq 2.3 is a classical formula; its quantum version will be eq 3 . 1 . The cumulative reaction probability at fixed angle y and fixed J is obtained by integrating over all variables subject to conservation of total angular momentum:
The tunneling probability is estimated with the usual semiclassical approximation pj,/(ET>y)= ( 1 + exp[Aj,/(ET,y) / h 1 I-’
(2.5)
where the tunneling action Aj,/is obtained by numerical integration:
Finally the cumulative reaction probability is obtained by integration over the bend angle: N,*(E) =
lr N,*(E,y) sin y d y 0
(2.7)
Since p J ( E ) is obtained by simple integration, N,*(E) is also obtained by integration rather than by averaging as in ref 19. Also note that the 2J 1 degeneracy cancels out in eq 2.1, and so it is not included in N,* or in pJ. The sudden TST presented so far has some simplifying assumptions in it: 1 and j are assumed to be conserved in the barrier region, and the diatomic vibration is taken with the asymptotic constants instead of those evaluated at the barrier. Before using such a theory to estimate quantal rates, these “drastic” assumptions should be tested. The classical trajectory tunneling method described in ref 10 does not use any of these simplifying assumptions. In contrast to ref 10, where only planar trajectories were run, here we apply the CTT method in 3D. In this method, a classical trajectory is integrated for a very long time T . At various times
+
(19) Pollak, E. J . Chem. Phys. 1985, 82, 106; 1985, 83, 1111.
2322 The Journal of Physical Chemistry, Vol. 93, No. 6, 1989
Berblinger et al. 12
lg k.s
lg k s
1-20
11
6
0
_1__
-6 00
02
04
06
10
08
12
E [lo3 cm-'I
6
L U Y & rU 0
1
li
__2
3
4
E [lo3 cm-'I I
1
I '
0
1
~
" / " " l " ' " ' '
3t~nsl
2
5
Figure 2. Convergence behavior of the classical trajectory tunneling (CTT) method; cf eq 2.8 of text. The accumulated rate (log k in s-I) is plotted for the H + channel of HD2+ at the energies shown in Table 11. (a, top) J = 20 and (b, bottom) J = 40. Note the different abscissa scales. 12
1
I
0' 1-20
I
8
0
1
2
4
3
5
6
7 tlnsl
8
9
10
,
, , ,:
10
lg k s
5
0'
1.40
0
-.j,, , ,
0
I , ,
1
, ,
,, 2
, ,
,
,
tlnsl
,
I
4
,
, , ,
5
Figure 3. Similar to Figure 2, but showing the two classically distinguishable D+ channels separately (full and dotted lines related by brackets in dubious cases).
Figure 4. Comparison of the rates given by classical sudden transitionstate theory (TST) and by C T T for the unimolecular decay of HD2+for (a, top) J = 20 and (b, bottom) J = 40 (note the different abscissa scales). Full lines: Sudden TST rate vs total energy for H + (lower curve), and D+ (upper curve). Dotted vertical lines: J barrier energies (D+at left). Triangles and crosses: CTT rates for H+ (X) and D+ (A). The dashed line in the D+ channel of Figure 4b denotes the classical RRKM result based on an exact phase space integration (cf. ref 7).
ti in its history it will reach a barrier in the R coordinate. At each such turning point Rtpit will have a probability Pi@,,) of crossing the J barrier. This transmission probability is estimated by using the usual semiclassical approximation for tunneling through a barrier (cf. ref IO). The unimolecular tunneling rate is then
Note that with this method there is no need to estimate the density of states; the comparison of the two methods verifies also that most of phase space is ergodic, so that a single trajectory suffices for the CTT method. In Figure 2 we show the convergence properties of the classical trajectory tunneling method (CTT) for the HD2+system at J = 20 and J = 40. Convergence for J = 40 is much faster than for J = 20 (note the different time scales), where over a very long integration period only a few turning points lead to noticeable dissociation. This points out an additional necessity for a simpler numerical estimate for the rates. In the TST approach there are no special convergence problems at low J (except J = 0); actually one expects sudden TST to be better at low J rather than at high J because for low J the barrier is at larger R* where the potential is less anisotropic. A different view of the convergence problems of the CTT method is presented in Figure 3. For the HD2+ system there are two identical channels leading to the D+ product. In a classical trajectory method one can, of course, evaluate the rate for each D+ separately, but because of symmetry these rates should be equal. In Figure 3 we plot these rates for the two D+ channels for J = 20 and 40 at different energies. Note again the different time scales, and that convergence becomes slower as the energy decreases. Once more, as E is lowered only a few turning points have a significant tunneling probability. In Figure 4 we compare the tunneling rates obtained via the CTT method (triangles and crosses) and the TST method (solid
Photodissociation Dynamics of H3+
The Journal of Physical Chemistry, Vol. 93, No. 6. 1989 2323
TABLE II: Comparison of the Classical Trajectory Tunneling Method (Upper Line at Each J , E ) with the Classical Version of Sudden Transition-State Theory (Lower Line)"
E , cm-I
T, ns
Nn+
ND+
20
329
10.16
40
38
305
20
439
9.43
52
64
309
20
658
7.26
97
112
318
20
878
5.56
142
157
327
20
1097
5.03
180
206
336
40
1097
5.56
422
48 5
171
40
1207
5.37
422
511
174
40
1317
5.08
545
623
177
40
1426
4.84
54 1
676
180
40
1646
3.68
58 1
553
186
40
1975
3.10
667
729
195
40
2195
2.81
654
838
20 1
J, h
hp,,
PS
kH+, S-I
kD+,S-I
(&,I++), cm-I
( E T , D + ) , cm-l
3.2 (8) 4.3 (8) 1.3 (9) 1.6 (9) 5.6 (9) 6.3 (9) 1.5 (10) 1.4 (10) 2.4 (10) 2.4 (10) 1.0 (-6) 1.6 (-6) 7.7 (-5) 1.3 (-4) 4.7 (-2) 6.8 (-3) 9.3 (-1) 2.5 (-1) 4.5 (1) 1.5 (2) 2.9 (5) 3.8 (5) 1.2 (7) 2.7 (7)
1.2 (9) 1.6 (9) 4.1 (9) 3.7 (9) 1.2 (10) 1.0 (10) 2.2 (10) 2.0 (10) 3.2 (10) 3.3 (10) 4.7 (7) 1.6 (7) 2.9 (8) 1.7 (8) 9.9 (8) 7.9 (8) 3.9 (9) 2.3 (9) 1.1 (10) 9.1 (9) 2.5 (10) 2.9 (10) 5.8 (10) 4.8 (IO)
267 246 266 285 345 36 1 430 436 51 1 511 905 979 1069 1071 1254 1163 1251 1182 1431 1434 1587 1702 1826 1878
198 189 226 226 300 300 379 374 484 447 983 1002 1014 1076 1124 1141 1244 1203 1317 131 1 1446 1443 1496 1524
For different total angular momenta J, total energies E (referenced to the classical dissociation energy), and decay channels (H+ or D+) we provide the duration T of the CTT trajectory, numbers N of turning points leading to each channel, the classical density of states p,(E), and the decay rates k and average product kinetic energies ( E T ) in each channel.
lines) for J = 20 and 40. Quantitative numerical data are given in Table 11. Note the excellent agreement. For J = 40 in the D+ channel we also show (dashed line) the results of a purely classical TST estimate of the rate. It is based on a purely classical Monte Carlo estimate (Le., without tunneling corrections) of the number of states at the transition state, which is taken on the J barrier. The excellent agreement obtained by these three independent methods indicates that the sudden TST method is probably a reliable tool and that it really does not make a big difference whether one uses the J barrier or the 1 barrier as the transition state in this application. Both the CTT and the TST methods may be also used to estimate product-state distributions. The probability for observing ET is just the tunneling probability at ET. Accordingly the products' average translational energy for the sudden TST method is given by
/
l 0 ~0 ~ 43 ~ - ~ 1 /
02
111. Isotope Effects II1.A. Quantal Sudden Transition-State Theory. In the quantal version of TST, variables which are continuous in the
'
"
'
'
02
"
I/, 0
'
04
E
0
An analogous expression for the CTT method was given in ref 10. ( E T ( J , E ) )is plotted as a function of E for J = 20 and 40, and for the two arrangement channels in Figure 5 . The CTT results (triangles and crosses) are again in good agreement with the TST estimates (solid lines). In Table I1 we also provide quantitative numerical data for the comparison of the CTT and classical TST estimates of ( E T ( J , E ) ) . One could also present comparisons of the actual distribuions. However, as noted in ref 10 and 11, the distributions are extremely narrow, so that the added information would be marginal. As mentioned in the Introduction, the results presented in this section indicate that, for energies such that the rates are within the experimental window, D+ is by far the dominant product. The reason for this is the neglect of vibrational zero-point energy. In the next sections we use the sudden TST method with zero-point energy corrections to analyze the photodissociation dynamics of HD2+ and H2D+.
-
01
00 ~ ~ 00
,
,
~
'
06
'
E
~
1" " ' '
~
08
12
10
[lo3 cm-l]
, , ,
1
'
2 [lo3 cm-'1
/
3
,
,
,
,
i I
4
Figure 5. Comparison of the average product translational energy obtained from sudden TST and CTT,respectively. Legend as in Figure 4, except that D+is here the lower curve. Note that in the tunneling region ( E T ) equals total E.
classical limit become discrete, and discrete sums replace integrations. At total energy E, vibrational quantum number n, and rotational quantum number j , the translational energy is
E - [(n + h ) h w , - (n
+ )/2)2hwex,]-
h2jG + I )
2mrt2
- AEI (3.1)
AEI is the difference in the ionization energies of H and D (30 cm-I), so that for the D+ channel the threshold energy is larger by an additional AEI compared with the Hf channel, for which AEI is taken as zero. This additional effect was not taken into account in ref 12, so that there are some small differences between
2324
The Journal of Physical Chemistry, Vol. 93, No. 6,1989
Berblinger et al.
12
lg k s
I
500 t
hP
6
[cml
[PSI
10
300
0
200 3
100
-6
0
2
1
3
4
E [lo3 cm-l]
0
Ll
0
L
i
L
L_
3
2
1
-A
0
4
E [lo3 cm-l] Figure 7. Classical density of states (i.e., energy derivative of phase space volume in units of h6) vs total energy. The curve parameter is J .
lg k s 1
______
-
6 C
I
O
t
0
1
2
3
4
E [lo3 cm-'] Figure 6. Unimolecular decay rate of HD2+(log k in 8)into (a, top) H+ + D2 and (b, bottom) D+ HD vs energy as computed by quantal sudden TST. E is referenced to the zero-point energy of D1. The curve parameter is J (=lo, 20, 30,35, 40,45,50 from left to right). The dotted
+
2
1
E
3
4
[lo3 cm?]
vertical lines indicate the respective barrier energies. The leftmost region in Figure 6b is forbidden because of the additional zero-point energy of
Figure 8. Branching ratio (log of) r = k ~ / k , + vs energy with parameter J (=lo, 20, 30,35, 40,45, 50 from left to right) computed by quantal
HD.
sudden TST.
a few of the HD2+ results presented here and in that reference. The cumulative (fixed angle) reaction probability is
logarithmic scale) the energy dependence of the rates for both channels; the energy scale is relative to the D2 zero-point energy. For low J values, one notes a step structure in the energy dependence of the rate which does not exist in the classical analogue, Figure 4. This structure is not an artifact; it is the result of the quantization of rotational states. At low J the barrier heights are small, and only a few j states are accessible, so that the opening of each additionalj state contributes significantly to the rate. We believe that this stepped structure is also not a peculiarity of the TST used to estimate the rates. Similar effects associated with the thresholds for new vibrational states are well-known from numerically exact quantal collinear scattering computations.20 Another interesting feature of the rates presented in Figure 6 is the change in slope as one goes from low to high J values. At low J the barriers are broad, and the imaginary frequency of the barrier is small. The tunneling probability depends exponentially on the inverse of that frequency, so that the slope is very large. In different words, if the energy is just slightly below the barrier the tunneling probability already becomes very small. At higher J , the barriers become thinner and therefore the slopes smaller. This implies that the energy window associated with an experimental lifetimes range will grow with increasing values of J. Note also that the slopes for the H+ channel are generally smaller than for the D+ channel because of the ease with which the light H+ tunnels relative to D+. In Figure 7 we plot the classical densities of states evaluated via the Monte Carlo method. Note that the densities are smooth and slowly varying functions of energy. Quantum fluctuations around these functions will not change the branching, and it is difficult to see how they could change absolute values of the rate appreciably. The energy and angular momentum dependence of the branching ratio is plotted in Figure 8. For small J there exists a finite range of energies for which H+ is the predominant product.
-
J+i
where, in practice, the summation over n will include only the ground state. Because of the large vibrational quanta involved, vibrationally excited product molecules can only be obtained at energies which drastically exceed the J barrier heights for n = 0 products. Therefore, any state which might lead to n > 0 products will be very short-lived (shorter than the experimental lifetime window of ref 1 and 2), and an overwhelming fraction of its decay will be into high ET but n = 0 products rather than low ET n > 0 ones. The tunneling probabilities are estimated as in the previous section (cf. eq 2.5, 2.6), with the slight difference that here the I-dependent barrier is defined as c
hZI(1 4- 1)
-
2hR2 The cumulative reaction probability is then obtained by integration over the angle y as in eq 2.7. The average product translational energy is also obtained by using summations:
The unimolecular quantal rate is then estimated by using eq 2.1 with the classical Monte Carlo estimate for the density of states p J ( E ) . The justification for this use has been outlined in the previous section. III.B. Unimolecular Dissociation of HD2+. Unimolecular dissociation rates were evaluated for the D+ and H+ channels for a large range of Ss and energies. In Figure 6 we plot (on a
(20) Bowman, J . M.; Kuppermann, A. Chem. Phys. Lett. 1971, 12, 1 .
Photodissociation Dynamics of H3+
The Journal of Physical Chemistry, Vol. 93, No. 6,1989 2325
ET,H+ [lo3 cm
25
35
30 J
40
[rJ
E
Figure 9. Total angular momentum dependence of (log of) the branching ratio r = kH+/kD+ in the unimolecular decay of HD2+. r is plotted here for energies corresponding to thefiwed liferimes T = (kH++ kD+)-'of lo9 s (lower curve) and 10" s (upper curve). There is practically only one decay product outside the hatched region 0.1 5 r 6 10. Concurrent observation of H+ and Dt is possible only in the cross-hatchedJ range.
As long as the energy is below the J barrier height which leads to D+,the ratio is large compared to 1, but falls off rapidly with energy. As E becomes larger than this J barrier, the branching ratio becomes almost energy independent. As J increases, the D+ barrier becomes ultimately lower than the H+ barrier, and then for most energies D+ is the predominant product. The parabola-like shape of the curves comes as a result of the mass dependence of the tunneling probability. At very low energy, although the H+ barrier is higher than the D+ barrier, the light mass of the H+ causes the tunneling probability of that particle to be larger than that of D+.This occurs, though, only when the unimolecular rates are extremely small. As the energy increases, energetics takes over, and the lower D+ barrier leads to predominant D+ formation. As energy is further increased, one approaches the H+ barrier energy, at which the probability of H+ formation rises exponentially because of tunneling, while in the D+ channel the energy is already greater than the barrier height and the rate increases only as a power law. As a result, the branching ratio again increases until it becomes almost energy independent at energies which are greater than the H+ barrier height. From the results presented in Figure 6, one can deduce the ranges of J which, within the experimental lifetime window, lead to formation of H+ and D+, respectively. This is shown in Figure 9. (Note that it differs slightly from Figure 2 of ref 12 because the effect of the different ionization potentials of H and D has now been included. In addition, in the caption of that figure the s were mistakenly interchanged.) The two rates of 10" and upper solid curve shows the J dependence of the (logarithm of the) branching ratio at the fixed unimolecular dissociation rate of lo6 s-I, the lower curve at the rate of lo9 s-l. The branching ratio changes from 10 to 1/10 in the cross-hatched region; this area determines the range of J values for which both branches would in practice be accessible. Figure 9 is, therefore, one of the main results of this paper-it shows clearly that for most values of J a state leading to H+ will not lead to D+ and vice versa, in agreement with the experimental observations of Carrington and Kennedy. The transition-state theory we are using also predicts the translational energy distributions. In Figure 10 we plot the E and J dependence of the average product translational energy for the H+ and D+ channels. The undulations at low J are again a reflection of the quantization of internal rotational states. The average product translational energy drops with each opening of a rotational state, then increases until the next state opens, etc. As J increases, the barrier height increases, more rotational states contribute, and the undulations disappear. The threshold for D+ production is shifted because of the zero-point energy and ionization potential differences discussed above. In order to compare with experimental results one should study the dependence of (ET)on J for all rates within the experimental window. This is presented for both channels in Figure 11. The
1
0
Em+
3
3
2 [lo3 cm-'I
4
t
/ . I
1
0
3
2
E
4
[lo3 cm-l]
Figure 10. Average product translational energy ( E T )computed from quantal sudden TST of (a, top) the H+ and (b, bottom) the D+ decay channels from HD2+vs total energy (referenced in both cases to the zero-point energy of D2). The curve parameter is J (=lo, 20, 30, 3540, 45,50 from bottom to top). The wavy nature of the low-J curves reflects the opening of new j channels of the diatomic product (D2 and HD, respectively). ET.H'
r-A
I:/ .-;-I
2'5
[lo3 cm-'1
0.5
00
, , , . .
10
20
15
25
30
J
25
~
8
I , -
I
I
,
~
I , ' ,
1
8
40
35
45
50
[EJ
,
I
,
,
,
I
I
~
'
I
I
,
, ,,
ET D+ [lo3 cm-l]
!
c
15 :
10
15
20
30
25 J
35
40
45
50
[EJ
Figure 11. Total angular momentum dependence of the average product
translational energy computed as before for (a, top) the H+ channel and (b, bottom) the D+ channel from HD2+. Energies are taken (as in Figure 9) such that the unimolecular lifetime is lod s (lower curve) and lo4 s (upper curve), which brackets the observation window of ref 1 and 2. The kinks in the curves come from the opening of the D+ channel at J N
21.
lower line is ( E T )when the unimolecular rate is lo6 s-', the upper line for lo9 s-I. Consider first the H+ channel. From Figure 9 one concludes that the H+ channel is practically closed for J 1 3 1. From Figure 11 one can then deduce that the maximal average translational energy of H+ that will be observed experimentally
Berblinger et al.
2326 The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 TABLE 111: Results of the Quantum Version of Sudden TST for HD,"'
12
lg k s 6
20
30
40
50
200 400 1000 2000 4000 100 200 400 1000 2000 4000 100 200 400 1000 2000 4000 400 600
302 311 342 400 535 355 359 368 397 449 574 295 298 306 328 371 467 192 198 1000 209 1500 224 2000 240 4000 313 1000 88 2000 107 3000 132 4000 158
2.76 (IO) 7.90 ( I O ) 2.02 (11) 3.20 (11) 4.53 (11) 4.68 (0) 7.01 (7) 3.25 ( I O ) 1.20 (11) 2.58 (11) 4.08 (11) 5.85 (-23) 1.23 (-1 3) 8.01 (-4) 1.28 (10) 1.79 (11) 4.12 (11) 1.33 (-24) 3.89 (-17) 2.19 (-7) 1.80 ( I ) 4.66 (6) 3.01 (11) 1.20 (-24) 3.77 (-9) 1.69 (0) 1.75 (6)
0.00 1.23 ( I O ) 1.87 (11) 3.60 (11) 6.06 (11) 0.00 0.00 8.38 (-5) 9.48 ( I O ) 3.18 (11) 5.58 (11) 0.00 0.00 1.33 (-29) 4.68 (IO) 2.68 (11) 5.95 (11) 0.00 3.71 (-21) 2.15 (-2) 1.13 (9) 1.13 (11) 6.37 (11) 3.56 (-21) 5.53 (1) 3.13 ( I O ) 4.55 (11)
149 213 483 1041 2173 100 199 309 646 1119 2224 100 200 381 890 1441 2478 39 1 567 925 1351 1770 3067 949 1846 2698 3484
29 286 830 1803
0
-6
'The total energy E is measured from the lower of the two possible product zero-point energies (zpe), in this case from the zpe of D2, which is 371 cm-' below that of HD. p J ( E ) is the classical density of states, k the rate in each channel, and (ET)the average product kinetic energy in each channel. is 680 cm-'. Moreover, the proximity of the two curves, together with the small width of the translational energy distributions themselves, indicates that from a measured ( E T ) one can almost uniquely identify the total angular momentum of the state leading to that ( E T ) . Similarly, for the D+ channel we predict that the lowest observable translational energy is 286 cm-', since lower energies will only be found for Ss which lead predominantly to the H+ channel. These quantitative predictions on the relationship between ( E T ) ,J , and the unimolecular lifetime could change somewhat if the DIM potential energy surface21 used so far in our work would be replaced by a more accurate one. Unfortunately the recent very accurate computations of Meyer's group22 do not yet span the whole configuration space needed for the TST computations. In Table 111 we provide numerical data on the rates and on product translational energies for the HD2' system. 1II.C. Unimolecular Dissociation of H2D+. Qualitatively, the branching pattern of H2D+is very similar to that of HD2+. The threshold for formation of H + is lower than that for D+ by 317 cm-l because of the lower zero-point energy of H D relative to H2, and the ionization energy difference between D and H. However, the reduced mass of D+.H2 is larger than that of H+.HD giving rise to a crossover from H+ formation at low J to D+ formation at high J , as discussed already in the Introduction. In Figure 12 we plot the E and J dependence of the dissociation rates into the H+ and D+ channels-note the overall similarity to the HD2+ system shown in Figure 6. Densities of states are plotted vs E and J in Figure 13; again results are similar to Figure 7. As expected, densities are somewhat lower here because of the smaller mass of H2D+. Given the rates and the experimental window one can determine the range of J values that lead to formation of H+ and D+. This is shown in Figure 14. As in Figure 9, the cross-hatched region (21) Preston, R. K.; Tully, J. C. J. Chem. Phys. 1971, 54, 4297. (22) Meyer, W.; Botschwina, P.; Burton, P. J . Chem. Phys. 1986, 84, 891, and private communication.
2
3
4
3
4
E [lo3 c K 1 ]
29 542 1068 2038 229 622 1075 1421 2455 626 1555 2427 3082
1
0
29 430 834 1820
F
"
0
2
1
E [lo3 c i ' ] Figure 12. As in Figure 6 but for H2D+.E is referenced to the zero-point energy of HD.
P ---7 ,
hP500
T---
c
[PSI
[cml
10
300
200 5 100
-1
0
0
0
2
1
4
3
E [103 cm-l] Figure 13. As in Figure 7 but for H2Dt. E is referenced to the zero-point
energy of HD. 7 -T-
--T-T
7
lg
r 5
0
- 5 [ , ,
,
,
,
,
,
,
J
[GI
,
,
,
,
,
,;
-10 25
30
35
40
Figure 14. As in Figure 9 but for H2D+.
denotes the crossover from predominant H+ production for J 5 30 to predominant D+ production for J 1 35. There is, though, a quantitative difference when comparing the HzD+ system with the HD2+ system: The ratio ~ H + . H D / ~ D + . H=~ 3/4 in the H2D+ system is larger than the ratio pH+.Dz/pD+.HD = 2/3 in the HD2+ system. As a result, the difference of the barrier energies for the two channels in the H2D+ system changes at a slower pace than in HD2+. This leads to a broader range of overlap of the two product channels, as can easily be seen by comparison of Figures
The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 2327
Photodissociation Dynamics of H3' 35
TABLE I V Same as Table 111 but for the H2D+ IsotopomeP
E,H+ [io3 cm-*]
25 20 15 10
20
05 00 10
20
15
30
25
35
40
45
50
JM 3 5 p8
I
,
,
!
,
, . I
8 1 8
1
7
,
30
! , I , / , ' I , ,
1
%,D+ [lo3 cm-'1
25 20 15 10 05 00
[
, ,
I " ' ' , ' , , .
A
.
1 1
40
50 t
i 10
15
20
25
30 J
35
40
45
50
[fi
200 400 1000 2000 4000 100 200 400 1000 2000 4000 100 200 400 1000 2000 4000 400 600 1000 1500 2000 4000 1000 2000 3000 4000
212 218 238 277 365 231 234 240 258 292 370 169 171 176 190 216 272 88 91 97 105 115 156 24 31 40 51
7.55 (10) 1.65 (11) 4.05 (11) 6.62 (11) 8.87 (11) 2.97 (0) 3.34 (7) 5.81 (10) 2.44 (11) 4.92 (11) 8.52 (11) 1.04 (-22) 2.05 (-13) 7.94 (-4) 6.42 (9) 3.63 (11) 9.16 (11) 2.78 (-24) 6.50 (-17) 3.36 (-7) 1.94 (1) 3.41 (6) 6.20(11) 4.75 (-27) 6.07 (-11) 3.41 (-1) 2.12 (6)
0.00 9.17 (9) 7.56 (10) 1.81 (11) 3.50(11) 0.00 0.00 5.42 (2) 6.99 (10) 1.71 (11) 3.24 (11) 0.00 0.00 3.26 (-20) 9.20 (9) 1.60 (11) 3.53 (11) 0.00 1.93 (-24) 2.73 (-8) 6.74 (2) 1.17 (9) 3.87 (11) 1.96 (-29) 5.45 (-8) 4.68 (3) 2.82 (10)
132 217 466 96 1 2174 100 200 335 66 1 1201 2213 100 200 398 924 1501 2524 400 589 946 1403 1846 3248 960 1861 2736 3628
83 440 953 1766
83 440 953 1865 83 653 1154 2225 283 68 1 1138 1597 2713 683 1603 2532 34p3
"The total energy is now measured from the zpe of HD, which is
Figure IS. As in Figure 11 but for H2D+
317 cm-l below that of H2.
14 and 9. The same effect implies that the spread in translational energies is somewhat larger in HzD+ as shown in Figure 15 (cf. Figure 11). Here the experimental lifetime window limits the I1190 cm-', translational energy of H+ to the range 0 I(ET) while the apparent threshold for D+ is (ET)1 540 cm-I. Detailed numerical results for H2D+ are provided in Table IV.
would probably not change the results too much. When compared to the classical trajectory tunneling method, the TST approach is much less time consuming. The advantage of the CTT method is that it does not need a separate evaluation of the density of states. This advantage is offset by the difficulties of incorporating zero-point energies and of evaluating very low rates. All computations reported in this paper are for averaged unimolecular rates. In principle, the rates of specific resonance states will fluctuate around the classical average. For example, if dynamical bottlenecksz4existed in this system one could seriously question the practical implications of our predictions. However, the good agreement between the CTT method and the TST estimate demonstrates that such bottlenecks do not exist to any significant extent in H3+,a fact which is also known from other observations, e.g., from a multitude of trajectory plots. If motion is truly chaotic then one expects that the deviation of densities and rates from the mean will be sma1LZ4The way to remove all doubt is to actually determine experimentally the rate distribution as described above. An exact quantal computation in 3D is still virtually impossible. Another interesting aspect of this computation is the effect of a heavy mass on substitution. Klots estimated15 that, in contrast to intuitive expectations, tunneling is possible also for heavy masses. Inspection of Figures 6 and 12 shows that, for both the HzD+ and the HDz+ systems, and for both the D" and H+ channels, almost all rates are determined by tunneling through the barrier provided that the rate is lower than lo7 s-l. The effect of the light mass is to decrease the slope of k ( E ) vs E . However, if one observes either H+ or D+ at a given low rate, both products are formed via tunneling. This computation might serve as a further indication that tunneling could be observed in very heavy mass systems such as Ar3+, as suggested in ref 25. In this paper, we have not studied the rotating horseshoe orbits for the various isotopes as was done for H3+ in ref 1 1. As mentioned in the Introduction, these are important for understanding the coarse-grained spectra of the isotopic systems. A detailed study
IV. Discussion The results presented in this paper are to a certain extent a quantitative verification of Klots's a n a l y s i ~of ' ~ the unimolecular decomposition at low energy of CH3D+ and other isotopes of methane. Klots proposed that one observes only H+ because of the lower zero-point energy of formation of H+ + CH2D relative to D+ CH3. This is exactly the case also in the unimolecular decomposition of the isotopes of H3+. The main qualitative difference between our work and Klots's is the identification that it is the total angular momentum which differentiates between the two isotopes. The light mass is formed at low J, and the heavy mass at high J even though the absolute energy is not necessarily low. The detailed results presented in this paper should help in guiding the experimentalist in further studies of these interesting long-lived states. It is becoming clear that knowledge of the translational energy distributions and their correlation with the fragment masses and the laser frequency is essential. For example, it should be possible to measure the maximal translational energy for formation of H+, and alternatively the minimal energy for formation of D+ in both isotopic species. Similarly, it would be interesting to scan the whole spectral range at a fixed and well-resolved translational energy. This would give much more insight into the density of resonance states at a fixed total angular momentum. Beyond the immediate practical implications, we have demonstrated that sudden transition-state theory is a useful tool for estimating unimolecular dissociation rates. We note that one could, in principle, also evaluate a fully adiabatic transition-state theory.lg This is the underlying idea of the adiabatic channel however, such a computation is much more tedious and
+
(23) Quack, M.; Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1974, 78, 240.
(24) Berry, M. V. Proc. R. SOC.London 1985, A400, 229. (25) Ferguson, E. E.; Albertoni, C. R.; Kuhn, R.; Chen, Z.Y.; Keesee, R. G.; Castleman, Jr., A. W. J. Chem. Phys. 1988, 88, 6335.
2328
J. Phys. Chem. 1989, 93, 2328-2333
of rotating horseshoes in these systems is under way; here we report the preliminary result that for the HD2+ system one finds stable rotating horseshoes in the potential of ref 22. Their vibrational frequency is approximately a factor of 21/2less than in H3+,and the rotational constant is approximately half the rotational constant of H3+. Finally, one should also study intensities of the spectra in the various channels, since variations between the D+ and H+ channels have been observed; this is left for the future.
Acknowledgment. We thank Dr. J. M. Gomez Llorente for stimulating discussions and for providing us with the CTT program. This work has been supported by grants of the U S . Israel Binational Science Foundation, the Minerva Foundation, and the Deutsche Forschungsgemeinschaft (Schwerpunktprogramm Atomund Molekiiltheorie). Registry NO. HD2+, 12444-53-0; H2D+, 12517-67-8; H,', 28 132-48-1; D,, 7782-39-0.
Matrix-Induced Intersystem Crossing in the Photochemistry of the 1,2-DichIoroethenes Sandra L. Laursen and George C. Pimentel* Chemical Biodynamics Division, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 (Received: July 26, 1988)
The photoproducts of the 1,2-dichloroethenes(DCE) in xenon matrix at 12 K differ from those observed in krypton matrix. In xenon, photolysis at 237 nm of both cis- and trans-dichloroethene results in elimination of both CI2 and HCI as well as isomerization, whereas only HCI elimination and isomerization are observed in krypton. Longer wavelength irradiation has no effect on either DCE in Kr but produces small, distinct amounts of products in Xe. The results indicate that in xenon, chemistry is occurring through a triplet state as well as from the directly excited singlet state. Enhanced spin-orbit coupling in the heavy-atom environment facilitates intersystem crossing from the initial singlet to a triplet surface, as well as, no doubt, enhanced absorption directly into the triplet state. These effects provide access to the normally spin-forbidden chlorine elimination channel. The appearance of products in Xe at the lower photon energies is ascribed to direct Tl+So absorption, assisted by the external heavy atom.
Introduction Haloethene photochemistry has been studied in the gas phase by using both direct photolysis and m e r ~ u r y ( ~ photosensitizaP) tion.14 Elimination of H X (X = F, C1, Br) is the most common reaction pathway for photoexcited mono- and dihaloethenes in the gas phase, although isomerization, CI atom detachment, and ~ molecular CI2 elimination have also been r e p ~ r t e d . Vacuum-UV photolysis of the dichloroethenes isolated in cryogenic matrices likewise yields HC1 and its matrix cage partner C2HCl as the principle product^.^^^ However, recent matrix isolation studies of the metal-atom(3P)-sensitized photochemistry of some haloethenes contrast with gas-phase results in the finding of other primary products than the H X elimination For both difluorochloroethene and dichloroethene, insertion of Hg into the CCI bond occurs upon selective excitation of Hg codeposited with the olefin in krypton matrix. The formation of the organomercuric halide indicates that chemical reactivity plays a role in photosensitization along with energy transfer and exemplifies the type of transient reaction intermediates that participate in the sensitization process. The second important realization from these studies is that matrix photochemistry of these molecules is constrained to the reaction surface of the initial singlet or triplet excited state. For cis- and 1,l-dichloroethene in solid krypton, chlorine elimination occurs upon Hg(3P)-sensitized photolysis but not upon direct (11 Berrv. M. J. J . Chem. Phws. 1974. 61. 3114. (2j Be& M. G.; Wan, J. K.'S.; Allen, W. F.; Strausz, 0. P.; Gunning, H.E. J . Phys. Chem. 1964.68,2170. (3) Strausz, 0. P.; Norstrom, R. J.; Salahub, D.; Gosavi, R. K.; Gunning, H. E.; Csnmadia, I. G. J. A m . Chem. SOC.1970, 92, 6395. (4) Tsunashima, S.; Gunning, H. E.; Strausz, 0. P. J. Am. Chem. Soc 1976 98 .. -, . -, 1690 - - - -. ( 5 ) Ausubel, R.; Wijnen, M. H. J. Ini. J . Chem. Kinet. 1975, 7 , 739; J. Phoiochem. 1975, 4, 241; J. Photochem. 1976, 5, 233. (6) Warren, J. A.; Smith, G. R.; Guillory, W. A. J. Photochem. 1977, 7 , 263. (7) McDonald, S. A.; Johnson, G. L.; Keelan, B. W.; Andrews, L. J. Am. Chem. Soc. 1980, 102, 2892. (8) Cartland, H. E.; Pimentel, G. C. J. Phys. Chem. 1986, 90, 1822. (9) Cartland, H. E.; Pimentel, G. C. J. Phys. Chem. 1986, 90, 5485 (I).
singlet excitation, indicating that the C12 elimination channel is made accessible via triplet excitation. This aspect, namely, the extent to which the photochemistry is determined by the initial excitation surface, has been the focus of our recent investigations of the photochemistry of the 1,Zdichloroethenes in xenon matrix. The heavy-atom environment facilitates intersystem crossing and thus may be expected to alter the accessibility of normally spinforbidden reaction channels. The use of an external heavy atom instead of a triplet sensitizer simplifies the reaction dynamics by excluding the chemical reactivity of the sensitizer from involvement in the energy-transfer process. We present here the photochemistry of cis- and trans-l,2-dichloroethene in xenon matrix, using laser and Hg-Xe lamp irradiation at wavelengths longer than 200 nm.
Experimental Section The cryogenic apparatus, infrared spectroscopy, and Hg-Xe lamp photolysis were essentially the same as those described by Cartland and Pimentel.* In a typical experiment, 0.5 mmol of a xenon/dichloroethene mixture at M/R = 100 was deposited with a flow rate of 0.3 mmol/h onto a CsI substrate held at 25 K. The matrix was cooled to 12 K for subsequent spectroscopy and photolysis. Infrared spectra were taken with an IBM-Bruker IR97 FTIR spectrometer or in some experiments with an IBM IR44 FTIR. Both spectrometers were equipped with a globar source, Ge-coated KBr beam splitter and liquid-nitrogen-cooled Hg/ Cd/Te detector. Spectra were collected between 4000 and 400 cm-' with a resolution of 0.5 cm-'. Photolyses were performed with both monochromatic and broad-band light sources. The second harmonic (532 nm) of a Quanta-Ray DCR Nd:YAG laser was used to pump a PDL-1 pulsed dye laser equipped with a WEX-1 wavelength extension system. Generation of the dye second harmonic in the WEX and mixing of this with the 1.064-wm fundamental of the Nd:YAG laser enabled tunability of the photolysis wavelength over the range 217-265 nm. In these experiments rhodamine 640 dye was used to attain a photolysis wavelength of 237 nm. Typically the laser power at a pulse frequency of 10 Hz was 700 pJ/pulse at the target as measured with a Scientech 380105 power meter. Some ex-
0022-3654/89/2093-2328$01.50/00 1989 American Chemical Society
