J. Phys. Chem. 1984,88, 5799-5803 the reaction field is nonzero and dependent on E = nz for nonpolar solvents). In light of our results above the slightly superior modeling characteristics of the dipole-dipole model is not a surprising result. There is a danger though in treating this as a general result, which it clearly is not. As has been generally acknowledged, and as a referee of an earlier version of this paper pointed Out: “(a) The more similar an unknown process is to a known process, the better the correlation and the greater the understanding therefrom derived and, (b) theoretical analysis of solvent parameters is a difficult and chancy business.” Despite the general recognition of these points
5799
very little has been done in providing quantitative examples of the effects of decreasing process similarity in a controlled and known fashion. We have sought to address this gap in the present work and have outlined a reasonable procedure for examining the sensitivity of linear model correlations to model misrepresentation or perturbations in the assumed form of the model.
Acknowledgment. James E.Brady was a recipient of an ACS Analytical Division Full Year Fellowship sponsored by the Upjohn Co., Kalamazoo, MI. This work was supported by National Science Foundation Grant CHE-8205 187.
The Possibility of Reducing the Threshold Field Intensity for Laser-Induced DynamicaD Effects in Chemical Reactions K. Duffy and J. M. Yuan* Department of Physics and Atmospheric Science, Drexel University, Philadelphia, Pennsylvania 191 04 (Received: February 22, 1984; In Final Form: June 1 1 , 1984)
Collinear collisions of an F atom with a hydrogen molecule (H2, HD, DH, and D2)in the presence of a laser field have been studied by using the surface-hopping and Miller-George models. The emphasis here is on the possibility of lowering the threshold field intensity of laser-induced dynamical effects by varying field frequency, isotopic mass, and collision energy, and of correlating these dynamical effects to the ”distortions” of the field-dressed potential energy surfaces. It is found that variation of frequency and collision energy can lower the threshold field intensity by one to three orders of magnitude. Although isotopic substitution has strong effects on reactive probabilities, it does not affect the threshold significantly. Furthermore, intensity and frequency effects are explainable in terms of the change of the field-dressed potential energy surfaces with field parameters, and isotopic effects in terms of a kinematic model. Results of this study are consistent with the observation that to enhance the laser-induced dynamical effects one should choose conditions so as to make the parameter defined by the product of the Rabi frequency and the effective resonance time large.
I. Introduction Laser-induced chemical processes have stimulated much experimental and theoretical interest in recent One way to treat the effects of an intense laser field on a reactive system while the reaction is taking place is to employ the field-dressed (1) C. B. Moore, Ed., “Chemical and Biochemical Applications of Lasers”,
Academic Press, New York. See any volume of the series. (2) See, for example, articles in Physics Today, Nov 1980, pp 25-59. (3) T. F. George, J. Phys. Chem., 86, 10 (1982). (4) P. Polak-Dingels,J. F. Delpeck, and J. Weiner, Phys. Rev. Lett., 44,
1663 (1980). ( 5 ) (a) P. Hering, P. R. Brooks, R. F. Curl, Jr., R. S . Judson, and R. S . Lowe, Phys. Rev. Lett., 44,687 (1980); (b) T. C. Maguire, P. R. Brooks, and R. F. Curl, Jr., ibid., 50, 1918 (1983). (6) J. K. Ku, G. Inou, and D. W. Setser, J. Phys. Chem., 87,2989 (1983). (7) N. M. Kroll, and K. M. Watson, Phys. Reu. A , 13, 1018 (1976). (8) J. C. Light and A. Altenberger-Siczek, J. Chem. Phys., 70, 4108 (1979). (9) K. C. Kulander and A. E. Orel, J . Chem. Phys., 74, 6529 (1981); 75, 675 (1981). (10) J. M. Yuan, T. F. George, and F. J. McLafferty, Chem. Phys. Lett., 40, 163 (1976). (11) A. E. Orel and W. H. Miller, J. Chem. Phys., 73, 241 (1980). (12) D. R. Dion and J. 0. Hirschfelder, Adv. Chem. Phys., 35, 265 (1976). (13) S . C. Leasure, K. F. Milfeld, and R. E. Wyatt, J . Chem. Phys., 74, 6197 (1981). (14) M. G. Payne and M. H. Nayfeh, Phys. Reu. A, 17, 1695 (1976). (15) S . I. Chu and W. P. Reinhardt, Phys. Rev. Lett., 39, 1195 (1977). (16) A. M. F. Lau and C. R. Rhodes, Phys. Rev. A, 15, 1570 (977). (17) J. M. Yuan, J. R. Laing, and T. F. George, J. Chem. Phys., 66,1107 (1977).
(18) I. H. Zimmerman, T. F. George, J. R. Stallcop, and B. C. F. M. Laskowski, Chem. Phys., 49, 59 (1980). (19) J. M. Yuan and T. F. George, J . Chem. Phys, 70, 990 (1979). (20) I. Last, M. Baer, I. H. Zimmerman, and T. F. George, Chem. Phys. Lett., 101, 163 (1983). (21) R. D. Taylor and P. Brumer, J . Chem. Phys., 77, 854 (1982). (22) M. Mohan, K. F. Milfied, and R. E. Wyatt, Chem. Phys. Lett., 99, 411 (1983).
or electronic-field potential energy surfaces.’-’ 1~16-zo Since these surfaces can be very different from the field-free ones, the reaction mechanism and thus the branching ratios can be significantly modified when a laser is shone on the system. There are a few reactive systems that have been studied theo r e t i ~ a l l y . ~ ~It~ seems ~ ~ ~ ~true ’ ~ -that ~ ~ for these systems the threshold field intensities required for observing these laser-induced effects is very high. But since only a very limited number of reactions have been studied, it is possible that some optimal systems can be found to demonstrate these effects at a field intensity that is easy to handle e~perimentally.~~ In order to find such optimal systems, one should look for the conditions under which the threshold field intensity can be reduced and try to delineate the relationship between the “distortions” of the potential energy surfaces and the laser-induced effects. These are the purposes of the present paper. Again, the collinear F Hz (HD, DH, D2) reactive system will be used as a model system, but instead of the modified Miller-George methodz4used in the previous study,Ig the surface-hopping modelz0325will be used (except for cases where comparison with the Miller-George method is carried out). Although the Miller-George methodz4is sounder in principle than the surface-hopping method, there are two practical drawbacks in its present applicati~n.’~ First, the positions of the branch points of the field-induced avoided crossings depend on the field intensity as well as the frequency. Second, more than ope set of branch points are found for a fixed set of field parameters. On the other hand, the diabatic seam (formed by the intersection of the field-shifted diabatic surface, Wl hv, with W2,where W, and Wzare the field-free ground-state and first-excited state adiabatic
+
+
K
(23) It has been reported recently (ref 5b) that complex formation of the kW. (24) M. H. Miller and T. F. George, J . Chem. Phys., 56, 5637 (1972). (25) J. C. Tully and R. K. Preston, J. Chem. Phys., 55, 562 (1971). (26) J. T. Muckerman, J . Chem. Phys., 57, 3388 (1972).
+ NaCl reaction can be assisted by a laser field of -3
0022-3654/84/2088-5799$01.50/0 , 0 1984 American Chemical Society I
,
5800 The Journal of Physical Chemistry, Vol. 88, No. 24, 1984
I
4
5
x
7
6
8
Duffy and Yuan
.
Figure 1. Field-freeground-state potential energy surface of the FHH system with the minimum energy path shown. The saddle point is indicated by a cross (x). The straight lines are diabatic seams at hu = 1.17 and 0.5 eV. All quantities are in atomic units. The potential energy is zero when the three atoms are infinitely far away from one another. potential energy surfaces) is only frequency dependent. For F H2 system, results from both methods will be compared. To find out how much the threshold field intensity can be reduced, there are several parameters which can be changed, for example, field frequency, isotopic mass, and collision energy. Collision probabilities as functions of laser field intensity, frequency, isotopic mass, and collision energy are shown in section 111. These results are explainable in terms of the gradual change of the field-dressed potential energy surfaces with field parameters. Some of the dressed surfaces and the potential energy curves along the reaction coordinates are presented in the next section. A simple kinematic model for isotope effects in the weak-field limit is also presented.
4
5
x
7
6
8
Figure 2. Lower field-dressed surface at hu = 1.17 eV and I = 0.1
TW/cmZ. The straight line is the diabatic seam. L
4.0-
+
11. Field-Dressed Potential Energy Surfaces
Tully and Preston’s surface-hopping modelzs is used to treat the nuclear dynamics semiclassically. The field-dressed potential energy surfaces, E , and El, on which classical trajectories are propagated, are constructed as before.19 That is, we diagonalize a 2 X 2 matrix with the field-free ground- and first-excited, electronically adiabatic surfaces ( W1,2)of FHH on the diagonal and the radiative coupling as the off-diagonal elements. on the other hand, are constructed by using the electronically diabatic surfaces (*2and ZII)of FHH, coupled via constant spin-orbit interactions. The 2Z surface we used is the Muckerman V surface26 and the 211surface is that calculated by Jaffe et aL2’ Several points along the seam of W, and W2are determined by using a Newton-Raphson iterative method. These points are then least-squares fitted to a straight line r3 = ar, + b (1) where r3 is the distance between F and the closer H atom and rl is the distance between the two H atoms. At photon energies hu = 1.17 and 0.5 eV, fitting parameters, a and b in bohr, are a = 0.6398, b = 1.448 and a = 0.2843,b = 2.606, respectively. The slope of the potential surface at the crossing point in the direction of the reaction is found from
-=aW,
az
[ 5 + 51
sin
e+
a wi
cos e i = 1 , 2 (2)
where z is the coordinate perpendicular to the seam in the direction of the reaction, rz is the distance between F and the farther H atom m2 + m3 j = tan-’ (3) amz + (1 + a)m3 (27) R. L. Jaffe, K.Morokuma, and T. F. George, J . Chem. Phys., 63, 3417 (1975).
3.0-
rl 2.0
-
I
4.0
5.0
6.0
7.0
8.0
Figure 3. Same as Figure 2, except I = 10 TW/cm2.
and m, ( i = 2, 3) is the mass of the H (or D) atom. The fieldshifted diabatic seams of the FHz system at photon energies hv = 1.17 and 0.5 eV are plotted with the field-free ground-state potential energy surface W, in Figure 1, where X is the conjugate skewed coordinate.z8 One should note that the two diabatic seams fall on different sides of the transition state. Since field-dressed surfaces are improtant for the understanding of the laser-induced effects obtained in section 111, some of them are displayed in this section. The lower field-dressed surface at hv = 1.17 eV and field intensity Z = 0.1 TW/cmz is shown in Figure 2. It can be seen that the region where the two surfaces W, and W2are joined together through the transition dipole moment is not very smooth. As the field intensity is increased to 10 TW/cm2, this region becomes much smoother as shown in Figures 3 and 4 for the lowerand upper-field-dressed surface, respectively. Using Figures 3 and 4 one can describe a reactive trajectory as follows: A representative particle starts out from the reactant valley (large X and small r , ) of the upper surface and is propagated up to the seam (the straight lines in the figures). A transition down to the lower surface is made at the seam. A trajectory may then wander around in the collision region, make transitions up and down many times, and eventually arrive at the asymptotic region of the product valley of the lower surface. In such cases, we try to sum up the probabilities of all possible paths as close to unity as practical. The situation becomes worse as the field intensity increases, because trajectories tend to stay in the collision zone longer and the number of trajectories to be summed over increases drastically. For each set of parameters (laser frequency and intensity, collision energy), a hundred trajectories, uniformly distributed over the (28) S. Glasstone, J. J. Laidler, and H. Eyring, ‘The Theory of Rate Processes“,McGraw-Hill, New York, 1941, p 102.
The Journal of Physical Chemistry, Vol. 88, No. 24, 1984 5801
Laser-Induced Dynamical Effects in Chemical Reactions
TABLE I: Reactive Probabilities at Irv = 1.17 eV and Specified Collision Energies F HD (0.086 eV) F F HH (0.049 eV)" field int 'v = 2 v' = 3 v' = 2 'v = 3 v' = 2
+
+
0W 1 GW 0.1 T W 1 TW 10 T W
0.39 0.39 0.39 0.36 0.15
(0.39)' (0.39) (0.42) (0.35) (0.15)
0.33 0.29 0.31 0.28 0.40
(0.33) (0.30) (0.31) (0.29) (0.42)
0 (0) 0 (0) 0.08 (0) 0.03 (0) 0.13
0.24 0.26 0.23 0.25 0.34
(0.24) (0.22) (0.22) (0.17)
+ DH (0.086 eV)
0.17 0.17 (0.17) 0.17 0.02 (0) 0 (0)
F
'v = 3
v'=4
yt-2
0.38 0.38 (0.38) 0.38 0.49 (0.48) 0.28 (0.31)
0.45 0.45 (0.45) 0.45 0.43 (0.47) 0.37 (0.37)
0 0.01 0.03 0 0.01
+ DD (0.129 eV) y"3
v'=4
0.43 0.44 0.36 0.34 0.29
0.30 0.30 0.32 0.31 0.19
"The numbers in parentheses in this row denote the relative collision energy between F and hydrogen molecules. 'The numbers in parentheses are results obtained by the Miller-George method. Previous results of ref 19 have been corrected for a program error in locating branch points. TABLE II: Nonreactive Probabilities at hv = 1.17 eV and Specified Collision Energies
F + HH (0.049 eV) field int 0w 1 GW 0.1 TW 1 TW 10 TW
F* 0
F* + HD
+ HH ( v )
v =
0 (0) 0 (0) 0 (0) 0.04 (0.03) 0.09 (0.09)'
v=l 0 (0) 0 (0) 0 (0) 0.04 (0.04) 0.21 (0.21)"
F*
+ DH ( v )
v =0
v=
(u)
v=o
elastic 0.28 (0.28) 0.32 (0.31) 0.30 (0.27) 0.28 (0.29) 0.09 (0.10)"
v=1 0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0.05 (0.04) 0.03 (0.08) 0.05 0.28
F + DD (0.129 eV) F* + DD
F + DH (0.086 eV)
F + HD (0.086 eV) elastic 0.76 (0.76) 0.74 (0.78) 0.64 (0.77) 0.59 (0.65) 0.14
0 (0) 0 (0) 0 (0)
(v)
1
elastic
0 (0) 0 (0) 0 (0)
0 (0) 0 (0) 0 (0) 0.05 (0) 0 (0) 0 (0) 0.13 (0.08) 0.11 (0.13) 0.07 (0.06)
=0
v = 1
0 (0) 0 0 0.03 0.11
0 (0) 0 0
v
0.04 0.24
elastic 0.27 0.25 0.27 0.24 0.10
In some cases, the sum of all probabilities is not equal to unity, as explained in section 11. TABLE III: Reactive Probabilities at bu = 0.5 eV and Specified Collision Energies
F+HH
F+HD
+
(0.049 eV) (0.086 eV) F DH (0.086 eV) field int v' = 2 v' = 3 v' = 2 u' = 3 v' = 2 u' = 3 v' = 4 0.28 0.17 0.37 0.46 1 GW" 0.39 0.31 0 0.1 T W 0.52 0.36 0.06 0.13 0.08 0.34 0.48 0.09' 0.19' 0.02 0.32 0.02 0.07 0.64 1 TW
"Zero field results are identical with those of hv = 1.17 eV. bNumbers are not as accurate as the rest, because the tunneling effect can be important for this case. TABLE IV: Nonreactive Probabilities at hv = 0.5 eV and Specified Collision Energies
, /
F+HH
4
x
5
6
7
. (0.049 eV)
8
Figure 4. Upper field-dressed surface at hv = 1.17 eV and I = 10 TW/cmZ. The straight line is the diabatic seam.
oscillation phase of the hydrogen molecule, have been integrated by using a modified Adams-Moulton fifth-order predictor-corrector variable-step method. We have considered trajectories which cross the seam up to 41 times in order to sum up the probabilities. At each crossing of the seam, the surface-hopping probability in the Tully-Preston method is calculated by using the Landau-Zener expression given as
P = exp(-2mP/(hulS1 - &I))
(4)
where d = p&,p is the transition dipole moment between the two electronic states at the seam, and 6 is the laser field. u is the velocity component of the representative particle perpendicular to the seam at the crossing point and Si( i = 1, 2) are the slopes of the field-diabatic surfaces a t the seam in the direction perpendicular to the seam. Changes of the field-dressed surface caused by field parameters are best represented by potential energy curves along the reaction coordinate of Wi. The curves for hv = 1.17 eV when I = 1 and 10 TW/cmZ, hv = 0.5 eV when I = 1 TW/cmZ and the field-free ground state are shown in Figure 5 . 111. Results and Discussion
Collision probabilities for the reactive processes F
+ Hz
hu -+
HF(v')
+H
(5)
and the isotopic variants of Hz are listed in Table I for hv = 1.17
F* field int 1GW 0.1 T W 1 TW
+ HH
(v =
0)
0 0.02" 0.42b
F* elasJic 0.30 0.06" 0.30'
(v
F+HD
F+DH
(0.086 eV)
(0.086 eV)
+ HD = 0)
0 0.01 0.27
F* elastic 0.72 0.78 0.34
+ DH
(v =
0) 0 0.02 0.24
elastic 0 0.02 0.03
"The sum of all probabilities may not be unity; see footnote a of Table 11. *Numbers are not as accurate as the rest, see footnote b of Table 111. TABLE V: Collision Energy Dependence of Total Reactive Probabilities for the F HD System at hu = 1.17 eV field int 0.049 eV 0.055 eV 0.065 eV 0.086 eV ow 0.37 0.37 0.31 0.24 (0.24) 1 GW 0.53 (0.53) 0.45 0.36 0.26 (0.22) 0.1 T W 0.44 (0.45) 0.41 0.41 0.31 (0.22) 1 TW 0.49 50.51 50.41 0.28 (0.17)
+
eV and Table I11 for hv = 0.5 eV. Probabilities for the corresponding inelastic processes, namely F
+ H2 + hv
-
F*('P,p)
+ H, (v = 0, 1)
(6)
and elastic processes are listed in Tables I1 and IV, respectively, for hv = 1.17 and 0.5 eV. The collision energy Ecoll= 0.049 eV has been chosen for the F + H, processesig such that the inelastic process (eq 6 without hv) will not take place without absorbing a photon. Collision energies for other cases29are determined by (29) In order to compare the results with those of the FHH system, the possibility of excitation of F to F*(ZP12) in the field-free case has been suppressed. On the other hand, a semiciassical calculation (J. M. Yuan et al., Isr. J. Chem., 19, 337 (1980)) shows that electronic transition probabilities arq small at a collision of 0.1 eV for the FHH system.
5802 The Journal of Physical Chemistry, Vol. 88, No. 24, 1984
."
I
:.,
;
I / / /
/-0.2
/
I
/
/
I
--. / ,
4
2
3
1
0
I
- S (bohr) Figure 5. Potential energy in atomic units along the field-free groundstate reaction coordinate (S). The dashed line (---) is the field-free
are field-dressed potential ground-state curve. The dotted lines curves for hv = 0.5 eV, I = 1 TW/cm*,but the repulsive upper curve has not been completely plotted for clarity. The solid lines (-) and the dot-dashed lines (. -) are field-dressed potential curves for hv = 1.17 eV, I = 1 and 10 TW/cm2, respectively. Arrows associated with EWll specify the collision energy measured relative to the asymptotic value of the potential energy surface. (e.
e)
-.
fixing the initial total energy with reference to the potential energy surface. The total reaction probabilities (P,) of the F + H D system as a function of the collision energy are represented in Table V. Information contained in Tables I-V will be discussed from the following aspects: dependence of probabilities on field intensity, on field frequency, on isotopic mass, and on collision energy. In subsections (a)-(d) we shall consider each of them separately. ( a ) Field Intensity Dependence. Probabilities in Tables I-V considered as functions of field intensity show the following features: 1. Results calculated according to the localized Miller-George model19 (numbers in parentheses), in general, agree well with those of the Tully-Preston model. 2. For a photon energy of 1.17 eV, the total reactive probabilities for the F H2, F + DH, and F D2 systems decrease as the field intensity (I)increases. However, Pr increase for the F H D reaction at various E,],. Curiously, all Pr seem to approach roughly 0.50 as I increases. The total inelastic probabilities (Pi,) increase for all systems and the elastic probabilities (Pel)decrease except for F DH. These general trends hold true also at hv = 0.5 eV, but with higher fluctuations. 3. The double excitation process of ( 6 ) , where the F atom is electronically excited and at the same time the hydrogen molecules is vibrationally excited to v = 1, has higher probability than the single excitation process (v = 0) at 10 TW/cm2 for hv = 1.17 eV. This results in a net population inversion in the vibrational distribution of H2, with the elastic channel included. Based on the potential energy surfaces of section 11, an explanation of this fact that P,,increases with I can be put forward. According to both the Tully-Prestonzs and M i l l e r - G e ~ r g e ~models, ~ * ~ ~ as the representative particle makes a transition down to the lower surface at the seam, all the energy gained goes into the kinetic energy of the nuclear motion along a direction perpendicular to the seam. Thus, the orientation of the seam plays an important role in determining the asymptotic vibrational state. The seam orientation in Figure 3 clearly favors the higher vibrational states. As for the enhancement of P,,, reference can be made to the potential
+
+
+
+
(30) J. R. Stine and J. T. Muckerman, J . Chem. Phys., 65, 3976 (1976).
Duffy and Yuan curves along the reaction coordinate (S) in Figure 5. At hv = 1.17 eV, the lower field-dressed potential curve has a field-induced barrier.31 For weaker fields the diabatic seam almost coincides with the top of the barrier along S, but for high fields, e.g., I = 10 TW/cm2, the seam is located at the reactant side of the barrier which can enhance the reflection probability and thus PI". For hv = 0.5 eV, there exists no field-induced barrier but only a field-free potential barrier on the lower surface, which is located always at the product side of the seam. 4. Results of the highest fields in Tables I-IV are always very different from the rest and a further order of magnitude increase of the field intensity would yield zero classical reactive probability. These facts again can be correlated to the change of the potential surface with I. The gap at the avoided crossing is proportional to the field strength. As the field intensity increases above a certain value, the diabatic seam falls inside the nonclassical region. Transition to the lower surface can take place only through tunneling, which cannot be treated properly with the current version of the surface-hopping model. (The problem of electronic transition through tunneling can be treated by using methods of average potential surfaces32or Wigner distribution functions.) The highest fields studied here represent the cases where the locations of the diabatic seam are in the closest vioinity of the classical turning points among all field intensities studied. In these cases, the representative particle spends a longer time in the vicinity of the seam, and this enhances the laser-induced dynamical effects. Accuracy of semiclassical results in the parameter domain where the seam and the upper-surface turning point come close to each other is not as high as that in the rest of the domain. In order to estimate numerically the accuracy of results in high fields, we have recorded the fraction of trajectories (out of a hundred) that have been reflected back by the potential barrier without reaching the seam. The fraction is usually small (zero from most cases) except for a few instances, where the fraction is about 10% and is labeled as inaccurate in the footnotes of the tables. ( b ) Effects of Frequency Change. The field-induced avoided crossing occurs on the reactant side of the field-free transition state for hv = 0.5 eV as contrasted with that of hv = 1.17 eV which occurs on the product side. How are the probabilities being affected by this change? Results for these two frequencies are listed in the tables, where in Tables I11 and IV the direct pumping of the H F vibrational state in the asymptotic product valley has been s u p p r e s ~ e dso~ ~that , ~ ~we can focus solely on the laser-induced dynamical effects. These effects in the reactive and nonreactive probabilities become appreciable at 1 TW/cm2 for hv = 1.17 eV for all systems in Tables I-VI, and become much more pronounced at 10 TW/cm2. The corresponding values are lower by one order of magnitude for hv = 0.5 eV. To correlate these frequency effects with the distortion of the potential energy surfaces, we refer again to Figure 5. At hv = 0.5 eV, the resonance region is located at the flat part of the field-free ground-state potential curves along the reaction coordinate. Thus, the effective resonance region is longer and the local velocity around the avoided crossing is lower than those of hv = 1.17 eV. Also due to the flatness of the field-free ground-state surface, the diabatic seam falls more quickly into the nonclassical region; thus the highest fields calculated for hv = 0.5 eV are smaller. ( c ) Isotopic Effects. Probabilities in Tables I-IV vary drastically as one or both of the H atoms are replaced by D atom^;^^.'^ the thresholds for laser-induced dynamical effects are not strongly affected. The reactive probabilities of FHD and FDD in Table I seem to suggest a shift of the thresholds toward a lower intensity (0.1 TW/cm2) than that of FH2 (1 TW/cm2). However, the Miller-George results for F H D and nonreactive probabilities in Table I1 do not support such a hypothesis.
+
(31) I. H. Zimmerman, M. Baer, and T. F. George, J . Phys. Chem., 87, 1478 (1983). (32) D. A. Micha, J . Chem. Phys., 78, 7138 (1983). (33) J. W. Hepburn, D. Klimek, K. Liu, R. G. Macdonald, F. J. Northup, and J. C. Polanyi, J . Chem. Phys., 74, 6226 (1981). (34) H. R. Mayne, J . Chem. Phys., 73, 217 (1980).
J. Phys. Chem. 1984,88, 5803-5806 The pronounced effect on PI of the isotopic substitution in the field-free case or the weak-field limit can be explained qualitatively by using a simple kinematic model, consisting of a sequence of elastic binary collisions. If we consider the collinear system, FAB, the first collision is between F and A, the second between A and B, and the third between F and A again. Only in F H D is the fourth collision between A and B still possible. We assume the magnitude of the collision time between F and A is of crucial importance in determining the reaction probability, namely, the longer the interaction time, the larger P, is. For the FDH system, the third collision time is the longest of all because both F and D move in the same direction. On the other hand, the shortness of the third collision time occurs in F H D and the existence of a fourth collision tends to reduce greatly the PI for the system. Thus, we expect that PI decreases in the following order: FDH > FDD = FHH > FHD. In fact, the calculated values in Table I show that PI = 1.OO for FDH, 0.73 for FDD, 0.72 for FHH, and 0.24 for FHD. If we define N,.,, as the number of times a trajectory crosses the seam, numerical results show N,,,,, is 1 for all the reactive trajectories of FDH and 3 for FHD. For FHH and FDD, N,,,, is 1 for nearly all reactive trajectories. These results are consistent with the above kinematical model. (d)Effects of Collision Energy. In Table V we have presented the total reactive probabilities of the FDH system at hv = 1.17 eV for several collision energies. Results in this table indicate that at low energies (0.049 and 0.055 eV) PI increase by over 20%, as the field intensity increases above 1 GW. Thus, the onset of
5803
the laser-induced dynamical effects occurs at a much lower intensity (by about two to three orders of magnitude) than that of the higher collision energy. This is consistent with the expectation that a slower particle motion increases the effective interaction time, or the resonance time with respect to the photon absorption time, thus enhancing the laser-induced effect. Again, the field-free PI is higher for the lower collision energy and can be correlated with the long collisfon time for the third binary collisions as discussed in subsection c.
IV. Summary Numerical studies of the F + Hz system and isotopic variants reveal a clear correlation between the surface distortions of the electronic-field surfaces and laser-induced dynamical effects. The most effective way to enhance laser-induced effects is to increase the resonance time (the time a representative particle passes through the resonance region) in comparison with the absorption time (the inverse of the Rabi rate). To achieve this, one can, for instance, vary the field frequency and/or lower the collision energy. Acknowledgment. We thank Professor Thomas F. George and Dr. I. Harold Zimmerman for helpful discussions. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the America1 Chemical Society, for the support of this research. Registry No. H2,1333-74-0; HD, 13983-20-5; D2,7782-39-0; F, 14762-94-8.
Formatlon and Relaxation of Hot Benzyl Radicals In the Gas Phase Noriaki Ikeda, Nobuaki Nakashima, and Keitaro Yoshihara* Institute for Molecular Science, Myodaiji, Okazaki 444, Japan (Received: March 2, 1984; In Final Form: June 12, 1984)
Benzyl chloride in the gas phase has been photolyzed with an ArF excimer laser (193 nm). Time-resolved absorption spectra show that the benzyl radical is formed by photodissociation of the C-Cl bond. A broad absorption spectrum obtained immediately after excitation sharpens gradually. This dynamical behavior is explained in terms of the collisional relaxation of the hot benzyl radical, which is formed in highly excited vibrational states of the ground electronic state. The vibrational temperature of the hot benzyl radical immediately after dissociation is tentatively estimated by simulation of the absorption spectra with a modified Sulzer-Wieland model. The molar extinction coefficients of the absorption peaks at 229, 253, and 306 nm of the relaxed benzyl radical are determined.
Introduction The benzyl radical has been extensively studied as one of the prototypical aromatic radicals. Though the electronic absorption spectra of the benzyl radical has been measured by flash photolysis and by other some contradictions and unsolved problems still remain. The extinction coefficients of the three major ultraviolet absorption bands in the gas phase were reported: but they were very different from those in the condensed phase. An intriguing spectral shift of the benzyl radical during the formation process was reported with flash photolysis on the microsecond time scale and some specific vibrational mode was suggested to be activated by photodissociation.5 Much greater time resolution is required to test this proposal. Under these circumstances, we have studied the dynamical behavior of the benzyl radical in the UV region by nanosecond time-resolved laser photolysis in l i e gas phase. (1) Porter, G.; Wright, F. J. Trans. Faraday SOC.1955, 51, 1469. (2) Friedrich, D. M.; Albrecht, A. C. J. Chem. Phys. 1973, 58, 4766. (3) Hiratsuka, H.; Okamura, T.; Tanaka, I.; Tanizaki, Y. J. Phys. Chem. 1980, 84, 285. (4) Bayrakpeken, F.; Nicholas, J. E. J . Chem. SOC.B 1970, 691. Bayrakpken, F. Chem. Phys. Len. 1980, 74, 298. (5) Ebata, T.; Obi, K.; Tanaka, I. Chem. Phys. Lett. 1981, 77, 480.
0022-3654/84/2088-5803$01.50/0
Because we use an ArF excimer laser (193 nm) as an exciting source for the photodissociation, vibrationally and/or rotationally hot radicals are expected to be formed in the gas phase. A photon energy of 193 nm is equivalent to 148 kcal/mol (620 kJ/mol), while dissociation energies of typical bonds are in the range of 60-100 kcal/mol. For example, the dissociation energy of the C-C1 bond of benzyl chloride is 69 kcal/mol (288 kJ/mol).6 Therefore much excess energy is available, after photodissociation, for vibrational and rotational excitation of radicals. The dynamical behavior of hot radicals is another interesting subject. Only a few spectroscopic studies of such processes in hot radicals are as well as in hot triplet statesI0Jl and in hot ground-state molecule^.^^-^^ A molecular beam photodis(6) Weast, R. C. “Handbook of Chemistry and Physics”; CRC Press: Cleveland, 1978. (7) Astholz, D. C.; Brouwer, L.; Troe, J. Ber. Bunsenges. Phys. Chem. 1981, 85, 559. (8) Hippler, H.; Schubert, V.; Troe, J.; Wendelken, H. J. Chem. Phys. Lett. 1981, 84, 253. (9) Glanzer, K.; Maier, M.; Troe, J. J. Phys. Chem. 1980, 84, 1681. (10) Formosinho, S.J.; Porter, G.; West, M. A. Proc. R. SOC.London, Ser A 1973, 333, 289. (11) Schroder, H.; Neusser, H. J.; Schlag, E. W. Chem. Phys. Lett. 1978, 54. 4.
0 1984 American Chemical Society
