J. Phys. Chem. 1995,99, 13652-13658
13652
Vector Correlations in the 193 nm Photodissociation of the NO Dimer Yukito Naitoh,*J9$Yo Fujimura? Kenji Honma,t and Okitsugu Kajimoto”” Department of Chemistry, Faculty of Science, Kyoto University, Kitashirakawa-Oiwakecho,Sakyo-ku, Kyoto 606-01, Japan, and Department of Material Science, Himeji Institute of Technology, 1479-1 Kanaji, Kamigori, Hyogo 678-12, Japan Received: March IO, 1995; In Final Form: June 1, 1995@
We have studied photodissociation at 193 nm of the NO dimer, which has cis planar geometry. The photofragment NO(A2Z+)was detected by laser-induced fluorescence using the E2Z+-A2Z+ transition around 600 nm. The recoil anisotropy p and the v-J correlation have been determined at several rotational levels N by analyzing Doppler profiles of the rotational line measured at six different geometries of linearly polarized photolysis and probe lasers. The values of /?and the v-J correlation indicate that the relations of three as N increases. Taking account of the vectors &bs, v, and N) reach the limiting case of P a b s l I V and VU result of the rotational alignment Af’ measured previously, we conclude that this dissociation proceeds mostly within the parent molecular plane. In the photodissociation of van der Waals molecules, the presence of low-frequency van der Waals vibrations accelerates the available energy dissipation from the N-N bond, where most of the energy is located after photoexcitation, to other vibrational modes. Since this energy randomization transfers a fraction of energy into the torsional motion, angular momentum not perpendicular to the original molecular plane is produced. As a result, the rotational alignment A f ’ and the v-J correlation deviate from their limiting values, particularly at lower N .
1. Introduction The stereodynamical aspects of photodissociation are essentially related to the dynamics on the potential energy surface (PES) near the transition state. Recent development of the theory and experimental technique enables us to detect directly the translational and rotational motions of photofragments and even the scalar and vector correlations in the fragmentation.’x2 These motions are determined not only by the partitioning of available energy among the freedoms of products but also by the constraint on the angular momentum. In addition to these constraints, the change of molecular structure after photoexcitation (linear to bent or planar to nonplanar for example) also affects the product motion. Therefore, the observation of the anisotropic distribution of product motions helps us to infer the topological nature of the PES near the transition state. For that purpose, three vector correlations are often measured: the recoil anisotropy p, the rotational alignment A!’, and the v-J correlation, which are defined as correlations among the transition dipole moment I(abs of the parent molecule, the velocity vector v, and the rotational angular momentum J of the phot~fragment.~.~ So far, the photodissociation dynamics of many polyatomic molecules such as H202,5.6 ICN,’ and RONOss9 has been successfully studied. Recently, even the vector correlations in photoinitiated bimolecular reactions such as H SiD4,’O O(ID) N20,” and O(3P) CS12 have been investigated. In these systems, photodissociation by a linearly polarized laser provides reactant atoms with a particular velocity vector. The vector correlations relative to this velocity vector can significantly contribute to the understanding of the reaction mechanism. On the other hand, in the photodissociation of weakly bound van der Waals (vdW) molecules, the vector correlations have
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* To whom correspondence should be addressed. Present address: Institute for Molecular Science, Myodaiji, Okazaki Japan. Kyoto University. 5 Himeji Institute of Technology. Abstract published in Advance ACS Abstrucrs, August 15, 1995. +
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0022-365419512099- 13652$09.0010
been measured in only a few cases such as the vibrational predissociation of ( H F ) 2 I 4 and (N0)215and the photodissociation of (RON0),.I6 Since these molecules possess many lowfrequency vibrational modes (vdW modes) in addition to the weak bond, the features appearing in the dissociation process can be different from those of ordinary molecules. Such lowfrequency modes usually enhance the intramolecular vibrational energy redistribution (IVR),” and rapid IVR must give a characteristic effect on the dynamical aspects of photodissociation as well as on the product energy distribution. Therefore, more studies using vector correlations are necessary to investigate the dynamics of weakly bound molecules. In the present article, we report the photodissociation dynamics of a van der Waals molecule, (N0)2, at 193 nm excitation. (NO), has cis planar geometry,I8 and the dissociation energy in the ground state is estimated to be 560-710 ~ m - ~ , ~ ~ ~ , The electronic excitation of (N0)2 cannot be considered as local excitation of one moiety of the dimer because its van der Waals bond has covalent character. Since the electronic absorption spectrum is broad and stru~tureless,’~ the photodissociation seems to be direct rather than predissociative. We found that the following two channels exist in the dissociation via the electronically excited PES reached by the 193 nm e ~ c i t a t i o n , ~ ~ - * ~
(NO),
+ hv - NO(A2Zf) + NO(X211)
(1)
We will focus our attention on only the first channel in this study. Previously, we measured a laser-induced fluorescence (LIF) excitation spectrum of the photofragment NO(A2Z+) utilizing the E-A transition and determined the vibrational and rotational distributions.22 The vibrational and rotational distributions are almost statistical and agree well with the prediction from phase space theory (PST),25except for an additional cool component in the rotational distribution. The presence of the cool
0 1995 American Chemical Society
Photodissociation of the NO Dimer
J. Phys. Chem., Vol. 99, No. 37, 1995 13653
-
ArF excimer l h e
dye laser
*
dye laser
Figure 1. Schematic diagram of the experimental apparatus used in the measurement of Doppler profiles: S,, Suprasil plate set at the Brewster angle; L,, lens; FR,double Fresnel Rhomb; P, polarizer, IF, interference filter; PMT, photomultiplier tube; N, pulsed nozzle. Dye laser radiation was introduced into the vacuum chamber either counterpropagating or perpendicular to the ArF excimer laser beam.
component is again predictable within the framework of statistical theory when one uses the correlated angular momentum (CAM) method, where the rotational and recoil motions of fragments are assumed to occur preferentially within the molecular plane of ( N 0 L 2 * The plausibility of such an assumption was assessed by measuring the rotational alignment Af’ of NO(A) utilizing the polarized LIF technique.23 The values are found to be negative and have a dependence on the rotational quantum number N , changing from 0 to -0.2 as N increases. According to a simple molecular orbital consideration, the transition dipole is predicted to be parallel to the N-N bond. Therefore, the observed Af’,i.e., anisotropic distribution of N,indicates that the NO dimer dissociates preferentially via a planar geometry, and this restriction becomes more pronounced at higher N . In the present study, we measured the polarized LIF and Doppler profile of rotational lines of the NO(A) fragment and determined the recoil anisotropy ,8 and the u-J correlation in order to obtain further support for the coplanar dissociation of the NO dimer. Although the two correlations, ,8 and Af’, are affected by the rotation of the excited parent molecule prior to dissociation, the v-J correlation is free from such effects and provides information on dynamical aspects of the dissociation process more directly. On the basis of these measurements, we will discuss the photodissociation dynamics of (N0)2.
2. Experimental Section The experimentalapparatus used in this study is schematically shown in Figure 1. The 193 nm light from an ArF excimer laser (Lambda Physik EMG 53 MSC) was used for the photolysis. For polarization measurements, unpolarized light from the ArF excimer laser was passed through a pile of twelve Suprasil plates at the Brewster angle in order to obtain linearly polarized light. The degree of polarization was about 98%. The direction of the electric vector c defines the Z axis of the laboratory frame. The linearly polarized photolysis laser light passing through a lens ( f = 500 mm) was introduced into a vacuum chamber while being defocused at the photolysis region. The output of a tunable dye laser (Molectron DL-11) pumped by an XeCl excimer laser (Lambda Physik EMG 50) was used to probe the Av = 0 sequence of the NO(E2Z+-A2Z+) transition around 600 nm. The probe laser beam was introduced either counterpropagating or perpendicular to the photolysis laser radiation. We measured the Doppler profiles of the rotational lines to determine the anisotropy B and the u-J correlation of the photofragments. By using a pressure-scanned intracavity etalon, the bandwidth of the probe laser light was narrowed. For the wavenumber calibration, we measured LIF spectra of
Figure 2. Six different pump-probe geometries used in the measurement of Doppler profiles: (a and b) mutually orthogonal geometry; (c and d) coaxially probed geometry; (e and f) coaxially detected geometry. The propagation and electric vectors of laser light are represented by k and c, respectively. The subscripts p, a, and d mean the photolysis, absorbed, and detected photon, respectively. I2 simultaneously. The powers of both photolysis and probe lasers were adjusted to avoid saturation, which distorts the polarization response. A trigger jitter of the excimer laser caused a 0-20 ns delay between the photolysis and the probe. A sheet of polarizer (Polaroid HNP‘B) was inserted to raise the polarization of the dye laser light. We used a double Fresnel Rhomb in order to rotate the linear polarization vector ca of the probe laser. The LIF was detected with a photomultiplier tube (HAMAMATSU R928) at right angles to the plane of the two laser beams. We did not distinguish the polarization of the LIF.An interference filter (Corion P10-F-600), whose center wavelength and fwhm are 600 and 10 nm, respectively, was placed in front of the photomultiplier tube to eliminate the emission from the NO(A) and NO(B) fragments. The LIF signal was processed by a boxcar integrator and an A D converter and stored in a microcomputer. The intensities of both laser lights were monitored by photodiodes and used to normalize the LIF signals. We performed these experiments at the six representative geometries in the combination of the propagation and the electric vectors of both the photolysis and probe lasers as shown in Figure 2. Repeated scans of the Doppler profiles were taken for several rotational lines. The NO dimer was produced by expanding a 15% NO/He (NO, Nippon Sans0 99.99%; He, Tesisan 99.99995%) mixture from a pulsed nozzle. A high-speed pulsed nozzle (GENERAL VALVE GV 9-279-900) with an 800 p m orifice was used. The opening period of the valve was less than 350 ps when.used under the stagnation pressure of 2.3 atm. The nozzle was placed 40 mm below the crossing region of the two laser beams to attain the collisionless condition. By comparing the stagnation pressure dependence of the LIF and the mass spectrum, we confirmed that the NO dimer was the only component producing the LIF signal.
3. Analysis A Doppler-broadened rotational line of the photofragment is generally expressed as4
13654 J. Phys. Chem., Vol. 99, No. 37, 1995
Naitoh et al.
(3) where V
AvD = vo-: maximum Doppler shift c
v - Yo A%
rotational and vibrational distributions of the NO(A) fragments were well reproduced by the CAM model, this estimate is not unreasonable. In fact, the results of the convolution reproduced the experimental data much better than those using the Maxwell-Boltzmann velocity distribution of a single temperature. We determined each Peffby the least squares fitting of the Doppler profiles to the following equation:
(-1 IXd I1): relative displacement from the line center
The parameter Peff is called the effective anisotropy and approximately consists of four bipolar moments, &(klk2), when the linearly polarized light is used for the photolysis and detection,
b&20) Be,
=
+ b43322) + b d t ( 2 2 ) bo + b,B%W
where
Ava: fwhm of the laser profile Vk
(4)
These bipolar moments, &(klkz), correspond to the following vector correlations:
F - Yo =c YO
Further, we must take into account the fine structure in the NO(E2Z+-A22+) transition, Le., the spin-rotation doubling, Fl(J=N+I/z) and Fz(J=N-IIz). The values of the splitting constants are y' = -3.15 f 0.20 MHz for the E statez6and y" = -80.35 f 0.15 MHz for the A state,27respectively. The line splitting in the P branch is expressed as
A v ~ ~ ( N=I )(f) - f')" fl(22): V - J correlation 8 3 2 2 ) :P-V-J correlation Bipolar moments, except for &(22), lie between -0.5 and 1, where the limiting values correspond to the case in which the directions of two vectors are perpendicular and parallel, respectively. The p-v-J correlation, &(22), which describes the mutual correlation among pabs, v, and J, has a limiting value of -1 when all three vectors are either perpendicular or parallel and 0.5 when two vectors are parallel with each other but perpendicular to the third. The coefficients b P b 4 are functions of the pump-probe laser geometry and angular momentum coupling factors. The numerical values of b p b 4 were evaluated for the probed transitions at the six different laser geometries. In the case of the rotationally unresolved fluorescence detection of the 22+-22+ transition, the contribution from P and R branches must be summed over. Since we did not select the polarization of LF, we also took account of this in the calculation of bo+. In the actual Doppler profile analysis, the translational motion of the parent molecule, the laser bandwidth, and the photofragment velocity distribution must be considered. Under the jet-cooled conditions, the translational temperature is generally very low and may be estimated to be a few Kelvin in this experiment. The influence of the parent molecule motion on the Doppler profile is, therefore, much smaller than the other two factors. The laser bandwidth was determined as 0.017 cm-' (fwhm) from the line shape analysis of a single rovibronic E-A transition via the A state of NO under jet conditions. The NO(A) was generated using the second harmonics of the dye laser output with ca. 0.5 cm-' fwhm. The value obtained includes the minor contribution from the translational motion of (N0)2. We used this value as the fwhm of the Gaussian laser profile. The photofragment velocity distribution W(v) was calculated on the basis of the phase space theory (PST). Since the
= 77.2"
1
- $7'
+ f')
+ 41.8 (MHz)
(6)
The two components almost overlap in the low N region because the magnitude of the splitting was comparable to the fwhm of the laser profile. Although AVIZincreases linearly with N, the PIand P2 components were not completely resolved even at high N. Since the Doppler profiles are almost symmetric for all N observed, we performed the fitting under the assumption that the population ratio of the two components depends only on the statistical weight determined from the rotational quantum number
(7) Finally, the values of befiwere determined for the six different geometries by fitting the Doppler profiles and were used to obtain the least squares solution of the simultaneous linear equations (eq 4) at a given N. Among the four bipolar moments of eq 4,&02) has already been evaluated in the previous experiments as the rotational alignment Therefore, only three moments were evaluated here. From these moments, we obtained B, the v-J correlation, and the p-v-J correlation. When a molecule possesses either spin-rotation interaction or hyperfine structure, further correction is necessary for the precession motion of the rotational angular momentum N around the total angular m o m e n t ~ m . ~The . ~ I4Nl6O molecule in the AzZ+ state has the nuclear spin I = 1 and takes Hund's case b p ~coupling where the spin-rotation interaction is large compared to the hyperfine interaction. Then, the nuclear rotation N couples to the electron spin, S(=I/2) to form J (=N S ) , which in turn couples to the nuclear spin I to form a total angular momentum F (=J I). In the case where the interval between the initial excitation by the photolysis laser and the absorption of the probe photon is long compared to the period
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Photodissociation of the NO Dimer
J. Phys. Chem., Vol. 99, No. 37, 1995 13655
0.05 cm“
0.05 cm-’
Figure 3. Doppler profiles of the NO(E-A) P(10) transition in two pump-probe geometries: left, coaxially probed geometry (d); right, coaxially detected geometry (f). The solid line is a fitting curve based on the method described in the text.
Figure 5. Doppler profiles of the NO(E-A) P(23) transition in two pump-probe geometries: left, coaxially probed geometry (d); right, coaxially detected geometry (f). The solid line is a fitting curve based on the method described in the text. TABLE 1: Vector Correlations of the NO(A2Z+) Fragment
p v-J correlation b-u-Jcorrelation A:’’ a 0.03 f 0.03 -0.06 f 0.12 7 1.01 f 0.01 0.21 f 0.19 10 1.12 f 0.03 0.16 f 0.20 -0.03 f 0.03 0.01 f 0.09 0.10 rt 0.02 -0.11 f 0.16 12 1.16 f 0.03 -0.18 f 0.27 -0.01 f 0.02 -0.08 f 0.14 15 1.10 f 0.01 0.10 f 0.30 18 1.26 f 0.01 -0.10 f 0.33 -0.48 f 0.04 -0.13 5 0.23 -0.20 f 0.12 0.40 f 0.04 20 1.37 f 0.02 -0.04 f 0.35 -0.03 f 0.01 -0.14 f 0.06 23 1.25 f 0.01 -0.16 f 0.26 a The value determined by the previous experiments (ref 23). N
0.05cm“
Figure 4. Doppler profiles of the NO(E-A) P(18) transition in two pump-probe geometries: left, coaxially probed geometry (d); right, coaxially detected geometry (f). The solid line is a fitting curve based on the method described in the text. of a precession motion, the observed alignment can be reduced as expressed in the following equation^:'^
P C ’ ( ~ I ~ ~ ) ( N ~=, O~ b~ kS’)( k l k 2 ) ( ~ i ) g ‘ ~ ’ ( ~ j ) (8) where
correlation. The results for several rotational quantum numbers are listed in Table 1 together with the values of the rotational alignment Here, we have to comment about the error and scatter of the derived correlations given in the table. First, one may notice the large difference between the errors of tfl and the v-J correlation. We evaluated the errors based on the law of propagation of error in calculating the least squares solution of the simultaneous linear equations (eq 4). The absence of a Q branch in the NO(E2Z+-A2Z+) transition unfortunately makes all the bs parameters in eq 4 positive, and this produces large errors in the v-J correlation. Next, the large scatter is observed in the p-v-J correlation. The reason is the smallness of the multiplier of &(22), b4, compared with b2. In the worst case, the former is about one-twentieth of the latter.
AK’.
5. Discussion
A similar consideration must be applied to the excited E2Z+ state. We assume this state to take Hund’s case b p ~coupling as in the A2Z+ state. The alignment of N in the excited state is also influenced in the same way when the period. between the absorption of the probe photon and the emission of the detected photon is long. These depolarizing effects are significant for low N levels. 4. Results
Figures 3, 4, and 5 show typical examples of the Doppler profiles measured at N = 10, 18, and 23 together with the fitted curves based on eq 5. Apparently, the profiles are quite different for the two different laser geometries. This immediately shows that the fragment NO(A) flies along the direction of the photolysis laser electric vector. The observed broadening of the profiles at higher N is due to the increase of the spinrotation splitting. We evaluated the effective anisotropy Peff as a fitting parameter of each profile and then used it to calculate the recoil anisotropy ,8, the v-J correlation, and the p-v-J
5.1. Recoil Anisotropy p. By the measurement of the recoil anisotropy tfl, we can determine the direction of the transition moment in 193 nm photodissociation of the NO dimer. On the basis of molecular orbital considerations, the NO dimer is initially excited to an “ionic” or a “Rydberg” state. In the former, an electron is promoted to the orbital where the unpaired n electrons of the two NO moieties are in an antibonding configuration, and in the latter the unpaired 7~ electron of one NO molecule is promoted to the Rydberg orbital of the N atom. Although we consider that the 193 nm photoexcitation mainly produces the ionic excited state, the Rydberg state may also be involved to some extentsz8 The transition to either excited state corresponds to the a1 bZ promotion in the molecular orbital description of the NO dimer with CzVsymmetry. Therefore, the transition dipole moment pabs must be directed parallel to the N-N van der Waals bond. As shown in Table 1, the recoil anisotropy tfl evaluated in the present study is positive for all N . Since the photofragment usually recoils along the breaking bond axis even in the dissociation of a polyatomic molecule, a positive tfl value means
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Naitoh et al.
13656 J. Phys. Chem., Vol. 99, No. 37, 1995 that the direction of the transition dipole moment is almost parallel to the N-N bond. That is, the transition is parallel. This observation agrees with the prediction based on molecular orbital considerations. However, a closer look at the table shows that the values of /3, 1.0-1.3, are lower than the limiting value for parallel transition, though they increase with increasing N . One possible reason for the deviation from the limiting value is rotation of photoexcited (N0)2 before dissociation. Such motion reduces the correlation between the Z axis of the laboratory frame and the velocity vector v and hence lowers the ,# value. Using the observed deviation from the limiting value, therefore, we can estimate the dissociative lifetime of the photoexcited (N0)z. On the basis of the classical method by Yang and B e r ~ o h n the ,~~ lifetime was estimated to be ca. 2.0 ps for p = 1.0 and ca. 1.0 ps for p = 1.3. However, such a big difference in lifetime cannot be caused by the small difference in the photofragment rotation, AN w 10, and therefore, the reduction in p should be attributed to another factor. Next, we will consider the possibility of deviation at the instance of the bond rupture. Since we think p a b s is parallel to the N-N bond, the reduction from the parallel limit corresponds to the situation where the photofragment NO(A) recoils with a certain angle to the N-N bond. Such a motion is related to the orbital angular momentum L between two fragments. That is, non-zero L always causes the reduction in p. According to conservation of angular momentum, the following equation should hold:
’
-0.2 -0.4
1
0
5
10
15
20
25
30
rotational quantum number N
Figure 6. Rotational alignment Ah*’ and (b) the v-J correlation of the NO(A*Z+;u=O) photofragment as a function of rotational quantum number N .
where JOis the total angular momentum, and jl and j 2 represent the rotational angular momenta of the photofragments. Because of the jet-cooled conditions, the total angular momentum JOof the initially photoexcited NO dimer must be nearly zero and, hence,
O = j,
+ j, + L
(11)
In principle, the direction and magnitude of L are unconstrained as long as eq 11 holds. Therefore, non-zero L means that ljlI is different from 1521. That is, an NO(A) fragment with a specific jl can pair with an NO(X) fragment with a different j 2 value. Such a random combination of jl and j 2 is warranted by the actually observed rotational distribution of the NO(A) fragments, which is almost statistical and predictable by the modified statistical theory (CAM).** 5.2. v-J Correlation and the p-v-J Correlation. As shown in Figure 6b, the values of the v-J correlation are in the range 0.2 to -0.2 and gradually decrease as N increases, though their uncertainties are large. From these values, the angle between the fragment angular momentum j and the recoil velocity v is expected to lie between 45” and 60”. When the bond rupture occurs from the cis planar geometry and v is nearly parallel to the N-N bond, one can consider two possible cases: “coplanar dissociation” (Figure 7a) and “cartwheel type dissociation” (Figure 7b). The two vectors, j and v, are perpendicular to each other in the former case and parallel in the latter one. The present case is considered to be near “coplanar dissociation”. This is consistent with the interpretation based on the result of the alignment At low N , the v-J correlation indicates that the average angle between v and N is about 45”. On the other hand, Af’ at the same N suggests the angle between p a b s and N to be about 60”. If v is perfectly in the plane, it is impossible to locate three
--
pabs
Figure 7. Schematic representation of four vectors, Le. the transition dipole moment &bs, the velocity vector v, the rotational angular momentum j, and the orbital angular momentum L: (a) coplanar photodissociation of (NO)z; (b) cartwheel type photodissociation.
vectors @ab$, v , and N) so as to satisfy the above two conditions. Therefore, the fragment at low N must be recoiling with the angle of 10-20” to the original plane. In addition, the N dependence of /3 indicates that this angle gradually decreases as N increases. Concerning the p-u-J correlation, the values seem to be nearly zero and show no N dependence. Because of the very large scatter, however, it is difficult to deduce any features from the results. In addition to the present measurements, we have already reported the values and tendency in the rotational alignment A:’, as shown in Figure 6a.23 From the above considerations, we can conclude that, as N increases, all three vector correlations approach the limiting values that correspond to the correlations, jdabsiIV, Pabs-Lbi, v m . In such a limiting case, the NO(A) fragment recoils along the direction of the N-N bond of the NO dimer and rotates within the original molecular plane. 5.3. Photodissociation Dynamics of (Noh. ( a ) Deviation from the Limiting Case. In the previous section, we found that
Photodissociation of the NO Dimer no vector correlation takes the limiting value, though they approach it as N increases. This fact indicates that the photodissociation is not perfectly coplanar, particularly for the photofragments of the lower rotational levels. In the following, we explore the reason why all vector correlations deviate from the limiting value and exhibit the rotational quantum number dependence. First, we must consider the contribution from the vibrational motion in the electronic ground state, Le., before the photoexcitation. The four low-frequency vibrational modes of (NO)z30 [the symmetric bend (263 cm-I), the antisymmetric bend (198 cm-I), the N-N stretching (170 cm-I), and the torsion (88.2 cm-I)] are related to the rotation of the photofragments; the former three modes give rise to the in-plane rotation, whereas the last one causes the out-of-plane rotation. We estimated the rotational energy Erot-out induced by this torsional motion using the vibration-to-rotation transformation model of Vasudev et al. based on the “s vector” method.3’ Under jet-cooled conditions, however, the vibrational and rotational excitation in the ground state is insignificant. Assuming that the dimer vibrational modes are cooled to the lowest energy level, this model gives Erot.out = 10.6 cm-I. The energy release to the out-of-plane rotation is too small to explain the deviation from the limiting value in the alignment Af’ and the v-J correlation. For the in-plane rotation, the estimated energy Erot.i, is 125.5 cm-’. This amount is also much less than the observed average rotational energy (Erot)= 1160 cm-I. Therefore, the contribution of the original vibrational motion is not important. Next, the effect of the torsion in the electronically excited state should be considered. For the van der Waals (vdW) vibrations, including the torsion, to get excited before the bond rupture, “partial energy randomization” must be operative after the photoabsorption. However, on the basis of the structureless absorption spectrum, (N0)2 is expected to dissociate along the repulsive potential energy surface. In order to check the possibility of predissociation, we measured the high-resolution photofragment yield spectrum by monitoring the 0-1 band of the NO(A-X) emission.32 But, the observed spectrum did not show any structure, confirming the direct photodissociation. To reconcile the direct dissociation and the excitation of van der Waals vibrations, we have to assume that the energy transfer in the electronically excited state is actually occurring during the fast photodissociation process. Such an idea seems to be implausible, judging from the ordinary photodissociation dynamics. However, we think that such features are most characteristic of the dissociation process of molecules with van der Waals vibrations. The nearly statistical energy distribution observed in the LIF excitation spectra of the NO(A) fragments supports this idea. Our picture of the photodissociation dynamics is then the following. Just after the photoexcitation, most of the energy is located at the N-N bond stretching mode. As the dissociation proceeds, this energy dissipates into other low-frequency vibrational modes including the torsion. If this energy flow is much faster than the rupture of the N-N bond, the product energy distribution would become statistical and vector correlations are expected to be reduced from the limiting value. On the other hand, if the bond fission occurs before the energy randomization, we should have the limiting values in the vector correlations. In the actual case, however, the energy dissipation competes with the dissociation, and both statistical and nonstatistical features appear. The above discussion can be interpreted from a different viewpoint. The energy randomization during the dissociation
J. Phys. Chem., Vol. 99, No. 37, 1995 13657 is essentially caused by the coupling on the potential energy hypersurface between the dissociation coordinate and other coordinates of vdW vibrations. For example, if the PES in the electronically excited state is very flat or has a shallow double minimum in the direction of the torsion, the out-of-plane motion is enhanced in the course of the dissociation along the repulsive potential surface. As a result, the angular momentum almost parallel to the N-N bond is produced, and this momentum couples with the angular momentum perpendicular to the original molecular plane, resulting in the tilted fragment angular momentum. In this way the value of the alignment A t ’ and the v-J correlation could deviate from the perpendicular limit. (b)N Dependence of the Vector Correlations. As mentioned above, the presence of low-frequency vdW modes facilitates a part of the available energy to dissipate during the dissociation into the vibrational motions of the NO dimer other than the N-N stretching. On the basis of such a partial energy flow mechanism, we can also explain the N dependence of the alignment Af’ and the v-J correlation as shown in Figure 6. To simplify, we divide the total rotational angular momentum of the fragment, N, into two components: Ni, for the in-plane rotation and Noutfor the out-of-plane rotation. Nin is the main component of N and is usually larger than Nout,since Ni” is created by the N-N bond fission in the photodissociation along the repulsive surface. On the other hand, No,t is caused by the torsional motion of parent (N0)2, which is enhanced by the partial energy dissipation. As a result of energy dissipation, a small amount of NOutalways exists and its relative importance increases when the total rotational angular momentum N decreases. Conversely, the relative contribution of N. ,,,becomes larger with increasing N . Therefore, the rotational axis of the NO(A) fragment becomes more perpendicular to the plane as N increases. Such a tendency causes the observed N dependence of the alignment Af’ and the v-J correlation A similar argument can be applied to the N dependence of the recoil anisotropy B. As stated in section 5.2, the photofragment at low N recoils with a certain angle to the original plane, and this angle decreases as N increases. Let us consider the effect of torsional motion on the direction of the recoil velocity v. The torsional motion detaches the center of mass of the NO moiety in (N0)2 from the original plane. If the bond rupture occurs during such motion, the photofragment has a velocity component perpendicular to the plane. Since this perpendicular component ought to be proportional to the magnitude of the torsional motion, the presence of more energy in this vibrational mode increases the deviation of B from the limiting value. Therefore, as N decreases, the available energy to be distributed into the torsional motion increases, and hence the reduction of ,L? becomes larger. In summary, vector correlations clarify that photodissociation of the NO dimer at 193 nm proceeds mostly within the molecular plane. Though all correlations deviate from the limiting value (perfect coplanar dissociation), we can explain the reason by considering fast energy flow in the excited state, which is in accordance with the statistical behavior of the rotational distribution of the NO(A) fragment. That is, the presence of a low-frequency van der Waals vibration accelerates the vibrational energy dissipation from the N-N bond, where most of the available energy could be located just after photoexcitation, to other vibrational modes. This energy randomization transfers a fraction of energy into the out-ofplane motion and, as a result, causes the angular momentum not perpendicular to the original molecular plane, so that the rotational alignment Af’ and the v-J correlation deviate from the limiting value, particularly at lower N . On the basis of this
13658 J. Phys. Chem., Vol. 99,No. 37, 1995
energy flow mechanism, we can also explain the observed N dependence of vector correlations.
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