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Mode dependence of the state-to-state vibrational dynamics of HCN–HF
Chemical Physics 239 Ž1998. 345–356
Mode dependence of the state-to-state vibrational dynamics of HCN–HF L. Oudejans, R.E. Miller
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Department of Chemistry, UniÕersity of North Carolina, Chapel Hill, NC 27599, USA Received 28 July 1998
Abstract The vibrational predissociation dynamics of HCN–HF have been studied at the state-to-state level by recording photofragment angular distributions resulting from excitation of both the C–H and H–F stretching vibrations. The results obtained from a combination of a parent molecule orientation technique and photofragment probe laser experiments show that most of the excess energy is found in rotational energy of the HF fragment. Nevertheless, in contrast with other systems studied to date, HCN–HF is very unusual in that a significant fraction of the available energy appears in the form of recoil kinetic energy Ž; 40%.. The dissociation energy of the complex is also determined to be 1970 " 10 cmy1. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction In recent years considerable progress has been made in the spectroscopic characterization of weakly bound complexes. For systems with very shallow intermolecular potentials, such as Ar–HCl w1–4x and Ar–HF w5–7x, the intermolecular vibrational spectroscopy can be quite complete, providing rather unique determinations of the corresponding attractive portion of the intermolecular potential w8–14x. For more strongly bound systems, such as hydrogenbonded complexes, there are many more bound states, many of which are spectroscopically inaccessible. Therefore, the available data sets often sample only a small portion of the potential energy surface, typically near the global minimum. Although analogous )
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to the problem of trying to determine the entire potential surface for a diatomic molecule by observing only one or two vibrational states, the situation is even more problematic due to the multidimensional nature of the surface of interest in the present context. As a result, we are a very long way from being able to provide enough spectroscopic data to enable us to determine the dissociation energy of such complexes from an extrapolation of the bound state energies to the dissociation limit. A more promising approach, that does not require a detailed characterization of all of the bound states of the system, is to study the dissociation of the complex in a way that will enable us to use conservation of energy between the parent complex and the fragments to determine the energy expended in the dissociation of the complex. This requires measuring the total energy of both the parent complex and the photofragments,
0301-0104r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 Ž 9 8 . 0 0 3 5 8 - 9
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which necessitates a detailed characterization of the associated initial and final state distributions. Data of this type are also extremely interesting so far as providing insights into the nature of the dissociation process. In the present study we consider the application of such an approach to the study of the HCN–HF complex. The hydrogen cyanide–hydrogen fluoride complex has been extensively studied using a variety of spectroscopy methods, spanning the microwave w15x, far infrared w16,17x, and mid-infrared w18–29x regions of the spectrum. All of the fundamental vibrational frequencies have been accurately determined and many vibrational hot bands and combination bands have been observed for a number of different isotopomers. In the context of the above discussion, however, only a small fraction of the intermolecular bound states of this complex have been observed. In addition to the experimental work on this complex, numerous ab initio studies w30–46x have been reported, which provide an estimate of the dissociation energy. Unfortunately, as is typical for such complexes, the binding energies Ž De . obtained from these studies vary considerably, namely from 5.5 to 9.2 kcalrmol, depending upon the basis set. As a result, these studies do not provide a definitive value. The HCN–HF complex is also one of the few complexes for which the dissociation energy Ž D 0 . has been experimentally derived. A first experimental estimate of 1580 " 90 cmy1 Ž4.52 " 0.26 kcalrmol. was derived by Legon and Millen w47x from absolute intensity measurements in the rotational spectrum, using equilibrium theory. More recently, Wofford et al. w48x obtained a somewhat higher value of 1737 " 18 cmy1 Ž4.97 " 0.05 kcalrmol. based on a similar equilibrium technique, in this case using integrated rovibrational transition intensities. The fact that the error bars for these two measurements do not overlap serves to further emphasize the difficulties associated with determining reliable dissociation energies. In the present study we use the optothermal detection method, in combination with an F-center laser, to study the vibrational predissociation of the HCN– HF complex for excitation of both the H–F and H–C stretching vibrations. From previous studies of this system it is known that the lifetimes are very different for these two initial states, namely 58 ps and 13.5 ns, respectively w23–25x. The state-to-state experi-
ments presented here provide further insights into the nature of the energy transfer processes that lead to dissociation and the source of this strong vibrational mode dependence.
2. Experimental The basic idea of the experimental approach used here is to measure the photofragment angular distribution resulting from vibrational predissociation of the HCN–HF complex. Since the translational energy release for a given final state channel, which in turn determines the laboratory scattering angle, is anti-correlated with the internal energy, data of this type can provide information on the complete photofragment distribution. Nevertheless, this requires that the structure observed in the angular distribution be assigned to specific internal photofragment states. The apparatus used in these experiments has been discussed in detail elsewhere w49,50x. An F-center laser is used to excite either the H–C or H–F stretching vibration of HCN–HF and the resulting photofragments are detected using a bolometer detector. The source can be rotated so that a complete photofragment angular distribution can be measured for a given initial state of the complex. A second F-center laser can also be used to probe the internal states of the fragments. Both laser systems are equipped with an evacuated chamber containing three confocal etalons with free spectral ranges of ´ 7.5 GHz, 750 MHz, and 150 MHz. These are used in combination with a wavemeter to monitor the tuning of the lasers. To obtain a full angular distribution, the pump laser must be kept in resonance with an HCN–HF transition for ; 30 min. This is accomplished by locking the laser to a 150 MHz Žtemperature stabilized. etalon fringe. The etalon is then ´ ´ adjusted to make the etalon fringe frequency coin´ cide with the transition frequency of interest. An angular distribution for the particular initial state of the complex is then recorded by varying the angle between the molecular beam and the line joining the photolysis volume and the detector in 0.258 increments. The detailed kinematics that relate these angular distributions to the associated kinetic energy release for a given dissociation channel have been discussed elsewhere w49,50x.
L. Oudejans, R.E. Millerr Chemical Physics 239 (1998) 345–356
As discussed in detail previously w51x, we have made extensive use of pendular state orientation Ž‘brute force’. w52,53x methods to enhance the information content in these experimental angular distributions. The basic idea is that when the parent molecule is oriented in the laboratory frame, the two fragments, in this case HCN and HF, recoil in opposite directions and can be detected separately. Since the bolometer is an energy detector, the relative signal levels depend upon the energy content of the two fragments. This information is extremely helpful in determining the internal states of the two co-fragments. Orientation of the parent complex is achieved by applying a moderate dc electric field to the photolysis region and taking advantage of the fact that the polar HCN–HF complex will tend to become oriented with the electric field. To ensure that the relative intensities of the two angular distributions are accurately determined, the intensities were compared at various angles by quickly reversing the polarity of the electric field. This essentially eliminates possible long-term signal fluctuations caused by laser power variations or changes in the bolometer sensitivity. In the present study the molecular beam was formed by expanding a mixture of 0.75% HF and 0.5% HCN in helium through a 60 mm diameter nozzle, from a source pressure of 450 kPa. The molecular beam velocity was determined using Doppler spectroscopy to be 1696 mrs.
3. Results In all of the experiments reported here, the laser electric field was aligned parallel to the static dc field, such that the relevant selection rule is D M s 0. For a linear molecule under these conditions, the electric field induced transitions appear near the vibrational band origin, as shown in Fig. 1 for the C–H stretching vibration. In this case the dipole moment changes very little upon vibrational excitation so that the pendular transitions are strongly overlapped. Fig. 2 shows an expanded view of the field-induced spectrum measured under two different experimental conditions, along with a fitted spectrum w51x obtained using the known rotational constants, vibrational band origin w25x, and vibrational ground
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Fig. 1. The pendular spectrum of HCN–HF corresponding to H–C stretch excitation in an electric field of 18.8 kVrcm. The laser electric field was aligned parallel to the static field. The zero field RŽ0. transition was used for the absolute frequency calibration of the pendular spectrum. In this case the vibrational dependence of the dipole moment is so small that the individual pendular transitions overlap, giving what appears to be a single peak near the vibrational origin.
state dipole moment of the complex Ž mY s 5.612 D. w15x. The only unknown parameters in this fit were the electric field strength and the upper state dipole moment, both of which are well determined by the fit. Indeed, the magnitude of the electric field primarily influences the absolute frequency of the lowest M s 0 transition in the pendular spectrum, while the upper state dipole moment controls the splitting between the individual pendular features. The best fit was obtained with a ŽH–C stretch. excited state dipole moment of mX s 5.649Ž5. D, which is 0.7% higher than the ground state dipole moment of 5.612 D w15x. This increase is similar to the corresponding change in the HCN monomer dipole moment upon H–C stretch vibrational excitation, namely 0.027 D w54x. The implication is clearly that the H–C stretch excitation has very little influence on the intermolecular bending vibrational motion of the complex, which we have shown in other studies to cause a significant change in the dipole moment w55,56x. The broader of the two experimental spectra in Fig. 2 was obtained under the conditions used in the photofragment experiments. The resolution in this spectrum is insufficient to separate the individual
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3.1. C–H stretch excitation
Fig. 2. An expanded view of the pendular state spectrum relative to the vibrational origin as observed ŽA. in the photofragment study and ŽB. in a separate study under higher instrumental resolution. ŽC. is a fit to the experimental spectrum using the pendular state Hamiltonian w51x.
pendular transitions, owing to the Doppler broadening associated with the spherical multipass cell w49x used in these experiments. The higher-resolution spectrum was obtained using a different experimental arrangement where the laser–molecular beam crossings are all at the same angle w55x. The relatively low resolution in the photofragment experiments, combined with the small change in the dipole moment upon vibrational excitation, makes it difficult to pump a pure M s 0 state, corresponding to the most highly oriented molecules. Because of this we found that we needed to use a slightly broader orientational distribution in analyzing the angular distributions than would be characteristic of the M s 0 state. Although the dipole moment change is considerably larger for the case of exciting the H–F stretch, the line widths are also much greater w23–25x so that a similar situation is encountered. Nevertheless, as the results presented below amply demonstrate, the orientation distributions obtained in this way are sufficient to ensure that the two co-fragments recoil in the opposite direction in the laboratory frame of reference.
We began these studies by recording an angular distribution in the absence of the electric field. As Fig. 1 shows, the RŽ0. transition associated with the C–H stretching vibration is easily resolved. The alignment generated upon excitation of this transition provides the best possible resolution in the zero electric field photofragment distributions Žassuming that dissociation occurs via axial recoil. if the laser polarization is oriented perpendicular to the molecular beam. Indeed, the excited state alignment imposed by the pump laser w50x ensures that the most probable recoil direction in the laboratory frame is orthogonal to the molecular beam, giving rise to the maximum possible laboratory frame recoil angle for a given translational energy release. As a result, fragment channels with different translational energies scatter to quite different laboratory angles. In contrast, if the laser polarization is aligned parallel to the molecular beam direction, the photofragments are preferentially ejected along the beam direction and the various final state channels all scatter near zero degrees in the laboratory frame. A detailed discussion of the theory of these zero electric field cases can be found elsewhere w50x. The angular distribution obtained by pumping the RŽ0. transition in the C–H stretching band is shown in Fig. 3. It is clear from a brief inspection of this
Fig. 3. The photofragment angular distribution for the HCN–HF complex corresponding to excitation of the RŽ0. transition of the H–C stretch band.
L. Oudejans, R.E. Millerr Chemical Physics 239 (1998) 345–356
distribution that there are a number of important final state channels with different kinetic energy releases. This is fortunate, since our goal is to assign the individual peaks in the angular distribution to specific final state channels. The more structure that is present in the angular distributions, the better are our chances of making a unique assignment. There are several problems that must be addressed if we are to explain the structure observed in this angular distribution. The goal is to determine which of the many open channels constitute the final state distribution. Fig. 4 shows an energy level diagram that illustrates the difficulty here. There are clearly many open channels, so many in fact that if all were populated statistically, we would not observe the distinct peaks evident in Fig. 3. From this we can immediately conclude that the dissociation process is non-statistical for this system, a situation that is generally encountered in the dissociation of these weakly bound systems. The assignment problem is made even more challenging given that we do not have an accurate value for the dissociation energy of this complex, so that the location of the horizontal lines in Fig. 4, which represent the available energy
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of the system upon excitation of either the H–F or C–H stretches, is not known. The final problem is that the bolometer used to measure these angular distributions is an energy detector and thus is sensitive to both the HCN and HF fragments. Thus the angular distribution shown in Fig. 3 has contributions from two fragments of different masses. Since conservation of momentum tells us that these two fragments have different recoil velocities, this angular distribution is really the superposition of two distributions, each final state channel giving rise to two peaks in the angular distribution. This makes the problem of assignment even more difficult. In what follows we will address these problems in turn. We begin with the problem of separating the angular distributions due to the HCN and HF fragments. This is done using the pendular state orientation method. As shown in Fig. 5, when the HCN–HF complex is oriented by a strong field, the HF and HCN fragments recoil towards the positive and negative electrodes, respectively. Thus by pumping the pendular state transitions discussed above, we were able to separately record angular distributions corresponding to the HF and HCN fragments. Fig. 6
Fig. 4. An energy level diagram representing the photodissociation of HCN–HF. The arrows on the left- and right-hand side of the figure indicate the total available energies upon excitation of the H–C and H–F stretch, respectively. All open rotational states of the HF fragment are depicted, upon which are built the HCN rotational states. Three sets of channels are shown corresponding to the three open vibrational states of the HCN, namely the ground state and the first and second bending excited states.
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Fig. 5. A slice through the square of the M s 0 pendular state wave function for HCN–HF at an electric field of 18.8 kVrcm. The arrows indicate the directions that the HCN and HF fragments will travel in the laboratory frame upon axial recoil dissociation.
shows a set of angular distributions obtained in this way. The structure in the angular distributions is now better resolved and each peak is due to a different set of photofragment channels. We can immediately see from the individual peak positions that the heavier
HCN fragment Žnegative angles. scatters to smaller angles than the lighter HF, confirming that the complexes are indeed oriented. The fact that we do not know the dissociation energy of this complex still makes the assignment of these peaks to specific final state channels difficult. Indeed, by varying the dissociation energy we can bring any number of channels to the correct energy to account for the peaks in the angular distribution. The next step in the process is to use the second, probe laser to determine the HF rotational state corresponding to one or more of the features in the angular distribution. To do this we first position the apparatus so that the detector observes the HF fragment. The inset in Fig. 6 shows a probe laser spectrum of the PŽ7. transition, recorded with the bolometer at 118. Although all other energetically accessible states of HF were probed, no other signals were detected at this angle. From this we can conclude that the first peak in the angular distribution corresponds to a final state channel in which the HF fragment is produced in j s 7. It now only remains
Fig. 6. The photofragment angular distributions for the oriented HCN–HF complexes, corresponding to excitation of the H–C stretch. The HF fragments scatter towards the positive electrode Žpositive angles., while the HCN fragments recoil towards the negative electrode Žnegative angles.. The inset shows the probe laser signal due to the PŽ7. transition of the HF monomer. The solid line through the experimental data is the result of a fit to the data, as described in the text. The probabilities indicated by the vertical bars represent the totals for a given rotational HF channel.
L. Oudejans, R.E. Millerr Chemical Physics 239 (1998) 345–356
to determine the rotational and vibrational state of the HCN co-fragment. It is interesting to note that in other linear complexes involving a heavy molecule and HF, such as CO 2 –HF w57x, we have shown in detail that the heavy molecule is produced with a rather cold, nearly Boltzmann distribution of rotational states. Indeed, the small rotational constant associated with this heavy fragment makes it difficult for it to carry away much of the available energy in rotation. It is also difficult to see how the heavy molecule could receive much of a torque in such a linear complex. On the other hand, the HF sub-unit undergoes rather wide amplitude bending and therefore spends much of its time in a bend geometry, where it can be torqued. Given all of this, we assume that the HCN fragment in the present system is also rotationally cold. Unfortunately, the signal levels were insufficient in these experiments to allow us to detect the HCN probe transitions. Nevertheless, the sharpness of the first peak in the angular distribution is indicative of a low HCN rotational temperature, since population of a wide range of HCN j states would tend to broaden the peaks. Given all of this evidence for low HCN rotational excitation, we proceeded to analyze the data assuming a Boltzmann distribution of HCN rotational states, the temperature of which was adjusted to reproduce the width of the peaks, as discussed in detail below. In the energy level diagram shown in Fig. 4 we have anticipated the dissociation energy that gives the best overall agreement with the present experimental results, namely 1970 cmy1 . For this value of the dissociation energy, it is clear from the figure that the only way the HF fragment could be produced in j s 7 is if the HCN fragment were in the ground vibrational state, since excitation of even the lowest bending vibration Ž011 0. puts the j s 7 state of the HF above the available energy. It is important to point out that if the dissociation energy were reduced by the HCN bending frequency Ž713 cmy1 w58x. there is a second solution that explains the data, namely with the HCN produced in the bending excited state. Nevertheless, as we will discuss in more detail somewhat later, a dissociation energy of 1970 cmy1 , although well outside the estimated errors in earlier experimental determinations w47,48x, is much more consistent with all of the available data, including the ab initio results discussed below. In addition,
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we can use the information contained in the relative signal intensities on the HCN and HF sides of the angular distributions. As noted above, the bolometer is an energy detector and fragments with more internal energy are detected with higher sensitivity. Thus the relative signal intensities for the HCN and HF fragments provide information on the relative internal energy. Once again, these data support the conclusion that the HCN is produced in the vibrational ground state. As a result, we conclude that the dissociation energy of the complex is 1970 " 10 cmy1 . The error bar on this dissociation energy is somewhat larger than we have obtained for other systems due to the fact that we have not explicitly determined the rotational distributions for the HCN fragment. Nevertheless, this is still by far the most accurate value available and certainly sufficient to compare with theoretical results. The solid lines shown in Fig. 6 represent the best fit to the experimental data. As noted above and shown in the inset, the first peak arises from HF j s 7. Probing experiments on the second peak revealed that it is due to HF j s 6. Although the third peak, as well as the weaker shoulder to its high-angle side, were too weak to perform probe laser experiments, their angular position corresponds exactly to what is expected for HF j s 5 and j s 4, again in coincidence with the ground vibrational state of the HCN fragment. Of course, these channels appear at larger angles owing to the fact that the associated internal energies are lower, meaning that their recoil translational energies are higher. The fits to the angular distributions, assuming that the HCN rotational distributions were Boltzmann, yielded HCN rotational temperatures for the HF j s 7, 6, 5, and 4 channels of 25 " 5, 140 " 10, 210 " 20, and 260 " 60 K, respectively. This systematic increase in HCN rotational excitation is certainly reasonable, given that as the recoil translational energy increases the torque on the HCN fragment is also likely to increase. Indeed, we have observed this same phenomenon for the case of CO 2 –HF w57x. From the fit to the data the relative probabilities for producing HF j s 7, 6, 5, and 4 are determined to be 0.12, 0.16, 0.40, and 0.32, respectively. These channels correspond to an averaged Žover the HCN rotational states. kinetic energy release of 179, 385, 582, and 755 cmy1 , respectively. Consequently, the
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partitioning of the available energy Ž1340 cmy1 . is between recoil translational energy Ž558 cmy1 or 42%. and rotational energy Ž782 cmy1 or 58%.. The majority of the latter corresponds to HF fragment rotation Ž652 cmy1 ., compared with 130 cmy1 in HCN rotation. It is interesting to note that, unlike several other systems we have studied where the HF was produced in only one or two rotational states w57,59x, the HF rotational distribution in this case is quite broad. At the same time the average kinetic energy release is much greater than in these other systems. 3.2. H–F stretch excitation As noted previously, spectroscopic studies of the HCN–HF complex w23–25x have shown that the vibrational predissociation is highly mode specific. In this section we consider the final state distributions for the H–F excitation. By comparing with the results given in the previous section we hope to address the question of whether or not this large difference in the rate of dissociation is due to Žor results in. dramatic differences in the final state
distributions. Our task is made considerably easier here by virtue of the fact that we already know the dissociation energy of the complex from the results in the previous section. In fact, the results discussed here provide very nice confirmation of the value determined above. Fig. 7 shows the experimental angular distribution obtained upon exciting the pendular feature associated with the H–F stretching vibration. Once again, the pendular transitions were not fully resolved so these results have contributions from some of the higher M states. Nevertheless, comparing the relative positions of the peaks in the angular distributions on the two sides confirms that the corresponding excited states are sufficiently oriented to separate the two fragments to either side of the apparatus. As shown in the energy level diagram in Fig. 4, the extra energy associated with the H–F stretch Žcompared with the C–H. results in the opening of one more HF rotational channel in the manifold of states correlated with the ground vibrational state of the HCN fragment, namely j s 8. It is interesting to note that the energy difference between the total available energy and the first open HF rotational state is larger for H–F excitation than for C–H excitation. Thus if
Fig. 7. Photofragment angular distributions corresponding to excitation of the H–F stretch. The solid line through the experimental data is the result of the fit described in the text. The probabilities indicated by the vertical bars represent the totals for a given rotational HF channel.
L. Oudejans, R.E. Millerr Chemical Physics 239 (1998) 345–356
we assume the HCN is produced again in low rotational states, the recoil energy for the first channel in the former case will be greater than in the latter. As a result, one would expect the first peak to occur at slightly larger angles for H–F excitation, compared with C–H excitation, which is precisely what is observed. In fact, the peaks in the angular distributions shown in Fig. 7 are separated in angle by just the right amount to be accounted for by the energy difference between the HF j s 8 and j s 7 states. Somewhat weaker peaks are also observed that can be attributed to HF j s 6 and j s 5. The solid lines in the figure correspond to the best fit to the experimental data. In this case the dissociation energy was held fixed at the value of 1970 cmy1 determined above. Once again, the HCN rotational distribution was assumed to be Boltzmann, yielding temperatures of 70 " 10, 110 " 20, 250 " 50, and 300 " 100 K for the j s 8, 7, 6, and 5, respectively. The corresponding dissociation probabilities for these four channels are 0.33, 0.30, 0.17, and 0.20, respectively. The fact that this distribution is well fit using the same dissociation energy is again consistent with the HCN fragment being rotationally cold and gives additional support for the present assignments. These channels correspond to an averaged Žover the HCN rotational distribution. kinetic energy release of 229, 526, 718, and 931 cmy1 for the j s 8, 7, 6, and 5 channels, respectively. These probabilities can be used to calculate the overall average kinetic energy release, namely 545 cmy1 or 31% of the total available energy of 1746 cmy1 . The average energy in HF rotation is 1093 cmy1 , while 108 cmy1 appears in HCN rotation. As in the case of H–C stretch excitation, the kinetic energy release is much greater than for other systems we have studied w57,59x.
4. Discussion In the previous sections we have presented data that give a rather complete picture of the state-to-state photodissociation dynamics of the HCN–HF complex resulting from excitation of the C–H and H–F stretching vibrations. Although the rates for dissociation from these two states differ by orders of magnitude, we find that the final state distributions are
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basically the same, namely the majority of the excess energy appearing as HF rotation ŽV-R.. The only real difference is that, due to the somewhat greater available energy for HF excitation, compared to C–H excitation, the HF distribution is shifted up one in j. It is interesting to note that although the complex could have chosen to dissociate into lower rotational states of the HF, by populating the HCN bending excited state, there is no evidence for these channels. This system clearly finds it easier to torque the HF fragment than to bend the HCN. This is perhaps not surprising, in retrospect at least, given that the hydrogen bond is highly anisotropic, while the linear nature of the complex makes it quite difficult to bend the HCN molecule. It is interesting to note that the average translational energy is somewhat lower for the case of HF excitation, compared with CH excitation. Since the translational excitation is generally inhibited by the poor Franck–Condon overlap between the corresponding bound and continuum states, this could account for some of the difference in lifetime. Related to this is the fact that the probability of populating this first open channel is higher for the H–F case Žthe first channel corresponding to j s 8. than for C–H Žwhere the first open channel is j s 7.. One simple explanation for this might be that the energy gap between HF rotor states is increasing with j so that the j s 8 level is more isolated than j s 7, the result being that in the former case the j s 8 level is more preferred. It is worth mentioning again that the HF rotational selectivity observed in this system is much lower than in some others we have studied w57,59x. In general we find that in the limit where the available energy is higher, such that the HF is produced in even higher rotational states Žas high as j s 12., dissociation results in the production of only a single HF rotational state for each vibrational channel of the co-fragment w57,59x. It appears, therefore, that the HCN–HF complex is in the intermediate regime, where the available energy is small enough Ždue to its very large dissociation energy. so that only moderate values of j HF are populated and at the same time the anisotropy of the potential is sufficiently large to populate a number of final states. The selective dissociation into the ground state of the HCN fragments seems to be a result of steric considerations, namely reflecting the fact that from a linear
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geometry the HCN fragment is difficult to bend. At higher available energies, where the parallel HCN stretching vibrational channels open, one might expect to see intermolecular vibrational energy transfer from the HF to the HCN. We have indeed observed such energy transfer in systems such as CO 2 –HF w57x.
5. Comparison of dissociation energy with ab initio calculations The dissociation energy of the HCN–HF complex has been determined in the present study to be 5.63 " 0.03 kcalrmol Ž1970 " 10 cmy1 .. This value can be compared with the large number of earlier studies, including ab initio w30–46x and semi-empirical w42,44x calculations, as well as experimental determinations w47,48x. Consider first the two experimental determinations of D 0 , namely 4.52 " 0.26 kcalrmol Ž1580 " 90 cmy1 . w47x and 4.97 " 0.05 kcalrmol Ž1737 " 18 cmy1 . w48x, both from equilibrium transition intensity measurements. Not only do these measurements not agree with the present determination within the error bars, but they also do not agree with one another. This is in comparison with the HF dimer case, where our value w49x agrees within the experimental uncertainty imposed by similar transition intensity measurements w60x. We conclude that the error bars on the previous measurements are much too small. Indeed, we attempted to fit the present angular distributions using these values, with no success. As noted above, the ab initio calculated hydrogen binding energies Ž De . vary between 5.5 and 9.2 kcalrmol Ž1924 and 3218 cmy1 .. Unfortunately, most of these calculations were done with small basis sets using methods that do not include correlation energy. As a result, we only compare the present result with the most recent MP2 calculations by Bevan and co-workers w42x. They performed several ab initio calculations which include the correction for the basis set superposition error ŽBSSE.. An adiabatic MP2 calculation yielded a De of 7.34 kcalrmol Ž2567 cmy1 . which, after correction for the zero-point energy, gave a dissociation energy of 5.39 kcalrmol Ž1883 cmy1 ., in reasonable agreement with the present value. Nevertheless, other
calculations reported in the same paper gave values spanning a wide range, covering the other experimental values quoted above. Therefore, the most we can say is that ab initio calculations can be found that are consistent with the present D 0 . It is interesting that the semi-empirical potential of McIntosh et al. w44x which was fit to a large set of intermolecular vibrations yielded a dissociation energy Ž D 0 . of 2037 cmy1 . Given that this potential gives excellent agreement for all 9 vibrational modes included in the fit at least shows that a potential with the D 0 determined here is consistent with the vibrational spectroscopy.
6. Conclusions We have presented the complete final state distributions for the vibrational predissociation of the HCN–HF complex following excitation of the H–C stretch and H–F stretch. The results show that the dissociation proceeds primarily by a V-R process, resulting in the majority of the available energy appearing as HF rotation. There is no evidence for V-V transfer into HCN vibrational bending modes, which is perhaps not surprising considering the linearity of the complex. The dissociation energy of this complex is determined by conservation of energy to be 1970 " 10 cmy1 . What is perhaps most surprising about this study is the similarity of the final state distributions resulting from C–H and H–F stretch excitation, given the dramatic difference in the associated predissociation lifetimes. From this we conclude that this large difference is primarily the result of the dramatic difference in the coupling strength between the intramolecular stretching vibration and the weak bond, rather than because of some form of resonance in the latter case Žwhich is clearly not present.. This enhanced coupling for the HF stretch is, of course, expected given that the latter is directly coupled to the dissociation coordinate. The most anomalous feature of the dissociation dynamics of this complex is the large fraction of the available energy that appears in product translation, accounting for the fact that the angular distributions extend to rather large angles. Presumably this has something to do with the extreme strong bonding in this system. Given the strong mode dependence of the vibrational
L. Oudejans, R.E. Millerr Chemical Physics 239 (1998) 345–356
predissociation lifetimes and this kinetic energy anomaly, this system is clearly deserving of further theoretical study. A more thorough understanding of the unique aspects of the dissociation dynamics of this system would clearly be extremely useful in obtaining better overall insights into these processes.
Acknowledgements This work was supported by the National Science Foundation ŽCHE-97-10026.. We also acknowledge the donors of The Petroleum Research Fund, administered by the ACS, for partial support of this research.
References w1x M.D. Marshall, A. Charo, H.O. Leung, W. Klemperer, J. Chem. Phys. 83 Ž1985. 4924. w2x B.J. Howard, A.S. Pine, Chem. Phys. Lett. 122 Ž1985. 1. w3x D. Ray, R.L. Robinson, D.-H. Gwo, R.J. Saykally, J. Chem. Phys. 84 Ž1986. 1171. w4x C.M. Lovejoy, D.J. Nesbitt, Chem. Phys. Lett. 146 Ž1988. 582. w5x G.T. Fraser, A.S. Pine, J. Chem. Phys. 85 Ž1986. 2502. w6x C.M. Lovejoy, M.D. Schuder, D.J. Nesbitt, J. Chem. Phys. 85 Ž1986. 4890. w7x C.M. Lovejoy, D.J. Nesbitt, J. Chem. Phys. 91 Ž1989. 2790. w8x J.M. Hutson, Annu. Rev. Phys. Chem. 41 Ž1990. 123. w9x J.M. Hutson, J. Chem. Phys. 89 Ž1988. 4550. w10x J.M. Hutson, J. Phys. Chem. 96 Ž1992. 4237. w11x J.M. Hutson, J. Chem. Phys. 96 Ž1992. 6752. w12x R.C. Cohen, R.J. Saykally, Annu. Rev. Phys. Chem. 42 Ž1991. 369. w13x R.C. Cohen, R.J. Saykally, J. Phys. Chem. 96 Ž1992. 1024. w14x R.C. Cohen, R.J. Saykally, J. Chem. Phys. 98 Ž1993. 6007. w15x A.C. Legon, D.J. Millen, S.C. Rogers, Proc. R. Soc. London, Ser. A 370 Ž1980. 213. w16x B.A. Wofford, R.S. Ram, A. Quinones, J.W. Bevan, W.B. ˜ Olson, W.J. Lafferty, Chem. Phys. Lett. 152 Ž1988. 299. w17x A.L. McIntosh, A.M. Gallegos, R.R. Lucchese, J.W. Bevan, J. Mol. Struct. 413,414 Ž1997. 167. w18x E.K. Kyro, ¨ R. Warren, K. McMillan, M. Eliades, D.A. Danzeiser, P. Shoja-Chaghervand, S.G. Lieb, J.W. Bevan, J. Chem. Phys. 78 Ž1983. 5881. w19x B.A. Wofford, J.W. Bevan, W.B. Olson, W.J. Lafferty, J. Chem. Phys. 83 Ž1985. 6188. w20x E.K. Kyro, ¨ M. Eliades, A.M. Gallegos, P. Shoja-Chaghervand, J.W. Bevan, AIP ŽAm. Inst. Phys.. Conf. Proc. 146 Ž1986. 474.
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w53x J.M. Rost, J.C. Griffin, B. Friedrich, D.R. Herschbach, Phys. Rev. Lett. 68 Ž1992. 1299. w54x T.E. Gough, R.E. Miller, G. Scoles, Faraday Discuss. Chem. Soc. 71 Ž1981. 77. w55x Z.S. Huang, K.W. Jucks, R.E. Miller, J. Chem. Phys. 85 Ž1986. 6905. w56x L. Oudejans, K. Nauta, R.E. Miller, J. Chem. Phys. 105 Ž1996. 10410.
w57x L. Oudejans, R.E. Miller, J. Chem. Phys. 109 Ž1998. 3474. w58x A.M. Smith, S.L. Coy, W. Klemperer, K.K. Lehmann, J. Mol. Spectrosc. 134 Ž1989. 134. w59x R.J. Bemish, E.J. Bohac, M. Wu, R.E. Miller, J. Chem. Phys. 101 Ž1994. 9457. w60x A.S. Pine, B.J. Howard, J. Chem. Phys. 84 Ž1986. 590.
Mode dependence of the state-to-state vibrational dynamics of HCN–HF L. Oudejans, R.E. Miller
)
Department of Chemistry, UniÕersity of North Carolina, Chapel Hill, NC 27599, USA Received 28 July 1998
Abstract The vibrational predissociation dynamics of HCN–HF have been studied at the state-to-state level by recording photofragment angular distributions resulting from excitation of both the C–H and H–F stretching vibrations. The results obtained from a combination of a parent molecule orientation technique and photofragment probe laser experiments show that most of the excess energy is found in rotational energy of the HF fragment. Nevertheless, in contrast with other systems studied to date, HCN–HF is very unusual in that a significant fraction of the available energy appears in the form of recoil kinetic energy Ž; 40%.. The dissociation energy of the complex is also determined to be 1970 " 10 cmy1. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction In recent years considerable progress has been made in the spectroscopic characterization of weakly bound complexes. For systems with very shallow intermolecular potentials, such as Ar–HCl w1–4x and Ar–HF w5–7x, the intermolecular vibrational spectroscopy can be quite complete, providing rather unique determinations of the corresponding attractive portion of the intermolecular potential w8–14x. For more strongly bound systems, such as hydrogenbonded complexes, there are many more bound states, many of which are spectroscopically inaccessible. Therefore, the available data sets often sample only a small portion of the potential energy surface, typically near the global minimum. Although analogous )
Corresponding author. Fax: q1-919-962-2388.
to the problem of trying to determine the entire potential surface for a diatomic molecule by observing only one or two vibrational states, the situation is even more problematic due to the multidimensional nature of the surface of interest in the present context. As a result, we are a very long way from being able to provide enough spectroscopic data to enable us to determine the dissociation energy of such complexes from an extrapolation of the bound state energies to the dissociation limit. A more promising approach, that does not require a detailed characterization of all of the bound states of the system, is to study the dissociation of the complex in a way that will enable us to use conservation of energy between the parent complex and the fragments to determine the energy expended in the dissociation of the complex. This requires measuring the total energy of both the parent complex and the photofragments,
0301-0104r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 Ž 9 8 . 0 0 3 5 8 - 9
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which necessitates a detailed characterization of the associated initial and final state distributions. Data of this type are also extremely interesting so far as providing insights into the nature of the dissociation process. In the present study we consider the application of such an approach to the study of the HCN–HF complex. The hydrogen cyanide–hydrogen fluoride complex has been extensively studied using a variety of spectroscopy methods, spanning the microwave w15x, far infrared w16,17x, and mid-infrared w18–29x regions of the spectrum. All of the fundamental vibrational frequencies have been accurately determined and many vibrational hot bands and combination bands have been observed for a number of different isotopomers. In the context of the above discussion, however, only a small fraction of the intermolecular bound states of this complex have been observed. In addition to the experimental work on this complex, numerous ab initio studies w30–46x have been reported, which provide an estimate of the dissociation energy. Unfortunately, as is typical for such complexes, the binding energies Ž De . obtained from these studies vary considerably, namely from 5.5 to 9.2 kcalrmol, depending upon the basis set. As a result, these studies do not provide a definitive value. The HCN–HF complex is also one of the few complexes for which the dissociation energy Ž D 0 . has been experimentally derived. A first experimental estimate of 1580 " 90 cmy1 Ž4.52 " 0.26 kcalrmol. was derived by Legon and Millen w47x from absolute intensity measurements in the rotational spectrum, using equilibrium theory. More recently, Wofford et al. w48x obtained a somewhat higher value of 1737 " 18 cmy1 Ž4.97 " 0.05 kcalrmol. based on a similar equilibrium technique, in this case using integrated rovibrational transition intensities. The fact that the error bars for these two measurements do not overlap serves to further emphasize the difficulties associated with determining reliable dissociation energies. In the present study we use the optothermal detection method, in combination with an F-center laser, to study the vibrational predissociation of the HCN– HF complex for excitation of both the H–F and H–C stretching vibrations. From previous studies of this system it is known that the lifetimes are very different for these two initial states, namely 58 ps and 13.5 ns, respectively w23–25x. The state-to-state experi-
ments presented here provide further insights into the nature of the energy transfer processes that lead to dissociation and the source of this strong vibrational mode dependence.
2. Experimental The basic idea of the experimental approach used here is to measure the photofragment angular distribution resulting from vibrational predissociation of the HCN–HF complex. Since the translational energy release for a given final state channel, which in turn determines the laboratory scattering angle, is anti-correlated with the internal energy, data of this type can provide information on the complete photofragment distribution. Nevertheless, this requires that the structure observed in the angular distribution be assigned to specific internal photofragment states. The apparatus used in these experiments has been discussed in detail elsewhere w49,50x. An F-center laser is used to excite either the H–C or H–F stretching vibration of HCN–HF and the resulting photofragments are detected using a bolometer detector. The source can be rotated so that a complete photofragment angular distribution can be measured for a given initial state of the complex. A second F-center laser can also be used to probe the internal states of the fragments. Both laser systems are equipped with an evacuated chamber containing three confocal etalons with free spectral ranges of ´ 7.5 GHz, 750 MHz, and 150 MHz. These are used in combination with a wavemeter to monitor the tuning of the lasers. To obtain a full angular distribution, the pump laser must be kept in resonance with an HCN–HF transition for ; 30 min. This is accomplished by locking the laser to a 150 MHz Žtemperature stabilized. etalon fringe. The etalon is then ´ ´ adjusted to make the etalon fringe frequency coin´ cide with the transition frequency of interest. An angular distribution for the particular initial state of the complex is then recorded by varying the angle between the molecular beam and the line joining the photolysis volume and the detector in 0.258 increments. The detailed kinematics that relate these angular distributions to the associated kinetic energy release for a given dissociation channel have been discussed elsewhere w49,50x.
L. Oudejans, R.E. Millerr Chemical Physics 239 (1998) 345–356
As discussed in detail previously w51x, we have made extensive use of pendular state orientation Ž‘brute force’. w52,53x methods to enhance the information content in these experimental angular distributions. The basic idea is that when the parent molecule is oriented in the laboratory frame, the two fragments, in this case HCN and HF, recoil in opposite directions and can be detected separately. Since the bolometer is an energy detector, the relative signal levels depend upon the energy content of the two fragments. This information is extremely helpful in determining the internal states of the two co-fragments. Orientation of the parent complex is achieved by applying a moderate dc electric field to the photolysis region and taking advantage of the fact that the polar HCN–HF complex will tend to become oriented with the electric field. To ensure that the relative intensities of the two angular distributions are accurately determined, the intensities were compared at various angles by quickly reversing the polarity of the electric field. This essentially eliminates possible long-term signal fluctuations caused by laser power variations or changes in the bolometer sensitivity. In the present study the molecular beam was formed by expanding a mixture of 0.75% HF and 0.5% HCN in helium through a 60 mm diameter nozzle, from a source pressure of 450 kPa. The molecular beam velocity was determined using Doppler spectroscopy to be 1696 mrs.
3. Results In all of the experiments reported here, the laser electric field was aligned parallel to the static dc field, such that the relevant selection rule is D M s 0. For a linear molecule under these conditions, the electric field induced transitions appear near the vibrational band origin, as shown in Fig. 1 for the C–H stretching vibration. In this case the dipole moment changes very little upon vibrational excitation so that the pendular transitions are strongly overlapped. Fig. 2 shows an expanded view of the field-induced spectrum measured under two different experimental conditions, along with a fitted spectrum w51x obtained using the known rotational constants, vibrational band origin w25x, and vibrational ground
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Fig. 1. The pendular spectrum of HCN–HF corresponding to H–C stretch excitation in an electric field of 18.8 kVrcm. The laser electric field was aligned parallel to the static field. The zero field RŽ0. transition was used for the absolute frequency calibration of the pendular spectrum. In this case the vibrational dependence of the dipole moment is so small that the individual pendular transitions overlap, giving what appears to be a single peak near the vibrational origin.
state dipole moment of the complex Ž mY s 5.612 D. w15x. The only unknown parameters in this fit were the electric field strength and the upper state dipole moment, both of which are well determined by the fit. Indeed, the magnitude of the electric field primarily influences the absolute frequency of the lowest M s 0 transition in the pendular spectrum, while the upper state dipole moment controls the splitting between the individual pendular features. The best fit was obtained with a ŽH–C stretch. excited state dipole moment of mX s 5.649Ž5. D, which is 0.7% higher than the ground state dipole moment of 5.612 D w15x. This increase is similar to the corresponding change in the HCN monomer dipole moment upon H–C stretch vibrational excitation, namely 0.027 D w54x. The implication is clearly that the H–C stretch excitation has very little influence on the intermolecular bending vibrational motion of the complex, which we have shown in other studies to cause a significant change in the dipole moment w55,56x. The broader of the two experimental spectra in Fig. 2 was obtained under the conditions used in the photofragment experiments. The resolution in this spectrum is insufficient to separate the individual
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3.1. C–H stretch excitation
Fig. 2. An expanded view of the pendular state spectrum relative to the vibrational origin as observed ŽA. in the photofragment study and ŽB. in a separate study under higher instrumental resolution. ŽC. is a fit to the experimental spectrum using the pendular state Hamiltonian w51x.
pendular transitions, owing to the Doppler broadening associated with the spherical multipass cell w49x used in these experiments. The higher-resolution spectrum was obtained using a different experimental arrangement where the laser–molecular beam crossings are all at the same angle w55x. The relatively low resolution in the photofragment experiments, combined with the small change in the dipole moment upon vibrational excitation, makes it difficult to pump a pure M s 0 state, corresponding to the most highly oriented molecules. Because of this we found that we needed to use a slightly broader orientational distribution in analyzing the angular distributions than would be characteristic of the M s 0 state. Although the dipole moment change is considerably larger for the case of exciting the H–F stretch, the line widths are also much greater w23–25x so that a similar situation is encountered. Nevertheless, as the results presented below amply demonstrate, the orientation distributions obtained in this way are sufficient to ensure that the two co-fragments recoil in the opposite direction in the laboratory frame of reference.
We began these studies by recording an angular distribution in the absence of the electric field. As Fig. 1 shows, the RŽ0. transition associated with the C–H stretching vibration is easily resolved. The alignment generated upon excitation of this transition provides the best possible resolution in the zero electric field photofragment distributions Žassuming that dissociation occurs via axial recoil. if the laser polarization is oriented perpendicular to the molecular beam. Indeed, the excited state alignment imposed by the pump laser w50x ensures that the most probable recoil direction in the laboratory frame is orthogonal to the molecular beam, giving rise to the maximum possible laboratory frame recoil angle for a given translational energy release. As a result, fragment channels with different translational energies scatter to quite different laboratory angles. In contrast, if the laser polarization is aligned parallel to the molecular beam direction, the photofragments are preferentially ejected along the beam direction and the various final state channels all scatter near zero degrees in the laboratory frame. A detailed discussion of the theory of these zero electric field cases can be found elsewhere w50x. The angular distribution obtained by pumping the RŽ0. transition in the C–H stretching band is shown in Fig. 3. It is clear from a brief inspection of this
Fig. 3. The photofragment angular distribution for the HCN–HF complex corresponding to excitation of the RŽ0. transition of the H–C stretch band.
L. Oudejans, R.E. Millerr Chemical Physics 239 (1998) 345–356
distribution that there are a number of important final state channels with different kinetic energy releases. This is fortunate, since our goal is to assign the individual peaks in the angular distribution to specific final state channels. The more structure that is present in the angular distributions, the better are our chances of making a unique assignment. There are several problems that must be addressed if we are to explain the structure observed in this angular distribution. The goal is to determine which of the many open channels constitute the final state distribution. Fig. 4 shows an energy level diagram that illustrates the difficulty here. There are clearly many open channels, so many in fact that if all were populated statistically, we would not observe the distinct peaks evident in Fig. 3. From this we can immediately conclude that the dissociation process is non-statistical for this system, a situation that is generally encountered in the dissociation of these weakly bound systems. The assignment problem is made even more challenging given that we do not have an accurate value for the dissociation energy of this complex, so that the location of the horizontal lines in Fig. 4, which represent the available energy
349
of the system upon excitation of either the H–F or C–H stretches, is not known. The final problem is that the bolometer used to measure these angular distributions is an energy detector and thus is sensitive to both the HCN and HF fragments. Thus the angular distribution shown in Fig. 3 has contributions from two fragments of different masses. Since conservation of momentum tells us that these two fragments have different recoil velocities, this angular distribution is really the superposition of two distributions, each final state channel giving rise to two peaks in the angular distribution. This makes the problem of assignment even more difficult. In what follows we will address these problems in turn. We begin with the problem of separating the angular distributions due to the HCN and HF fragments. This is done using the pendular state orientation method. As shown in Fig. 5, when the HCN–HF complex is oriented by a strong field, the HF and HCN fragments recoil towards the positive and negative electrodes, respectively. Thus by pumping the pendular state transitions discussed above, we were able to separately record angular distributions corresponding to the HF and HCN fragments. Fig. 6
Fig. 4. An energy level diagram representing the photodissociation of HCN–HF. The arrows on the left- and right-hand side of the figure indicate the total available energies upon excitation of the H–C and H–F stretch, respectively. All open rotational states of the HF fragment are depicted, upon which are built the HCN rotational states. Three sets of channels are shown corresponding to the three open vibrational states of the HCN, namely the ground state and the first and second bending excited states.
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Fig. 5. A slice through the square of the M s 0 pendular state wave function for HCN–HF at an electric field of 18.8 kVrcm. The arrows indicate the directions that the HCN and HF fragments will travel in the laboratory frame upon axial recoil dissociation.
shows a set of angular distributions obtained in this way. The structure in the angular distributions is now better resolved and each peak is due to a different set of photofragment channels. We can immediately see from the individual peak positions that the heavier
HCN fragment Žnegative angles. scatters to smaller angles than the lighter HF, confirming that the complexes are indeed oriented. The fact that we do not know the dissociation energy of this complex still makes the assignment of these peaks to specific final state channels difficult. Indeed, by varying the dissociation energy we can bring any number of channels to the correct energy to account for the peaks in the angular distribution. The next step in the process is to use the second, probe laser to determine the HF rotational state corresponding to one or more of the features in the angular distribution. To do this we first position the apparatus so that the detector observes the HF fragment. The inset in Fig. 6 shows a probe laser spectrum of the PŽ7. transition, recorded with the bolometer at 118. Although all other energetically accessible states of HF were probed, no other signals were detected at this angle. From this we can conclude that the first peak in the angular distribution corresponds to a final state channel in which the HF fragment is produced in j s 7. It now only remains
Fig. 6. The photofragment angular distributions for the oriented HCN–HF complexes, corresponding to excitation of the H–C stretch. The HF fragments scatter towards the positive electrode Žpositive angles., while the HCN fragments recoil towards the negative electrode Žnegative angles.. The inset shows the probe laser signal due to the PŽ7. transition of the HF monomer. The solid line through the experimental data is the result of a fit to the data, as described in the text. The probabilities indicated by the vertical bars represent the totals for a given rotational HF channel.
L. Oudejans, R.E. Millerr Chemical Physics 239 (1998) 345–356
to determine the rotational and vibrational state of the HCN co-fragment. It is interesting to note that in other linear complexes involving a heavy molecule and HF, such as CO 2 –HF w57x, we have shown in detail that the heavy molecule is produced with a rather cold, nearly Boltzmann distribution of rotational states. Indeed, the small rotational constant associated with this heavy fragment makes it difficult for it to carry away much of the available energy in rotation. It is also difficult to see how the heavy molecule could receive much of a torque in such a linear complex. On the other hand, the HF sub-unit undergoes rather wide amplitude bending and therefore spends much of its time in a bend geometry, where it can be torqued. Given all of this, we assume that the HCN fragment in the present system is also rotationally cold. Unfortunately, the signal levels were insufficient in these experiments to allow us to detect the HCN probe transitions. Nevertheless, the sharpness of the first peak in the angular distribution is indicative of a low HCN rotational temperature, since population of a wide range of HCN j states would tend to broaden the peaks. Given all of this evidence for low HCN rotational excitation, we proceeded to analyze the data assuming a Boltzmann distribution of HCN rotational states, the temperature of which was adjusted to reproduce the width of the peaks, as discussed in detail below. In the energy level diagram shown in Fig. 4 we have anticipated the dissociation energy that gives the best overall agreement with the present experimental results, namely 1970 cmy1 . For this value of the dissociation energy, it is clear from the figure that the only way the HF fragment could be produced in j s 7 is if the HCN fragment were in the ground vibrational state, since excitation of even the lowest bending vibration Ž011 0. puts the j s 7 state of the HF above the available energy. It is important to point out that if the dissociation energy were reduced by the HCN bending frequency Ž713 cmy1 w58x. there is a second solution that explains the data, namely with the HCN produced in the bending excited state. Nevertheless, as we will discuss in more detail somewhat later, a dissociation energy of 1970 cmy1 , although well outside the estimated errors in earlier experimental determinations w47,48x, is much more consistent with all of the available data, including the ab initio results discussed below. In addition,
351
we can use the information contained in the relative signal intensities on the HCN and HF sides of the angular distributions. As noted above, the bolometer is an energy detector and fragments with more internal energy are detected with higher sensitivity. Thus the relative signal intensities for the HCN and HF fragments provide information on the relative internal energy. Once again, these data support the conclusion that the HCN is produced in the vibrational ground state. As a result, we conclude that the dissociation energy of the complex is 1970 " 10 cmy1 . The error bar on this dissociation energy is somewhat larger than we have obtained for other systems due to the fact that we have not explicitly determined the rotational distributions for the HCN fragment. Nevertheless, this is still by far the most accurate value available and certainly sufficient to compare with theoretical results. The solid lines shown in Fig. 6 represent the best fit to the experimental data. As noted above and shown in the inset, the first peak arises from HF j s 7. Probing experiments on the second peak revealed that it is due to HF j s 6. Although the third peak, as well as the weaker shoulder to its high-angle side, were too weak to perform probe laser experiments, their angular position corresponds exactly to what is expected for HF j s 5 and j s 4, again in coincidence with the ground vibrational state of the HCN fragment. Of course, these channels appear at larger angles owing to the fact that the associated internal energies are lower, meaning that their recoil translational energies are higher. The fits to the angular distributions, assuming that the HCN rotational distributions were Boltzmann, yielded HCN rotational temperatures for the HF j s 7, 6, 5, and 4 channels of 25 " 5, 140 " 10, 210 " 20, and 260 " 60 K, respectively. This systematic increase in HCN rotational excitation is certainly reasonable, given that as the recoil translational energy increases the torque on the HCN fragment is also likely to increase. Indeed, we have observed this same phenomenon for the case of CO 2 –HF w57x. From the fit to the data the relative probabilities for producing HF j s 7, 6, 5, and 4 are determined to be 0.12, 0.16, 0.40, and 0.32, respectively. These channels correspond to an averaged Žover the HCN rotational states. kinetic energy release of 179, 385, 582, and 755 cmy1 , respectively. Consequently, the
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partitioning of the available energy Ž1340 cmy1 . is between recoil translational energy Ž558 cmy1 or 42%. and rotational energy Ž782 cmy1 or 58%.. The majority of the latter corresponds to HF fragment rotation Ž652 cmy1 ., compared with 130 cmy1 in HCN rotation. It is interesting to note that, unlike several other systems we have studied where the HF was produced in only one or two rotational states w57,59x, the HF rotational distribution in this case is quite broad. At the same time the average kinetic energy release is much greater than in these other systems. 3.2. H–F stretch excitation As noted previously, spectroscopic studies of the HCN–HF complex w23–25x have shown that the vibrational predissociation is highly mode specific. In this section we consider the final state distributions for the H–F excitation. By comparing with the results given in the previous section we hope to address the question of whether or not this large difference in the rate of dissociation is due to Žor results in. dramatic differences in the final state
distributions. Our task is made considerably easier here by virtue of the fact that we already know the dissociation energy of the complex from the results in the previous section. In fact, the results discussed here provide very nice confirmation of the value determined above. Fig. 7 shows the experimental angular distribution obtained upon exciting the pendular feature associated with the H–F stretching vibration. Once again, the pendular transitions were not fully resolved so these results have contributions from some of the higher M states. Nevertheless, comparing the relative positions of the peaks in the angular distributions on the two sides confirms that the corresponding excited states are sufficiently oriented to separate the two fragments to either side of the apparatus. As shown in the energy level diagram in Fig. 4, the extra energy associated with the H–F stretch Žcompared with the C–H. results in the opening of one more HF rotational channel in the manifold of states correlated with the ground vibrational state of the HCN fragment, namely j s 8. It is interesting to note that the energy difference between the total available energy and the first open HF rotational state is larger for H–F excitation than for C–H excitation. Thus if
Fig. 7. Photofragment angular distributions corresponding to excitation of the H–F stretch. The solid line through the experimental data is the result of the fit described in the text. The probabilities indicated by the vertical bars represent the totals for a given rotational HF channel.
L. Oudejans, R.E. Millerr Chemical Physics 239 (1998) 345–356
we assume the HCN is produced again in low rotational states, the recoil energy for the first channel in the former case will be greater than in the latter. As a result, one would expect the first peak to occur at slightly larger angles for H–F excitation, compared with C–H excitation, which is precisely what is observed. In fact, the peaks in the angular distributions shown in Fig. 7 are separated in angle by just the right amount to be accounted for by the energy difference between the HF j s 8 and j s 7 states. Somewhat weaker peaks are also observed that can be attributed to HF j s 6 and j s 5. The solid lines in the figure correspond to the best fit to the experimental data. In this case the dissociation energy was held fixed at the value of 1970 cmy1 determined above. Once again, the HCN rotational distribution was assumed to be Boltzmann, yielding temperatures of 70 " 10, 110 " 20, 250 " 50, and 300 " 100 K for the j s 8, 7, 6, and 5, respectively. The corresponding dissociation probabilities for these four channels are 0.33, 0.30, 0.17, and 0.20, respectively. The fact that this distribution is well fit using the same dissociation energy is again consistent with the HCN fragment being rotationally cold and gives additional support for the present assignments. These channels correspond to an averaged Žover the HCN rotational distribution. kinetic energy release of 229, 526, 718, and 931 cmy1 for the j s 8, 7, 6, and 5 channels, respectively. These probabilities can be used to calculate the overall average kinetic energy release, namely 545 cmy1 or 31% of the total available energy of 1746 cmy1 . The average energy in HF rotation is 1093 cmy1 , while 108 cmy1 appears in HCN rotation. As in the case of H–C stretch excitation, the kinetic energy release is much greater than for other systems we have studied w57,59x.
4. Discussion In the previous sections we have presented data that give a rather complete picture of the state-to-state photodissociation dynamics of the HCN–HF complex resulting from excitation of the C–H and H–F stretching vibrations. Although the rates for dissociation from these two states differ by orders of magnitude, we find that the final state distributions are
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basically the same, namely the majority of the excess energy appearing as HF rotation ŽV-R.. The only real difference is that, due to the somewhat greater available energy for HF excitation, compared to C–H excitation, the HF distribution is shifted up one in j. It is interesting to note that although the complex could have chosen to dissociate into lower rotational states of the HF, by populating the HCN bending excited state, there is no evidence for these channels. This system clearly finds it easier to torque the HF fragment than to bend the HCN. This is perhaps not surprising, in retrospect at least, given that the hydrogen bond is highly anisotropic, while the linear nature of the complex makes it quite difficult to bend the HCN molecule. It is interesting to note that the average translational energy is somewhat lower for the case of HF excitation, compared with CH excitation. Since the translational excitation is generally inhibited by the poor Franck–Condon overlap between the corresponding bound and continuum states, this could account for some of the difference in lifetime. Related to this is the fact that the probability of populating this first open channel is higher for the H–F case Žthe first channel corresponding to j s 8. than for C–H Žwhere the first open channel is j s 7.. One simple explanation for this might be that the energy gap between HF rotor states is increasing with j so that the j s 8 level is more isolated than j s 7, the result being that in the former case the j s 8 level is more preferred. It is worth mentioning again that the HF rotational selectivity observed in this system is much lower than in some others we have studied w57,59x. In general we find that in the limit where the available energy is higher, such that the HF is produced in even higher rotational states Žas high as j s 12., dissociation results in the production of only a single HF rotational state for each vibrational channel of the co-fragment w57,59x. It appears, therefore, that the HCN–HF complex is in the intermediate regime, where the available energy is small enough Ždue to its very large dissociation energy. so that only moderate values of j HF are populated and at the same time the anisotropy of the potential is sufficiently large to populate a number of final states. The selective dissociation into the ground state of the HCN fragments seems to be a result of steric considerations, namely reflecting the fact that from a linear
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geometry the HCN fragment is difficult to bend. At higher available energies, where the parallel HCN stretching vibrational channels open, one might expect to see intermolecular vibrational energy transfer from the HF to the HCN. We have indeed observed such energy transfer in systems such as CO 2 –HF w57x.
5. Comparison of dissociation energy with ab initio calculations The dissociation energy of the HCN–HF complex has been determined in the present study to be 5.63 " 0.03 kcalrmol Ž1970 " 10 cmy1 .. This value can be compared with the large number of earlier studies, including ab initio w30–46x and semi-empirical w42,44x calculations, as well as experimental determinations w47,48x. Consider first the two experimental determinations of D 0 , namely 4.52 " 0.26 kcalrmol Ž1580 " 90 cmy1 . w47x and 4.97 " 0.05 kcalrmol Ž1737 " 18 cmy1 . w48x, both from equilibrium transition intensity measurements. Not only do these measurements not agree with the present determination within the error bars, but they also do not agree with one another. This is in comparison with the HF dimer case, where our value w49x agrees within the experimental uncertainty imposed by similar transition intensity measurements w60x. We conclude that the error bars on the previous measurements are much too small. Indeed, we attempted to fit the present angular distributions using these values, with no success. As noted above, the ab initio calculated hydrogen binding energies Ž De . vary between 5.5 and 9.2 kcalrmol Ž1924 and 3218 cmy1 .. Unfortunately, most of these calculations were done with small basis sets using methods that do not include correlation energy. As a result, we only compare the present result with the most recent MP2 calculations by Bevan and co-workers w42x. They performed several ab initio calculations which include the correction for the basis set superposition error ŽBSSE.. An adiabatic MP2 calculation yielded a De of 7.34 kcalrmol Ž2567 cmy1 . which, after correction for the zero-point energy, gave a dissociation energy of 5.39 kcalrmol Ž1883 cmy1 ., in reasonable agreement with the present value. Nevertheless, other
calculations reported in the same paper gave values spanning a wide range, covering the other experimental values quoted above. Therefore, the most we can say is that ab initio calculations can be found that are consistent with the present D 0 . It is interesting that the semi-empirical potential of McIntosh et al. w44x which was fit to a large set of intermolecular vibrations yielded a dissociation energy Ž D 0 . of 2037 cmy1 . Given that this potential gives excellent agreement for all 9 vibrational modes included in the fit at least shows that a potential with the D 0 determined here is consistent with the vibrational spectroscopy.
6. Conclusions We have presented the complete final state distributions for the vibrational predissociation of the HCN–HF complex following excitation of the H–C stretch and H–F stretch. The results show that the dissociation proceeds primarily by a V-R process, resulting in the majority of the available energy appearing as HF rotation. There is no evidence for V-V transfer into HCN vibrational bending modes, which is perhaps not surprising considering the linearity of the complex. The dissociation energy of this complex is determined by conservation of energy to be 1970 " 10 cmy1 . What is perhaps most surprising about this study is the similarity of the final state distributions resulting from C–H and H–F stretch excitation, given the dramatic difference in the associated predissociation lifetimes. From this we conclude that this large difference is primarily the result of the dramatic difference in the coupling strength between the intramolecular stretching vibration and the weak bond, rather than because of some form of resonance in the latter case Žwhich is clearly not present.. This enhanced coupling for the HF stretch is, of course, expected given that the latter is directly coupled to the dissociation coordinate. The most anomalous feature of the dissociation dynamics of this complex is the large fraction of the available energy that appears in product translation, accounting for the fact that the angular distributions extend to rather large angles. Presumably this has something to do with the extreme strong bonding in this system. Given the strong mode dependence of the vibrational
L. Oudejans, R.E. Millerr Chemical Physics 239 (1998) 345–356
predissociation lifetimes and this kinetic energy anomaly, this system is clearly deserving of further theoretical study. A more thorough understanding of the unique aspects of the dissociation dynamics of this system would clearly be extremely useful in obtaining better overall insights into these processes.
Acknowledgements This work was supported by the National Science Foundation ŽCHE-97-10026.. We also acknowledge the donors of The Petroleum Research Fund, administered by the ACS, for partial support of this research.
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