J . Phys. Chem. 1984, 88, 3419-3425
3419
Photodissociation of C2N2,CICN, and BrCN in a Pulsed Molecular Beam R. Lu, J. B. Halpern,* and W. M. Jackson Laser Chemistry Division, Chemistry Department, Howard University, Washington, D.C. 20059 (Received: August 15, 1983; In Final Form: December 6, 1983)
The photolysis of C2N2,ClCN, and BrCN at 193 nm have been studied with a pulsed molecular beam apparatus to lower the internal rotational and vibrational distributions of the parent molecules. The results of these studies show how the initial internal energies of the ground-state molecules affect the rotational and vibrational distributions of the products. The observed CN distributions produced from BrCN and ClCN were insensitiveto changes in the original internal energies of the parents, while the rotational and vibrational distributions of the CN fragments produced from CzN2photolysis varied weakly with changes in the internal energy distribution of the parent. These observations have been used to describe parts of the dissociative electronically excited potential surface of the CzN2,ClCN, and BrCN molecules.
Introduction
Nascent quantum state distributions of the fragments yield important information about the details of the photodissociation process. The presence of large amounts of rotational energy in the fragments indicates that substantial geometrical changes occur when these species pass from the ground to the excited state. Of course, when photodissociation is studied at room temperature, the parent molecule's rotational and vibrational energies are distributed in accord with Boltzmann statistics. The bending vibrations have very low fundamental frequencies so that at 300 K a substantial population is expected in the first few levels. The rotational energy that is observed in the fragments could result from the angular momentum that is associated with these bending modes or it could result from the excitation or the thermal rotational excitation of the parent. In the case of transitions between a linear ground state and a linear excited state our earlier work1 had led us to the conclusion that the observed angular momentum of the fragments is due to the original angular momentum present in the rotational motion of the parent molecule. To test this conclusion we felt it important to experimentally vary the original amount of angular momentum and vibrational excitation in the parent and determine how this affects the angular momentum observed in the fragments. Free-jet expansion in seeded molecular beams is known to cool the internal degrees of freedom of the diluent molecule.2 Pulsing these molecular beams reduces the vacuum pump requirements and is consistent with the use of a pulsed tunable dye laser to determine the quantum state distribution. With this technique, depending upon the experimental conditions that were chosen, internal rotational and vibrational temperatures as low as 1 and 50 K, respectively, have been obtained. Thus the use of pulsed molecular beams allows one to vary the amount of vibrational and rotational energy that is present in the molecule before photoe~citation.~" For several years various workers in our laboratory have been involved in measuring the nascent quantum state distributions of fragments produced in the photolysis of linear cyanide containing molecule^.^*^-^^ Recently we reported on the photolysis of C2N2,' ClCN and BrCN9 at 193 nm by an ArF laser in an effusive beam.
TABLE I: Summary of Results from Beam Studies on the Photolysis of C,N, at 193 nm
beam effusive pulsed pulsed
carrier Ar Ar
torr 0.1 410 760 730 560
mm
K
0.2 0.8 0.8 0.8
900 800 550 540 620
N(v"=O);
0.35 0.22 0.10 0.1 1 0.12
CH4 pulsed CH4 pulsed "Nozzle diameter. * CN rotational temperature. CN vibrational population.
The results may be summarized as follows: in the case of C,N,, there are two ground-state C N fragments formed as a result of predissociation through the 2+ ground-state vibrational continuum of C2N2. Roughly 25% of the C N fragments are produced in the v" = 1 state. The rotational distribution of both the v" = 0 and v" = 1 fragments can be described by a 900 K Boltzmann distribution. This distribution can be reproduced by assuming that the excited state of the molecule is also linear and that each fragment carries away half of the rotational angular momentum of the parent. ClCN and BrCN, on the other hand, distribute about half of the available energy into rotation. If we assume that both halogen atoms are formed in the lowest spin-orbit state then the total amount of this excess energy is about 18 000 cm-I for ClCN and 22000 cm-l for BrCN. The rotational distributions of C N fragments are non-Boltzmann for all vibrational levels, being inverted with respect to thermal distributions. For the case of ClCN about 30% of the fragments are produced in u N = 1, 19% in v"= 2, and a trace is observed in v"= 3. For BrCN most of the population is found in v" = 0 while only a small amount of v" = 1 fragments are seen. In each of these cases a parameterized model that depended upon the initial population of the rotational and vibrational states of the respective parent molecules was suggested. Given the good fits to the data obtained with these models, we believed it worthwhile to test them further by cooling the reactant gas in a pulsed supersonic molecular beam. Experiment and Results
(1) J. B. Halpern and W. M. Jackson, J . Chem. Phys., 86, 973 (1982). (2) G. M. McClelland, K.L. Saenger, J. J. Valentini, and D. R. Herschbach, J . Phys. Chem., 83, 947 (1979). (3) M. G . Liverman, S . M. Beck, D. L. Monts, and R. E. Smalley, J . Chem. Phys., 70, 192 (1979). (4) T. G. Dietz et al., J . Chem. Php., 77, 4417 (1982). (5) F. M. Behlen and S. A. Rice, J . Chem. Phys., 75, 672 (1981). (6) F. M. Behlen et al., J . Chem. Phys., 75, 5685 (1981). (7) W. M. Jackson, J. B. Halpern, and C. S. Lin, Chem. Phys. Lett., 55, 254 (19781. ( 8 ) M. i.Sabety-Dzvonik,R. J. Cody, and W. M. Jackson, J . Chem. Phys., 66, 2145 (1977). (9) J. B. Halpern and W. M. Jackson, J. Phys. Chem., 86, 3528 (1982). (10) G. E. Miller, W. M. Jackson, and J. B. Halpern, J . Chem. Phys., 71, 4625 (1979).
0022-3654/84/2088-3419$01.50/0
The experimental apparatus has been previously des~ribed'.~ and consists of counterpropagating dye and excimer laser beams which cross a molecular beam at right angles in the experimental cell. Induced fluorescence is observed by a filtered and apertured photomultiplier perpendicular to both the laser and molecular beams. The supersonic molecular beam is formed by a pulsed valve with a 0.2-mm i.d. orifice. The valve opens with a 500-ps rise time and the pulse width is about 3 ms. The laser beams cross the molecular beam at a distance of 15 mm from the nozzle exit. The lasers are triggered so that they pass through the molecular beam 350 ps from its initial rise. The background pressure in the reaction cell rose to about 5 X torr when the pulsed valve 0 1984 American Chemical Society
3420 The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 R oo
P Do
BRANCH
Lu et al.
BRANCH
Roll
1-
R 11 BRANCH
,-
Pll
BRANCH
P
R,,
I 0
I
L Figure 2. R branch photofragment excitation spectrum of CN obtained when C2N2is photolyzed immediately after emerging from a pulsed supersonic nozzle valve and the CN product is excited about 20 nozzle
diameters from the valve. 0 0 .
e x c i t a t i o n w a v e l e n g t h (nm)
6 1
a*o
ClCN
O 0-pulsed
0
*O
Figure 1. CN nascent photofragment excitation spectra from the photodissociation of C2N, at 193 nm. The upper spectrum (a) was measured with an effusive source, while the lower spectrum (b) was measured with a beam of 35 torr of C2N2seeded in CHI. Cooling effects are noticeable in the lower spectrum especially with regard to the vibrationally excited CN radicals.
beam
00
o
*-effusive
beam
0 . O
00
*O
was running at 10 Hz. In some experiments a 0.8-mm hole was used along with a lower frequency of 1 Hz so that the cooling effect could be enhanced. Figure 1 shows typical excitation spectra of C N fragments produced from the photodissociation of both an effusive and a pulsed beam of C2Nz. Both argon and CH4 were used as the carrier gases in the pulsed beam experiments. Analyses of these pulsed beam experiments indicate that both the rotational and vibrational distributions of the C N products are cooled as compared to the result in the effusive beam. Table I lists the “rotational temperature” of C N radicals and the vibrational population ratio, N(v”= I)/N(v”=O) under a variety of experimental conditions. The parametric temperature and the population ratio were calculated by the same method as in previous work.’ The observed rotational temperatures of the fragments in the u” = 0 and u” = 1 levels are the same within experimental error in each of the beam studies. The rotational cooling effect observed in the pulsed beam photodissociation is, however, much less than one would have predicted with our earlier model.’ This model suggested that the temperature observed in the C N fragment should be approximately three times the original rotational temperature of the parent CzN2in its ground electronic state. The observed temperature of the C N fragment was never below 540 K, despite the fact that a range of expansion ratios and various carrier gases were used. With the original model these results would correspond to a parent rotational temperature of 180 K which is much higher than one would calculate for such pulsed beams. To determine the amount of rotational cooling that is actually occurring in the pulsed beam, experiments were done where C N was deliberately formed in the earlier part of the beam before the supersonic expansion was complete. The R-branch of the C N spectra from one of these experiments is shown in Figure 2. It is clear from this spectrum that the originally hot C N radicals have been substantially cooled in the expansion since most of the population occurs in the first few J levels. The “temperature” calculated from this spectra is less than 10 K. The temperature of the C2Nzparent should be even lower than this because it has a much smaller rotational constant which should promote more
*.O
00
O.,O
0 0 0
0 I
6000 ROTATIONAL ENERGY
10000
c6’
Figure 3. Nascent quantum state distributions of CN fragments from the dissociation of ClCN in a pulsed beam (open circles) and an effusive beam (filled circles). The pulsed beam used a mixture of argon (97%) and ClCN (3%) at a total pressure of 1 atm behind the valve.
effective cooling. Furthermore, starting from the nozzle, the CzNz would undergo expansion along the entire path. Thus, the higher rotational temperatures reported in Table I cannot be explained in terms of incomplete expansion and poor rotational cooling of the X’Z state of CzNz. Similar photodissociation experiments with BrCN and ClCN have also been done. The rotational distributions in Figure 3 show that in the photolysis of ClCN there is almost no observable change in the rotational distribution of C N fragments. The only measurable change is a 10% decrease in the vibrational population of u”= 1. This is, however, within the experimental error. The slight change that is observed in the rotational distribution of C N fragments produced from the photolysis of BrCN, which is evident in Figure 4, is also within the experimental error range. These results confirm the original observation9 obtained in an effusive beam, that the transition excited by the 193-nm laser in ClCN and BrCN is due to a linear to bent electronic transition.
Discussion CzN2. The results of the cooling experiments have forced us to reconsider our earlier model which is in agreement with the rotational distribution from effusive beam experiments at room temperature, but whose prediction does not agree with the present observations. A major difficulty is that the parent C2N2 is a tetratomic molecule. Although the configuration is linear in both ground and excited electronic states, Le., X’B, and BIAu, there are no
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 3421
Photodissociation of C2N2, ClCN, and BrCN l 0rCN
*
0-
pulsed beam
I
-I
e 3 0
e 0
ROTATIONAL ENERGY
C m '
Figure 4. Nascent quantum state distributions of C N fragments from the dissociation of BrCN in a pulsed beam (open circles) and an effusive beam (filled circles). The pulsed beam used a mixture of argon (97%) and ClCN (3%) at a total pressure of 1 atm behind the valve.
exact theories that can be easily applied to predict the internal state distribution of photofragments which come from polyatomic molecule containing four or more atoms. Kresin and Lester" have discussed an adiabatic approach to the photodissociation of a polyatomic molecule but at the present time their theory only predicts the vibrational product distributions though in principle it can predict rotational product distributions. The application of the theory also requires a detailed knowledge of the potential surface corresponding to the BIAu state. Freed et al.12-15have modeled dissociation processes of triatomic molecules. Since C2N2is a symmetric linear molecule one might consider it to be a quasitriatomic molecule. An attempt has been made to use Morse and Freed's ideas to qualitatively explain the rotational distribution from the dissociation of rotationally cooled C2N2. The rotational temperature predicted by this model, however, is still quite low when compared to our observations. On the basis of this model, the average rotational energy of C N fragments would be about 64 cm-' which includes the contribution from the angular momentum associated with the bending vibration of C2N2. This is much smaller than the average rotational energy of 372 crn-', obtained from the experiment. In order to understand the experimental results, a semiclassical interaction model will be suggested, but it is necessary to first discuss the nature of the upper electronic state of C2N2. The wavelength profile of the ArF laser measured in our lab is, as Figure 5 shows, the same as that measured by Sanders et a1.I6 in this wavelength region. The transition is a IA,, IZg with AA = 2. Such a transition becomes optically allowed by mixing the symmetry of the vibrational modes, Le., the bending modes, with the symmetry of the excited electronic state. There has been no complete set of fundamental vibrational frequencies measured to date. Thus we will use the theoretical results of an ab initio calc~lation'~ of the 'Au state along with the experimental absorption spectra of Woo and Badger,'* West,Ig and recent unpublished work of Halpern and Laufer20 to estimate the frequencies of the possible vibronic transitions that are excited by absorption of the radiation from the ArF laser. The estimated absorption peaks are shown in the bottom of Figure 5, while the probable transitions are presented in Figure 6 . The absorption cross sections of the strongest lines are approximately cm2. The linear nature of both the ground and excited state in this absorption system restricts the number of possible vibrational
1930 WAVELENGTH
1940
(A)
Figure 5. The upper trace shows the wavelength distribution of the ArF laser beam after passing through about 1 m of air. The lower trace shows the location of the principle absorption lines of CzNzas taken from Woo and Badger." The representation of the line shapes schematic, as given in ref 13.
3001 1
l A u 2201 1 30010 22010
+-
~
~~
(11) V. Z. Kresin and W. A. Lester, Jr., J . Phys. Chem., 86,2182 (1982). (12) Y . B. Bank and K. F. Freed, J . Chem. Phys., 63, 3328 (1975). (13) M. D. Morse, K. F. Freed, and Y . B. Bank, J . Chem. Phys. Lett., 70, 3604 (1978). (14) M. D.Morse, K. F. Freed, and Y . B. Bank, Chem. Phys. Lett., 67, 294 (1979). (15) M. D. Morse and K. F. Freed, J. Chem. Phys., 74, 4395 (1981). (16) R. K. Sander et al., Appl. Phys. Lett., 30, 150 (1977). (17) M. Dupuis and W. A. Lester, private communication. (18) S. C. Woo and R. M. Badger, Phys. Rev., 39, 932 (1932). (19) G. West, Thesis, University of Wisconsin. (20) J. B. Halpern and A. Laufer, private communication.
00010 l=g
00001 00000
Figure 6. Energy level diagram of C2N2showing all the electronic transitions excited by the ArF laser at 193 nm. The term symbol on the far left of the figure shows the electronic symmetry of the ground and excited states. The set of five numbers immediately next to this shows the number of quanta in the five vibrational modes of the molecule. The term symbol on the far right indicates the possible symmetry species of the individual vibronic states resulting from the combination of the electronic and vibrational symmetries.
transitions. In particular the quantum number of the u4 mode must change by an odd number of quanta, while the v g and u5 modes change by an even number of quanta. However, the Franck-Condon principle implies that the strongest lines in the spectrum will involve no change in the ug and u5 mode quantum numbers and a change of only 1 quanta in the u4 quantum number.
3422
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984
Lu et al. TABLE 11: Calculated Relative Population over the Low-Lying Vibrational Levels of C2N2 300 K 200 K 150 K 100 K
00000
00001
00002
00010
00011
1 1 1 1
0.65 0.37 0.21 0.068
0.21 0.068 0.022
0.17 0.051 0.015
0.11 0.019
Assuming that the original angular momentum of CzN2 is equally distributed between the two recoiling C N radicals one can write
J ] = R(J)+ jl’ Y2 = k(J)-7zt
tC)
Figure 7. This figure shows the effect on the impact parameter of vibrational motion in the parent molecule. (A) and (B) refer to the photolysis of C2N2. (A) shows the situation if only the v5 mode is excited, and (B) shows the situation if only the v4 mode is excited. ( C ) shows the situation for photolysis of XCN.
Even though the possible vibrational states of the molecules that can be initially excited by the A r F laser can be narrowed down to a few possibilities, none of these possibilities necessarily represents the configuration of the molecule just prior to dissociation. The reason for this is that the BIAustate correlates with two CN(AZII)radicals at infinite internuclear distance. There is not enough energy at 193 nm for the C2Nzmolecule to dissociate into two AZIIstate radicals. Thus, molecules originally excited to this state can dissociate only by predissociation through the ground-state continuum. It is not certain at what internuclear position this crossover will occur and it may require several vibrations to reach this point. During this time energy can be redistributed among the vibrational modes. The rotational angular momenta of the C N fragment must come from some combination of the original rotational angular momentum of the parent, its degenerate bending vibration and any additional angular momentum due to the final state interactions between the separating fragments. This is schematically shown in Figure 7. We assume that the separation of the two C N radicals occurs instantaneously on the repulsive potential surface during a v5 bending vibrational period (Figure 7a), so the two C N fragments are formed with equal but oppositely directed angular momentum vectors which give rise to J1‘= -J2’
(1)
or Jl’
= 72’
where j,’ and j,l are the quantum numbers representing the angular momentum produced by the repulsive potential. Since the CzN2 molecule is rotating during dissociation, conservation of angular momentum requires that
J=j+E
(3)
where is the total angular momentum_ofCzNp including bending vibrational angular momentum, and j = j , + j z is the rotational angular momentum of C N fragments. Following Morse’s calculation15 in the quasitriatomic case and neglecting the effects of final state interaction, one can express the orbital angular momentum L of the separating fragments in the large J limit as (4)
The parameters p and q are related to the moments of inertia of C2N2and CN, and in this case the ratio p / q is about 0.89. This means that a small amount of angular momentum of parent CzN2 molecule would be distributed into the rotation of CN.
(sa) (5b)
where R(J)is the part of the original angular momentum in CzNz that appears in the C N fragment. In the laboratory we are unable to distinguish the two C N radicals which are recoiling from the same CzNz molecule. What is detected is the number of C N radicals in ,a particular rotational state, so that the projection of the vector ji, onto the plane of dissociation will cause the final fragment angular momentum to range between K ( J ) j,’ and K ( J ) - j,l. There is no distinction between j , and j 2 observed in our experiments. The cooling of the parent C2Nzin the pulsed beam expansion should cmly decrease the value of K(J), Le., the contribution of the original angular momentum of the parent to the final angular momentum of the products. At small J , K ( J ) 0, so j , = j,’ = j,’ -jz (6)
+
-
which indicates that the rotational distribution of C N obtained under these conditions is dominated by the final state interactions. The distribution Po”)should be the observed rotational distribution in the pulsed beam experiments when the CzNz is the coldest. Thus the previous room temperature results which could be fitted is just a fortuitous with a model where jl = J / 2 and TCN= 3TC2N2 case where jl = K ( J ) + j ‘ = J / 2 . A comparison of the rotational distribution for both u” = 0 and -- 1 vibrational levels of C N shows that within experimental error they are the same. This agrees with the earlier assumption that the energy is transferred from the v4 to the v5 bending mode in the upper electronic state before dissociation. Classically, the interaction force is parallel to the line connecting the centers of mass of the two C N fragments, and the average impact parameter of the half-collision is so small that the recoil velocity does not influence the rotational distribution. As can be seen in Figure 7B, if the v4 vibration is still excited when dissociation occurs then the impact parameter would have been larger and the orbital angular momentum should have been different for the u” = 0 and u” = 1 levels since the relative velocity between the two fragments must be different for the two vibrational levels. As a consequence, the vibrational cooling observed in this experiment could not be caused by the rotational cooling because the rotational distributions are the same for u” = 0 and u” = 1 levels. Table I1 shows that at room temperature a significant amount of the ground-state CzNz molecules have their bending vibrations excited. The population of the stretching modes is, however, extremely small. In these beam experiments the most likely vibrational modes to be cooled are those associated with the bending vibrations. As the beam expansion ratio increases the population of the bending modes will decrease. This implies that the observed decrease in the CN(v”=l)/CN(u”=O) ratio is a result of the decrease in the population of the bending mode in the CzN2 parent. The population of thermally excited vibrational states above (00001) is too low to account for the observed decrease. Further, since they are at higher energies more collisions will be required to cool them. This would disagree with our observation that the effect is observed for fairly low expansion ratios. The dependence of the vibrational distribution of the C N fragment upon the vibrational excitation of the bending mode in the ground state may at first glance be attributed to the fact that
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 3423
Photodissociation of C2N2,CICN, and BrCN a higher energy level of the upper state is excited by a photon with the same energy that excites the 00000 state of the ground state. The difference in energy between the 00000 state and the 00001 state of the ground state of CzN2is, however, much less than the energy difference between the u” = 0 and u” = 1 levels of CN. Thus it is not expected that this small increase in energy can account directly for the production of the u” = 1 level of CN. Rather we feel that during the vibrational redistribution within the excited BIAustate prior to cross over to the vibrational continuum of the ground state, the presence of extra quanta of energy in the u5 vibrational mode must favor the formation of a configuration which dissociates in part via CzNz(X’2:g,00001)
-
CN(u”=O)
+ CN(v”=l)
where wXCN is the reduced mass of the separating atomic and diatomic fragments, u, the final velocity of separation of the fragments in the frame centered in the X-CN molecule before photoexcitation, and, b, the impact parameter. Conservation of energy requires that
+ E, = J ( J + l)h2/2zCN + ( ~ ~ ) / L x c N(9) V~
(21) J. D. McDonald et al., presented at the 1983 Conference on the Dynamics of Molecular Collisions, Gull Lake, MN.
e #ee e
6
e -I I
e
v”=O
0
v”=l
e e
e
e
3 3
a 0
4
e
-
I
(7)
The molecules that are in the lowest vibrational level upon predissociation will yield C N fragments only in the u” = 0 level. These arguments based upon the observations in pulsed molecular beams and the complete absence of C N radicals in the u” = 2 level suggest that statistical theories cannot be invoked to explain the observed vibrational distributions. Our work differs considerably from the work that has been recently reported by McDonald et al. on the photolysis of cyanogen at 193 nm in a supersonic molecular beam.21 In that work the u” = 0 and the u” = 1 levels had different rotational distributions and could not be described by a single rotational temperature because the Boltzmann plots were curved. Even the slope of the linear part of the u” = 0 curve was flatter than we observed, which would suggest that if it could be described by a single temperature it would be considerably higher than the one that has been observed in this work. The slope of their u” = 1 curve was closer to the shape of the curve observed in the present work. At first glance one might suppose that these results would suggest that our results had been marred by collisions in the beam or in the static gas. As was reported earlier the results of our studies have been reproduced in a static cell at pressures as low as torr and delay times of 0.5 FS. We have also reproduced the static gas results in an effusive beam with over more than two orders of magnitude differences in the beam density. The only explanation we can offer for the present discrepancy is the possibility that we are looking at different transitions even though both studies use a pulsed ArF laser. In McDonald’s work the ArF laser is run under low gain, with oxygen between the mirrors, conditions which narrow and shift the line. They have informed us that a spectral scan of the laser light showed a single relatively narrow peak and that they have not yet accurately measured the position of this peak. Thus, they may be exciting a single transition, and one that is not strongly pumped by our broader structured line. This may account for the difference between the sets of experiments. ClCN and BrCN. The observed quantum state distribution of C N fragments is the same when we start with a thermal (300 K) beam of ClCN molecules or a seeded beam. It is apparent that one can ignore any contribution to the rotational state distribution of C N product from thermal rotational excitation of the parent. This is equivalent to viewing the dissociation as occurring in the nonrotating fixed frame of the XCN molecule. In this frame the total angular momentum of the parent molecule is zero. Thus, the sum of the orbital and rotational angular momentum of the fragments must also be zero. The distribution of the latter is measured directly by LIF. Therefore
hv -Do = Ex
C l C N P H O T O L Y S I S AT 1 9 3 n m
2
4 IMPACT
8
6
PARAMETER
nm
Figure 8. Transformed impact parameter population distribution for the photolysis of ClCN at 193 nm. See the text for details of the transformation.
z
-c0 4: 2 3
a
0
a
z
wu
a
2
I
0
4
2 IMPACT
6
PARAMETER
8
nm
Figure 9. Transformed impact parameter distribution for the photolysis of BrCN at 193 nm. The open circles show the distribution if the Br atoms were all produced in the lowest P(3/2) electronic state. The closed circles show the distribution assuming that the Br atoms are all produced in the excited P(1/2) electronic state.
where Y is the frequency of the 193-nm laser photons, Do the dissociation energy of the X-CN molecule, Ex the electronic energy of the halogen atom, which we will assume to be in its ground state, and E, is the vibrational energy of the C N fragments. ZCN is the moment of inertia of the separated C N radical. Combining eq 8 and 9 and setting ZCN equal to pcNr2 one finds that
where ETis the translational energy from photolysis and re the equilibrium distance between the C and N atoms in the fragment. Using eq 10 one can transform the measured distribution of the fragment rotational state P(J), shown in Figures 3 and 4 for ClCN and BrCN, respectively, to distributions of the impact parameter, shown in Figures 8 and 9, which are characteristic of the halfcollision photolysis process. It is important to understand that eq 8 and 9 are simple statements of conservation laws as applied to the stationary system before and after dissociation. Thus, eq 10 is a straightforward consequence of the observation that the angular momentum of the parent has no effect on the rotational distribution of the C N fragment. The only simplification that has been made is the neglect of the single unit of angular momentum carried by the photon which is small compared to the 40 to 60 units found in the fragments. A further transformation of the fragment distributions can be made when the C N radicals are produced in their lowest vibra-
3424
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984
Lu et al.
tional state. For halogen X-CN molecules, the bond distance of C N is almost the same as in the ground vibrational state of the free radical. If the C N radical can be considered “stiff“ and unchanged during photolysis, then the impact parameter is just equal to [ m N / ( m C+ m N ) ] r esin a where a is the angle between the X-CN bonds at the instant of dissociation. Thus, for v” = 0 C N fragments
The value of sin a calculated for b = 6.1 nm is greater than unity. The failure in calculation of CY with eq 11 implies that the interaction is so strong that the X atom running on the potential energy surface which is schematically shown in Figure 10 travels not along the lowest energy path but along the energy gradient which gives rise to large impact parameters, with the maximum value of 9.2 nm for ClCN and 6.5 nm for BrCN. As was discussed in ref 9 and shown in Figure 10, transitions between a linear ground state and a bent excited state favor the population of a few highly excited vibrational levels in the bending mode of the upper state. Therefore, the Franck-Condon principle requries that the only levels in the mode that can be reached from the linear ground state are those that are very close to the inversion barrier at P radians. For X-CN molecules, this point on the potential energy surface is stationary in both the C-N bond length and the interbond angle. The absorption profile could therefore be used to obtain the dissociative potential energy curve in the X-C bond direction via the Franck-Condon reflection principle. Unfortunately, the only published absorption profiles for ClCN and BrCN are schematic. In the region of 193 nm, their general shape and lack of structure suggests that the bond becomes purely dissociative. It is clear that the strong repulsive interaction contributes most of the rotational angular moment while the contribution of the parent’s rotation is small so that the fragment distribution is the same for the thermal and expanded beams. There may be another possibility that a selection effect associated with the linear-bent nature of the transition allows excitation only from low rotational states of the fragment. If this is the case then the total number of C N fragments will increase as the beam is cooled. This experiment is in progress. The sharply peaked rotational distributions that are observed for the C N fragments in the photodissociation of BrCN and ClCN give us additional information about the dissociation process. The repulsive interaction between the halogen atoms and the C N fragment must occur on a time scale that is short compared to the period associated with the vibrational bend. Otherwise, because of the size of the halogen atoms, interfragment collision will occur which should smear out the peaked distribution, i.e., a direct dissociation. A crude estimate of this period can be obtained by calculating the rotational period of the C N radical at the peak of the rotational distribution. In the first approximation this motion is just a continuation of the bending motion associated with the highly vibrationally excited upper electronic state. Since the dissociation is direct the rotational angular velocity of the C N will equal the angular velocity from bending in the asymptotic limit. Consideration of the nature of the bending potential shows that the angular velocity will be a smoothly increasing function starting from the time of photoexcitation. A C N radical with a J 60 will have a rotational period of 1.4 X s. If in this time the C N radical moves 4 8, (about a unit of the equilibrium distance of the ground state) it will have an initial velocity of 3 X lo5 cm/s and if the state is purely repulsive this would imply that approximately 1 eV of the available energy in BrCN ends up in recoil translational energy. This estimate uses the rotational quantum number at the peak population. Though it is crude, it is in reasonable agreement with the inferred translational energy. N
Conclusions Spectroscopy and nascent fragment energy distributions probe the two endpoints of the dissociation process. The general shape of the dissociation potential energy surface may be deduced from a careful consideration of such information. It has been seen above
0,2K
0
IT BENDING
ANGLE
2Tl
,a
Figure 10. (A) A conception of the upper dissociative potential energy surface of XCN in the rest frame of the CN moiety. The distance from the CN center of mass represents the separation of the halogen atom from the CN fragment. Two possible schematic paths are shown. The first (curve I), resulting in an impact parameter b‘corresponds to dissociation down the sloping valley, centered at angle a, which is the equilibrium bending angle of the excited state. This would correspond to the case where the bending and repulsive motion occurred on the same time scale. The second (curve 11), which results in a larger impact parameter b, is the result of an extremely rapid bending motion coming at the same time as the molecule is dissociating. At least initially, this bending dominates the motion. However, the repulsive force takes over before a single cycle is completed and breaks the molecule apart. A third possibility, which is not shown would involve a rapid bending and a very slow separatory motion. In such a case the molecule would oscillate down the valley, emerging with a very large spread of impact parameters. (B) The cut of the surface indicated by the dotted line in part A. The barrier at a = T is the position where the X atom stands at the moment of photon excitation.
J . Phys. Chem. 1984,88, 3425-3431 how results from cooled seeded and thermal effusive beams can be used to study the excited potential energy surface for predissociative (C2N2) and directly dissociative (BrCN and ClCN) photolysis. Reexamination of the structured B'A, X'Z+ spectrum of C2N2with ab initio calculation of the vibrational frequencies of the upper state identified the transitions at 193 nm as 194; 5: and 1; 2t4; 5: where n represents the quantum number of thermal population of the v 5 mode. The well-defined structure of the spectrum shows the upper state to be predissociatively coupled to the vibrational continuum of the ground state. The nascent quantum state distribution of C N fragments is indicative of a zero impact parameter dissociation. The rotational excitation of the C N fragments in this case must come from repulsive interaction between the two C N radicals in v5 mode during dissociation, and these two fragments will be rotating in an opposite sense. The orbital angular momentum will come mainly from parent's rotation. This implies that during the dissociation process, energy must flow out of the v4 mode and into the v5 mode. A quantitative decrease is measured in the amount of vibrationally excited C N productas the C2N2is cooled. In unexcited C2N2, no measurable population will be found with excited stretching modes. The beam cooling will primarily affect the bending v 5 mode of C2N2. Thus, a small amount of the extra energy in the v5 mode must couple to channels leading to vibrational excitation of the C N fragment. The most interesting discovery about the 193-nm photolysis of ClCN and BrCN is that there is no measurable difference between the measurements in the cooled and thermal beams. This means that the rotational distribution is dominated by the repulsion and can be treated in the nonrotating frame of the parent molecule.
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Simple use of the conservation of energy and angular momentum then allows a one-to-one mapping of the rotational state distribution onto the distribution of impact parameters. The large average amount of fragment rotational energy shows that the electronic transition is linear to bent. The sharply peaked distribution of fragment rotational quantum states and the large impact parameter imply that the dissociation is direct. Thus there is no smearing of the distribution as would be expected if the bending motion, which gives rise to the fragment rotation, were able to execute one or more cycles. Application of the FranckCondon principle shows that the photoexcitation can only reach a bending mode level in immediate contact with the inversion barrier to bending. The carbon-nitrogen bond length in the XCN molecule is very close to that of the free C N radical. Thus, the motion on the dissociative potential energy surface consists of a rapid lengthening of the X-CN bond while the molecule is undergoing a rapid, but not completed bending motion. The relative paucity of energy transferred into vibration must be a result of the maximum repulsion between the halogen atom and the C N radical occurring when the bond angle is close to ~ / 2 .The bond angle when dissociation occurs is more linear for ClCN than BrCN as there is more fragment vibrational excitation in the former case than the latter.
Acknowledgment. The work, of which this paper forms a part, was supported by the Department of Energy under Contract No. DE-AS05-76ER05056. We also acknowledge the provision of the excimer laser through NASA Grant NSG 5071. J.B.H. received support from NASA under Grant NSG 5-17. Registry No. C2N2,460-19-5; CICN, 506-77-4;BrCN, 506-68-3;CN, 2074-87-5.
Rotational Motions of the Tris( 1,lO-phenanthroline) and Tris(2,2'-bipyrldine) Complexes of Ruthenium(II)and Cobalt( III ) Ions in Solution Yuichi Masuda and Hideo Yamatera*+ Department of Chemistry, Faculty of Science, Nagoya University, Chikusa-ku, Nagoya 464 Japan (Received: September 6, 1983; In Final Form: November 28, 1983)
Rotational motions of hydrophobic complex ions, [RUL,]~'in D20 and CD3OD and [CoL3I3+in D20 (L = 1,lO-phenanthroline and 2,2'-bipyridine), were investigated by the nuclear magnetic relaxation technique. The measured spin-lattice relaxation rates of the I3C nuclei of the complex ions showed that the rotational motions of the ions were nearly isotropic. Rotational correlation times, 7, at infinite dilution, measured at different temperatures showed a linear dependence on q / T (q and T being the viscosity of the solvent and the absolute temperature, respectively) in all the present cases. In the D 2 0 solutions of [ C O L ~ ] ~ ( Sand O ~ in ) ~the CD30D solutions of [RuL3]S04,the T values of the complex ions increased with increasing concentration to a greater extent than expected from the increase in the viscosity of the solutions. These increases in the T values were attributed to the formation of the 1:l ion pairs of the complex and sulfate ions. On the other hand, a similar but more remarkable increase in the 7 value of [Ru(phen),12+in DzO was attributed to the formation of aggregates containing two [Ru(phen),lZ+ions. The observed rotational correlation times (in 10-'os, at 33 "C) of the complex ions at infinite dilution ( 7 M ) , those in the ion pair with S042- (7MX), and those in the aggregate containing two complex ions (7MM) were as follows: 7 M = 1.2, TMM = 3.4 (in D@), 7 M = 0.77, 7 M X = 0.94 (in CD3OD) for [Ru(phen),]SO,; 7 M = 1.0 (in DzO), 7~ = 0.67, 7 M x = 0.96 (in CD3OD) for [R~(bpy)j],SO4; 7 M = 1.0, 7 M X = 1.2 (in DzO) for [C~(phen),l~(SO,)~; 7 M = 0.92, 7 M X = 1.1 (in D20) for [Co(bpy),I2(SO4),. Dynamic features of the ion pairs and the aggregates are discussed by comparing the observed rotational correlation times with those obtained from a hydrodynamic treatment of prolate models of the ion pairs and the aggregate.
1. Introduction The rotational motion of nlolecules or ions in solution is one of the important features ,f the dynamic structure of solutions and is often specified by the rotational correlation time, 7. The T value for the nonpolar molecule is usually treated with a hyAdjunct Professor of the Institute of Molecular Science, Okazaki, Japan (April 1981-March 1983).
drodynamic model' or a quasi-hydrodynamic model: which has been proved to predict the 7 values satisfactorily unless specific interactions exist between solute molecules or between solute and (1) Bauer, D. R.; Brauman, J. I.; Pecora, R. J . Am. Chem. SOC.1974.96, 6840. (2) Dote, J. L.; Kivelson, D.; Schwartz, R. N. J . Phys. Chem. 1981, 85, 2169.
0022-3654/84/2088-3425$01.50/00 1984 American Chemical Society
