Collision-induced dissociation of formaldehyde cations: The effects of vibrational mode, collision energy, and impact parameter

Transcription

1 JOURNAL OF CHEMICAL PHYSICS VOLUME 116, NUMBER 13 1 APRIL 2002 Collision-induced dissociation of formaldehyde cations: The effects of vibrational mode, collision energy, and impact parameter Jianbo Liu, Brian Van Devener, and Scott L. Anderson Department of Chemistry, University of Utah, Salt Lake City, Utah Received 30 November 2001; accepted 15 January 2002 We report a study of collision-induced dissociation CID of H 2 CO, including measurement of the effects of collision energy (E col ) and five different H 2 CO vibrational modes on the CID integral and differential cross sections. CID was studied for collision with both Xe and Ne, and the Ne results provide a very detailed probe of energy transfer collisions leading to CID. The CID appearance threshold is found to depend only on total energy, but for all energies above threshold, vibrational energy is far more effective at driving CID than E col, with some mode-specificity. Results are fit with an impact parameter-based mechanism, and considerable insight is obtained into the origins of the E col and vibrational effects. A series of ab initio and RRKM calculations were also performed to help interpret the results American Institute of Physics. DOI: / I. INTRODUCTION Collision-induced dissociation CID is an important method used to probe ion structure 1 4 and bond energies. 5 9 CID is typically done by colliding the molecular ion of interest with a rare gas atom, eliminating any complications from chemistry or internal states of the target. In the threshold CID method, bond energies are extracted from the collision energy dependence of the CID integral cross section, (E). The analysis of the experimental (E) typically involves assuming a true (E) function, convoluting the function with experimental broadening factors possibly including kinetic shifts, then adjusting parameters of the true (E) function until the experimental data is fit see, for example, Armentrout 10. The most common form for the true (E) function is generalized from the line-of-centers LOC model 11 developed for atom atom collisions, to include the contributions from vibrational or rotational energy of the reactants, (E) 0 (E tot E 0 ) n /E m col, where 0 is a normalization constant, E tot is the total energy, E col is the collision energy, E 0 is the threshold energy to be determined by fitting, and n and m are fitting parameters used to adjust the shape of (E) both equal to 1.0 in the canonical LOC model. There are also variations on this approach based on adjusting the parameters of a true energy transfer function, however, the energy transfer functions used have been designed to replicate the LOC model behavior. 10,12 A key assumption in extracting physically meaningful threshold energies from CID data, is that the true (E) rises directly at the threshold energy, i.e., there is no energy gap between the threshold and the onset of CID. This condition corresponds to assuming that for near-threshold collision energies, at least some fraction of collisions is 100% inelastic, i.e., all the collision energy is converted to internal energy to drive CID. The fact that the threshold CID method has been used to extract accurate dissociation energies for a wide variety of ions, indicates that this assumption is usually justified, at least within the precision of the method. On the broader issue of the dynamics of polyatomic ion atom energy transfer collisions, there is not a great deal of detailed experimental information in the low E col range of interest for threshold CID. Perhaps the most detailed study to date was recently reported by Muntean and Armentrout, 13 on the CID of Cr CO) 6 in collision with Xe. That study, and others, will be discussed in more detail below. In the present study, we have measured the effects of collision energy and five different modes of reactant vibration on both the integral and differential cross sections for the CID of H 2 CO in collisions with Xe and Ne. The detailed nature of the measurements, along with excellent kinematics, provide unprecedented insight into the dynamics of a simple CID reaction. In fitting thresholds as described above, it is commonly assumed that internal energy present in the parent ion has an effect similar to that of collision energy on the CID appearance energy. For small molecular ions, the initial internal energy for thermalized reactant ions is so small that the assumption is difficult to test. For large polyatomic ions, the initial vibrational energy can be a significant fraction of the threshold energy. It is still difficult to test the assumption, however, because the ion internal energy distribution is broad and often not precisely known. In addition, there are few, if any, large cations for which independently established bond energies exist, that can be compared to the E 0 values extracted from CID threshold fitting. The assumption of equal effect for all forms of initial energy is somewhat counterintuitive. Collision energy requires T V transfer to be effective, while vibration is already in the correct form to drive CID. Indeed, particular modes might be expected to be especially effective if they involve significant motion along the dissociation coordinate. To our knowledge, the only previous study of the effects of reactant ion vibration on CID was our study of OCS (v) Ar, Xe. For the relatively low levels of vibrational excitation accessible in OCS, we found that vibration and collision energy had similar effects in the thresh /2002/116(13)/5530/14/$ American Institute of Physics

2 J. Chem. Phys., Vol. 116, No. 13, 1 April 2002 Dissociation of formaldehyde cations 5531 FIG. 1. Schematic diagram of the guided ion beam instrument. old energy range, but vibration was more effective for higher energies. 14 In many ways, H 2 CO is a near-ideal ion for dynamics studies. H 2 CO is simple yet chemically interesting, with two types of bonds, and several possible dissociation channels in the E col 10 ev range. The energetics for all dissociation channels are well established or can easily be calculated ab initio, thus introducing no uncertainties for interpretation of the dynamics. Reactions of H 2 CO are significant in stratospheric 15 and combustion chemistry, 16 and to molecular synthesis in interstellar clouds, 17,18 where nonequilibrium conditions make vibrational and rotational effects important. Dissociation of H 2 CO has been studied by a number of experimental approaches, including electron impact, photoionization mass spectrometry, multiphoton ionization, 26,27 and photoelectron photoion coincidence techniques Semiempirical and ab initio calculations have also been carried out to determine the potential energy surfaces and photodissociation pathways, and the most important processes leading to dissociation induced by initial electronic excitation are well understood. There have been no previous studies of H 2 CO CID in the threshold energy regime. II. EXPERIMENTAL AND COMPUTATIONAL DETAILS The guided-ion-beam tandem mass spectrometer used in this study is shown in Fig. 1. The instrument, along with the operation, calibration and data analysis procedures, has been described previously. 34 Only a brief description is given here, emphasizing the modifications made for this experiment. State-selected ions are generated by resonance-enhanced multiphoton ionization REMPI, mass and energy-filtered, then guided through a scattering cell that surrounds a 10 cm length of an 8-pole radio frequency rf ion guide. 35 The cell is filled to either Torr or Torr with neon or xenon, respectively. Product ions and unreacted primary ions are collected by this ion guide, then guided by a second ion guide to the final mass spectrometer/detector, where they are counted. Time-of-flight TOF is used to measure both primary and product ion velocity distributions. The H 2 CO precursor was generated by heating a mixture of solid paraformaldehyde Aldrich 95% and anhydrous MgSO 4 Merck, held in a stainless steel tube connected directly to a pulsed molecular beam valve. The tube and pulsed nozzle were heated to 60 C causing the paraformaldehyde to liberate monomeric H 2 CO and water. 36 The water was absorbed by the MgSO 4, and the monomeric H 2 CO was swept into the pulsed valve by a flow of helium at 1 atm. The vapor pressure of H 2 CO is estimated to be around atm at 60 C, 37 hence the concentration of H 2 CO in the molecular beam was around 5%. Because H 2 CO readily repolymerizes in the presence of water, 38 the entire gas line was baked at 400 K before use, the distance from the generation of H 2 CO to the supersonic expansion was minimized, and the helium was passed through a molecular sieve trap maintained at 77 K. This procedure greatly reduced the repolymerization of H 2 CO; no dimer, trimer or fragments attributable to them could be detected in the mass spectra. The REMPI procedures used to prepare vibrational stateselected H 2 CO have been discussed in detail previously. 27 H 2 CO in its ground electronic state can be prepared by 2 1 REMPI through the 1 A 2 (3p x ) Rydberg state. Ionic vibrational levels associated with 2 CO stretching, 3 CH 2 scissors, 4 CH 2 out-of-plane bending, 5 CH 2 asymmetric stretching, and 6 CH 2 in-plane rock modes, can be produced by pumping through the corresponding vibrational levels of the intermediate. Photoelectron spectroscopy PES shows that the state purity is 100%, with the possible exception of the 2 1 state, where the intensity was too low to allow PES measurements collection efficiency in our electron spectrometer is Given the very strong propensity for preservation of the vibrational level in ionization of the 3p x Rydberg, we assume that the 2 1 state also has high purity. This assumption is supported by the observation below that the CID threshold shift for this ionic state is, within the experimental uncertainty, equal to the 2 vibrational energy. A summary of the ionic vibrational state from each REMPI transition is given in Table I. Under even low intensity REMPI conditions, H 2 CO produced in the ground electronic state is readily photodissociated to HCO and CO by absorbing additional photons. To remove these fragment ions from the beam, the source was modified as shown in Fig. 1. Ions were generated inside a short quadrupole ion guide 9.5 mm rods, cm long which focused the ions through a pair of ion lenses into a conventional mass-selecting quadrupole 19 mm rods, 22.9

3 5532 J. Chem. Phys., Vol. 116, No. 13, 1 April 2002 Liu, Van Devener, and Anderson TABLE I. Transitions used state selection of H 2 CO X 2 B 2. Laser nm Transition to the H 2 CO 1 A 2 (3p x ) state Ion vibrational energy E vib (mev) Ionic state H 2 CO X 2 B Ground state in-plane CH 2 rock out-of-plane bend CH 2 scissors 208 a 2 1 CO stretch asym CH 2 stretch a Data from Refs. 78, 79. cm long. At the exit of the mass filter, the ions were collected and collimated by a lens set equipped with variable apertures, allowing us to restrict collection to ions within a variable distance of the mass filter center line. The aperture was designed to minimize interaction of the collected ions with the strong fringe fields in the quadrupole-lens gap. 39 In addition, the collection lens set included a split center electrode that was used to time-gate the ion pulse. The combination of controlled collection radius and time-gating allowed us produce a mass-selected beam with narrow kinetic energy spread ( E 0.1 ev). Our procedures for integral and differential cross section measurement have been described previously. 34,40,41 Briefly, for integral cross section measurement, the ion guides were operated at high rf amplitude and with a 1 V potential drop between the scattering and TOF segments of the guide, to aid in collection of slow ions. For differential measurements, the TOF guide segment was set only 0.1 V negative with respect to the scattering region, to minimize loss of velocity resolution. Integral cross sections were calculated from the ratio of reactant and product ion intensities, the target gas pressure measured with a Baratron capacitance manometer, and the effective length of the target gas cloud. The effective length factor was determined by calibration, using the well established cross section for the Ar D 2 ArD D reaction, 42 and is within 10% of the geometric length of the scattering cell. Two types of differential cross section data are presented below. Because we measure all ion signal with a multichannel scalar, TOF data are always available. The TOF data can be converted to product ion axial velocity distributions, i.e., the projection of the full velocity distribution on the ion guide axis. In our experimental geometry, the relative velocity of the reactants and the velocity of the center-of-mass in the lab (V CM ) are both coaxial with the ion guide, on average. As a consequence, some dynamical information can be gleaned directly from the axial velocity (v axial ) distributions. For example, if reaction proceeds via a complex with lifetime ( complex ) long compared to its rotational period ( rotation ), typically a few picoseconds, the resulting v axial distribution must be symmetric about V CM. Conversely, an asymmetric v axial distribution is a clear sign that the reaction is not mediated by a long-lived complex, and also reveals the predominant scattering mechanisms i.e., forward or backscattering. In addition, the deviation of the velocity distribution from V CM is a measure of the maximum energy going into recoil in the forward and backward scattering directions. The v axial distributions provide no information about the extent of sideways scattering, however, and quantitative interpretation e.g., extracting angular or energy distributions requires assumptions to be made regarding the nature of the reaction mechanism. The complete doubly-differential cross section can be recovered from a series of TOF measurements taken with different ion guide rf amplitudes, as described in detail by Gerlich 35 and Mark and Gerlich. 43 The method is based on the idea that for a given rf amplitude, only ions with radial velocities (v radial ) up to a well-defined cutoff value are confined by the guide. By measuring TOF distributions for a series of rf amplitudes, we obtain a series of v axial distributions subject to the corresponding v radial cutoffs. These distributions can be subtracted from one another to give a series of v axial distributions for ions with v radial between two cutoff values, which can be plotted as a product ion recoil velocity map. This approach, used by Muntean and Armentrout 13 in their CID study, gives a velocity map convoluted with the distributions of primary ion and target velocities. The main features of the differential scattering are apparent, but to extract quantitative information, it is necessary to account for the experimental broadening factors. Our approach has been to use a Monte Carlo-based simulation of the experiment, 40 in which a trial recoil velocity map is convoluted with the experimental distributions, and adjusted until good agreement with experiment is obtained. More details about this fitting process are given below. Because the effects we are measuring are subtle, it is important to minimize systematic variations in experimental conditions that might be caused by drifting potentials, changes in laser intensity, etc. For each state, we cycled through the different collision energies several times. As a check on reproducibility, we measured the cross sections for the ground state at both the beginning and end of each complete experimental run. Finally, the entire set of experiments was repeated several times to check the reproducibility. Based on the reproducibility of the cross section measurements taken over a 5 month period, we estimate that the relative error is 10%. To aid interpretation, ab initio calculations were performed at B3LYP and CCSD T levels of theory with G** and G** basis sets, using GAUSSIAN Rice Ramsperger Kassel Marcus RRKM and density-of-states calculations were done with the program of Zhu and Hase, 45 using its direct state count algorithm,

4 J. Chem. Phys., Vol. 116, No. 13, 1 April 2002 Dissociation of formaldehyde cations 5533 and scaled frequencies and energetics from the B3LYP/6-311 G** calculations. III. RESULTS AND ANALYSIS A. Integral cross sections Many product channels are energetically accessible in collision of H 2 CO with Xe Ne in the energy range of interest ev, H 2 CO Xe Ne) HCO H Xe Ne) H 1.09 ev 1a COH H Xe Ne) H 2.49 ev 1b CO H 2 Xe Ne) H 3.22 ev 2 H 2 CO Xe Ne) H 4.54 ev 3 H HCO Xe Ne) H 6.53 ev 4a H COH Xe Ne) H 8.39 ev 4b H H CO Xe Ne) H 7.22 ev 4c Xe H 2 CO H 1.26 ev 5 XeH HCO H 1.43 ev 6a NeH HCO H 4.49 ev. 6b The energetics for reactions 1a, 2, 3, and 4a are obtained from dissociative photoionization mass spectral data, and other energetics were calculated from tabulated thermochemical data, 46 and from our ab initio results. Despite the plethora of channels, only one, HCO H Rg, is observed in the collision energy range from 0.3 to 3.6 ev for Xe and from 0.3 to 9.5 ev for Ne. The integral CID cross sections for ground state H 2 CO in collision with Xe and Ne are plotted in Fig. 2. All collision energies given are in the CM frame. Because of the distribution in collision energy, the experimental cross sections rise from zero somewhat before the true threshold, indicated by arrows in the figures. Fitting of the CID (E) data to account for experimental broadening is discussed below, in the section on vibrational effects. For comparison, Fig. 2 also shows the nonreactive scattering cross sections NR right-hand scale, which are estimated from the H 2 CO velocity distributions, as follows. Figure 3 shows the velocity distribution of the H 2 CO beam with the scattering cell empty and filled, and also the difference in H 2 CO velocity distributions filled empty. When the cell is empty, the H 2 CO beam has a sharp velocity distribution. Upon filling, the sharp peak is slightly attenuated, and the intensity increases on the long TOF side of the peak. The attenuation results from a combination of CID, removing H 2 CO from the beam, and nonreactive scattering that simply slows the ions. The nonreactive cross section was estimated by integrating the distribution of slow ions in the difference spectrum, and thus corresponds to all nonreactive scattering that results in a sufficient reduction in v axial to be FIG. 2. CID and nonreactive scattering cross sections as a function of E col, for ground state H 2 CO colliding with Xe top and Ne bottom. distinct from the main primary beam TOF peak. Grazing collisions or others that do not change v axial significantly, are not included. For these systems at collision energies above a few ev, long range forces are negligible, and we expect that the hard sphere cross section HS 38 Å 2 for Xe and 23 Å 2 for Ne should be a reasonable estimate of the collision cross section. At sufficiently high energies, we expect that nearly every hard sphere collision will lead to dissociation, therefore, CID should approach HS and become independent of collision and vibrational energy. In contrast, the measured CID FIG. 3. Time of flight spectra for primary beam H 2 CO with scattering cell filled or empty of Xe, showing the nonreactive scattering.

5 5534 J. Chem. Phys., Vol. 116, No. 13, 1 April 2002 Liu, Van Devener, and Anderson FIG. 4. Axial velocity distributions with different radial velocity cutoffs, for HCO produced by CID with Xe at E col 2.5 ev. cross sections for Xe appears to level off at E col 2 ev with a value of 1.8 Å 2, and CID Ne) shows signs of leveling off above 8 ev with a value near 2.5 Å 2. In both cases, CID is well below HS. This discrepancy is an artifact, as shown by the velocity distributions, discussed below. Also shown in Fig. 2 is a corrected neon CID cross section, based on fits to the velocity distributions. The corrected CID is still well below HS, but continues to increase rapidly throughout the experimental energy range, suggesting that CID may indeed approach HS in the high energy limit. B. Recoil velocity distributions Typical sets of raw HCO velocity distributions are given in Fig. 4 for Xe at E col 2.50 ev, and in Fig. 5 for Ne at E col 2.70, 3.31, and 3.96 ev, respectively. These figures show axial velocity distributions measured for a range of radial cutoff velocities, i.e., each data series gives the v axial distribution for ions with v radial up to the indicated cutoff value. Also shown as a solid vertical line in each figure is V CM, i.e., the average velocity of the CM frame in the lab. Because the experiment is cylindrically symmetric, lab frame v axial distributions can be approximately converted to the CM frame by simply subtracting V CM. In the discussion below, forward and backward are defined as product ions with axial velocities faster or slower, respectively, than V CM. As shown in Fig. 4, the kinematics for the H 2 CO Xe system are such that for the collision energies studied, V CM is so low that product ions backscattered in the CM frame have low or negative lab velocities. In our experiment, the lens at the entrance end of the ion guide is positively biased, in order to reflect the ions scattered to negative lab velocities. These ions are therefore collected, but their TOFs are uninterpretable. In addition, the TOFs of slow ions are most strongly affected by small potential inhomogenetities, and the effect is exacerbated by the singular Jacobian for TOF-to-velocity conversion. Because it is clear that the peak of the velocity distribution is in the range where quantitative interpretation is not possible, further analysis of the Xe CID data has not been attempted. FIG. 5. Axial velocity distributions with different radial velocity cutoffs, for HCO produced by CID with Ne at E col 2.70, 3.31, and 3.96 ev. Solid symbols: experimental. Open symbols: simulation based on impact parameter model. The kinematics for CID in collision with Ne are quite favorable for ion collection, and for extracting information from velocity distributions. V CM is large at all E col of interest, so that all products are scattered with substantial velocities in the lab frame. The HCO recoil velocity distributions for Ne CID are backward-peaked at all collision energies where the signal is large enough for velocity measurement down to 1.5 ev, see Fig. 7, below, indicating that Ne CID goes by a direct i.e., collision time rotational period mechanism even at energies near threshold. To extract additional information from the velocity distributions, it is necessary to fit the data, thus correcting for experimental broadening factors. Our fitting program includes the possibility for generating arbitrary physics-free trial velocity maps, however, it is far more informative if the data can be fit with velocity maps based on some physical scattering mechanism. In the limit of a direct, impulsive mechanism, as might be expected to dominate for collision with Ne over our energy range, the scattering dynamics will be determined primarily by impact geometry i.e., by the impact parameter and H 2 CO orientation. We recently reported 47 use of a simple impact parameter-based scattering model to fit v axial distributions for reaction of CH 3 CHO with water, and have adapted that model to fit the present CID results. The model works as follows: The distribution of impact parameters from b 0 to b d is sampled, where d is the effective hard sphere radius. For each impact parameter, b, the collision energy is partitioned as in collisions of spheres, into energy along the line-of-centers, E LOC, and the rest of the energy, E rest,

6 J. Chem. Phys., Vol. 116, No. 13, 1 April 2002 Dissociation of formaldehyde cations 5535 E LOC E col 1 b/d 2, 7 E rest E col E LOC. 8 E rest is assumed to remain in translation for the products, as would be required by angular momentum conservation in the case of spherical collision partners. E LOC is added to the vibrational energy of the cation to give E react, the energy assumed to be available to drive the reaction. Our ions are generated by photoionization of supersonically cooled H 2 CO, thus the rotational energy is negligible. If E react is less than the endoergicity, the collision is assumed to be nonreactive. This constraint establishes a maximum reactive impact parameter b LOC, as in the line-of-centers model. For reactive collisions, the recoil energy is taken as the sum of E rest and some fraction of the remaining available energy, E recoil E rest E react E 0 /N deg, 9 where E 0 is the endoergicity and N deg is an effective number of degrees of freedom involved in energy partitioning. The scattering angle is defined by the requirements that the component of momentum perpendicular to the line-ofcenters i.e., corresponding to E rest is conserved, and that the component of momentum along the line of centers is consistent with E recoil, as defined above. The resulting relation between b and is given by the following: tan arccos 2, 10 tan tan 2 where b tan d 2 b, 11 2 and E react E 0 /N deg. 12 E LOC Here, is the angle between the initial velocity vector and the line-of-centers, and is the fraction of the LOC velocity that appears in recoil. The model maps a particular impact parameter onto particular values of E recoil and, as would be appropriate for scattering of spheres. To account for the expectation that E recoil and will also depend on the H 2 CO orientation, the model applies Gaussian broadening functions to the E recoil and calculated for each collision. While this model is clearly over simplified, it captures the essential physics of impulsive scattering with a minimum number of adjustable parameters. A very similar approach was used by Muntean and Armentrout 13 to generate limits of scattering angles and energies for comparison with their CID data. By carrying out a full fitting analysis, we are able to further constrain the model, obtaining additional information about the dependence on b of energy partitioning and scattering angle. It is important to note that the simulated recoil speed and angular distributions are for the collisionally activated H 2 CO parent, while the experiments measure the HCO velocity. Our use of these simulations to fit the data is reasonable only if several criteria are met. The first criterion is that the collisional activation and dissociation processes must be sequential, as assumed in the model. This assumption undoubtedly fails at high collision energies, where impulsive knock-out collisions are likely. In the low E col range of our experiments, however, kinematic considerations see Discussion suggest that the sequential mechanism should dominate. These considerations are confirmed by preliminary results from a direct-dynamics trajectory study of H 2 CO Ne CID. Trajectories are calculated using the VE- NUS program of Hase and co-workers 48 to set up trajectory initial conditions, and the method of Schlegel and co-workers, 49 implemented in GAUSSIAN 99, 50 to integrate trajectories. To date, we have examined 500 trajectories for ground state H 2 CO at E col 2.7 ev and 6.03 ev, calculated at the B3LYP/6-31G** and MP2/6-31G** levels of theory. At 2.7 ev, only sequential CID is observed. At the higher energy, a few direct H atom knock-out collisions have been recorded, but 90% of the CID collisions are still sequential. The second criterion is that the perturbation on the HCO velocity from dissociation of the H 2 CO should be small. There are three factors to consider. As indicated by the very slow rise in CID signal with increasing E col Fig. 2, and also seen in the direct-dynamics calculations, energy transfer in Ne H 2 CO collisions is quite inefficient. The result is that the excess energy available to drive H HCO recoil is small. Because this is a simple bond-scission process, there is no reason to expect a large fraction of this excess energy to appear in recoil. Finally, because the HCO/H mass ratio is large, only 3.3% of the separation velocity of the HCO H pair is carried by the HCO. The net result is that the difference between the velocity of the H 2 CO parent and the resulting HCO fragment is small. The final criterion is that the small! velocity perturbation from the dissociation step should be random, i.e., should simply broaden, rather than shift the velocity map. For this to be true, the dissociating H 2 CO should be randomly oriented with respect to the direction of the initial H 2 CO recoil velocity. There are two randomization mechanisms. First, because the reactants are oriented randomly, the scattered H 2 CO will tend to have a wide range of orientation angles with respect to its recoil velocity vector. In addition, rotation of the scattered H 2 CO prior to dissociation will tend to wash out any initial correlation between the directions of the H 2 CO and HCO recoil velocity vectors. Here again, the preliminary trajectory work provides confirmation. At E col 2.7 ev, for example, the average product rotational energy is about 0.5 ev for all impact parameters where CID is observed. The amount and type of rotation depend on the impact geometry, however, most trajectories result in H 2 CO rotation on a time scale fast compared to dissociation. In summary, the CID mechanism is sequential as assumed in the model, and the velocity perturbation from the dissociation step is small and random. The effect, therefore, is simply to broaden the recoil energy and angular distributions slightly. This broadening is negligible compared to the broadening built into the model to account for the orientation dependence of the scattering.

7 5536 J. Chem. Phys., Vol. 116, No. 13, 1 April 2002 Liu, Van Devener, and Anderson With the scattering dynamics defined as above, the inputs to the impact parameter model are N deg, the width parameters for the E recoil and broadening functions, and an opacity function, P(b), that describes the probability of CID as a function of impact parameter. N deg is constrained by the peak value of the velocity distribution in the backward direction, and the width factors assumed to be angle and energyindependent are adjusted to fine-tune the fits. Note that for the LOC model P(b) 1 for b b LOC, and P(b) 0 for b b LOC, where b LOC is the maximum b such that E react E 0, as defined as above. Fits to the data obtained using the impact parameter model are shown in Fig. 5 as open symbols. The fits are based on a LOC-like opacity function, P(b) K for 0 b b max, where K is a constant determined from normalization, and b max is a fitting parameter. The fits are surprisingly good, considering the small number of adjustable parameters b max, N deg, and the angle and energy width factors, suggesting that this simple impact parameter model really does capture the important physics. The deviation observed for the highest v radial curves at the higher collision energies is a collection efficiency artifact, discussed below. One important deviation from strict LOC scattering is that b max Table II is smaller than b LOC.Ifb max is forced to equal b LOC, the resulting velocity map is too forwardscattered to fit the data. Such a reduction in the maximum effective impact parameter leading to CID is not unreasonable. In the LOC model as derived for spherical collision partners, there can be no collisional torque, thus the collision energy is assumed to be partitioned only between recoil and vibration or some form of internal energy assumed to be efficient at driving reaction. For the real interaction, there are torques that couple translation and rotation, and the fraction of energy partitioned to rotation will tend, on average, to increase with b. H 2 CO rotational energy is necessarily relatively inefficient at driving dissociation, because angular momentum conservation demands that much of this energy must remain in rotation of the HCO product. As a consequence, it is not unreasonable that CID efficiency drops at large b an effect appearing in the model as a sharp cutoff at b max. In reality, P(b) undoubtedly varies smoothly. The main observable consequence of a sharp P(b) cutoff would be the corresponding sharp cutoff of the angular distribution. This cutoff is smeared-out in the fitting by Gaussian broadening built in to account for the orientation dependence of the scattering angle. The velocity map extracted from the fit to the data for E col 2.70 ev is plotted in Fig. 6. The distribution peaks at a scattering angle ( peak ) near 109 with a full width at half maximum FWHM, and the associated recoil speed (S peak ) peaks at 1550 m/s with m/s FWHM. The important parameters of the velocity maps for other collision energies are collected in Table II. The principle change with increasing energy is that b max increases, increasing the fraction of products scattered in the forward hemisphere. Figure 7 shows v axial distributions of HCO from CID with Ne for a wide range of collision energy, with corresponding impact parameter model fits. The fits up to E col 3.96 ev are based on full v axial /v radial data, so the impact FIG. 6. Center-of-mass velocity map extracted from fitting v axial /v radial data for HCO produced in Ne CID at E col 2.70 ev. parameter model is well constrained. For the higher energies, we did not make the time-consuming v radial measurements, thus we are assuming that the impact parameter model continues to provide a reasonable description of the mechanism. The fact that the high and low velocity limits of the v axial distributions are well fit, supports this assumption. The fits are reasonable up to E col 4 ev, but at higher energies there is a glaring discrepancy, that might be taken as evidence of the failure of the impact parameter model. In fact, it is clear that the hole that appears in the v axial distributions in the velocity range around V CM, is an experimental artifact, and it exactly what the impact parameter model predicts. As shown by the v axial /v radial data at lower energies, CID tends to produce a large fraction of sidewaysscattered products. For any reasonable scattering mechanism, the average speed of these sideways-scattered product ions must increase with collision energy, such that they become increasingly difficult to collect, even using ion guides. This drop in collection efficiency explains the observation, noted above, that the CID integral cross sections Fig. 2 level-off at values much smaller than the HS limit. The loss of sideways-scattered product ions also explains why the leveling-off occurs at much lower energies for Xe than for Ne. For Xe the light ionic product carries a much larger fraction of the recoil energy than for Ne CID, thus the onset of the collection efficiency problem occurs at lower collision energy. The loss of sideways-scattered ions depends on two factors, 35 and illustrates the need for caution in interpreting guided-ion-beam integral cross sections at high collision energies. In order for ions to have stable trajectories in a rf trap, the rf frequency should be large enough that the field changes polarity frequently on the time scale of the ions radial motion in the trap. For light ions with high radial velocity, this adiabaticity requirement dictates a high rf frequency. On the other hand, the magnitude of the effective potential (U eff ) confining the ions radial motion is proportional to V 2 rf /m 2, i.e., high rf frequencies result in low U eff, allowing fast ions to escape. U eff can be increased by increasing the rf amplitude (V rf ), however, there are limits set by arcing, and higher V rf also tends to exacerbate the breakdown of adiabaticity. For the mass ratios in this system,

8 J. Chem. Phys., Vol. 116, No. 13, 1 April 2002 Dissociation of formaldehyde cations 5537 TABLE II. HCO velocity distribution fit results by impact parameter model. E col E avail a ev b max /d b LOC /d b max /b LOC N deg ev E recoil ev E recoil / E avail % S peak b m/s peak c deg Ground state , E vib ev , E vib ev , E vib ev , E vib ev , E vib ev a mean value. b Peak recoil speed. c Peak scattering angle. there is simply no way to avoid loss of ions at high collision energies. Despite the loss, some information can be extracted from the v axial distributions at high collision energies. It can be seen that the distributions shift from strongly backwardpeaked at low E col, to roughly equal intensities in the forward and backward hemispheres at high E col. This shift is expected from a line-of-centers picture larger impact parameters contribute more to CID at high energies, and these collisions tend to result in smaller scattering angles. The impact parameter model fits the high and low velocity edges of the distributions, and these constrain the b max and N deg parameters, respectively. If we assume that the fits are right, we can use this information to correct the integral cross sections Fig. 2 for the nonunit collection efficiency at high energies 86% at 4.73 ev, 62% at 6.03 ev, and 55% at 7.86 ev. The analogous correction for the Xe results was not attempted because it is impossible to quantify the loss of ions initially backscattered in the lab frame. The fitting results, obtained as described above, are listed in Table II. In the upper frame of Fig. 8 we give the extracted opacity functions, plotted as the product P(b) b, and normalized such that the integral of P(b) b db is proportional to the measured corrected CID cross section at that energy. As expected from the LOC model considerations, the maximum b for which CID occurs increases with increasing collision energy. In addition, the magnitude of P(b) increases with energy, i.e., the fits use P(b) constant, but the constant is less than unity and increases with energy, unlike the simple LOC model, where P(b) 1. The middle frame of Fig. 8 gives the extracted CM frame angular distributions, showing that the peak scattering angle decreases with collision energy, as a consequence of the increasing contribution of large b collisions. The fitting analysis also gives the partitioning of the available energy into E recoil and internal energy. In this case, E recoil refers to the recoil of H 2 CO * from Ne, while we measure the HCO velocity. As already discussed, however, the HCO velocity must be close to the recoil velocity of H 2 CO *. As shown in the Table II, the fraction of the available energy ( E recoil / E avail ) increases from 50% at low energies to over 70% at high energies. The increasing partitioning to E recoil reflects two factors. First, the contribution of large b collisions to the CID signal increases with increasing energy, and these collisions partition more energy into translation, as required by angular momentum conservation. In addition, the N deg parameter decreases from 4 at low energies to 2 at high energies, so that more of the energy along the line of centers is also partitioned into recoil of the products. This change in N deg presumably reflects faster, more direct collisions where less energy redistribution is possible. C. Vibrational effects Figure 9 gives the Xe and Ne CID cross sections for H 2 CO initially in different vibrational states. Note that the cross sections have not been corrected for loss of sidewayscattered products, and are thus quantitative only for energies up to 1.75 ev for Xe, and 4 ev for Ne, respectively. The vibrational frequencies are ev, ev,

9 5538 J. Chem. Phys., Vol. 116, No. 13, 1 April 2002 Liu, Van Devener, and Anderson FIG. 7. Axial velocity distributions for HCO from Ne CID at different E col. Solid symbols: experiment. Open symbols: simulation based on impact parameter model ev, ev, and ev. The cross sections are plotted versus total energy E tot E col E vib to allow comparison of the relative effects of collision energy and vibrational energy. If E col and E vib caused identical enhancement, the cross sections for different vibrational states would be superimposable. For Xe CID, the cross sections for different energy states appear to converge on approximately the same threshold, but at energies even slightly above threshold, vibration leads to substantial enhancements. For Ne, a similar pattern is observed, although the lower signal in the Ne threshold region makes it more difficult to judge whether the different states converge on a common E tot threshold. The inset in each frame of Fig. 9 shows the vibrational enhancement / ground state plotted as a function of vibrational energy, where each point is one of the six states studied. Enhancement factors are shown for several collision energies. For Ne, to compensate for lower signal to noise ratios, we averaged the data for three points around each E col e.g., the points for 2.0 ev are the averages of vibrational enhancements at E col 1.5, 2.0, and 2.5 ev. If there were no FIG. 8. a Opacity functions plotted as P(b) b extracted from fitting the HCO recoil velocity distributions from ground state CID at different collision energies. b HCO angular distributions in the CM frame. c Opacity functions plotted as P(b) b extracted from fitting the HCO recoil velocity distributions from Ne CID of H 2 CO in different vibrational states. vibrational effects, the enhancement factor would be unity. If the enhancement were simply proportional to vibrational energy, each curve would be a straight line. At high collision energies this is nearly true, i.e., the enhancements are nonmode specific within the experimental uncertainty 10%. At collision energies near threshold, however, there is some mode-specificity, as shown by deviations from the dashed line, which indicates the average trend of enhancement vs E vib for the lowest collision energy. An obvious question regarding the vibrational effects is how the vibrational energy contributes to the CID threshold. In analysis of CID cross sections to extract thresholds, it is

10 J. Chem. Phys., Vol. 116, No. 13, 1 April 2002 Dissociation of formaldehyde cations 5539 TABLE III. Integral CID cross section fit results using the modified line-ofcenters model. H 2 CO Xe H 2 CO Ne Ionic state E vib (mev) n 0 (Å 2 ) n 0 (Å 2 ) Ground state FIG. 9. Vibrational effects on H 2 CO CID with Xe top and Ne bottom. Insets to each frame give vibrational enhancement factors vs E vib, for different E col. The dashed line shows the average trend of vibrational enhancement vs E vib. usually assumed that all forms of energy are equivalent, at least insofar as their effects on the CID threshold energy. To address this issue, the energy dependence of the integral cross sections for each vibrational state was fit using the typical modified LOC model, 10,12 E col 0 E col E vib E rot E 0 n E col, for E col E vib E rot E 0, otherwise, E col 0, 13 where (E col ) is the cross section, E vib and E rot are the vibrational and rotational energy of the reactants, E 0, 0, and n are as defined above. In order to fit experimental data, this model (E col ) function is convoluted with the experimental distribution of ion beam and target velocities, and the parameters usually E 0 and n are adjusted to obtain a fit in the threshold energy region. In typical CID experiments E vib and E rot are not selected, but are assumed to be thermal. In our case, E 0 is well known 1.09 ev, 25 E vib is well defined, and E rot is negligible, because our ions are produced by REMPI of a supersonic beam. Our interest is in probing the question of whether E vib and E col contribute equally to overcome E 0, as is implied by the modified LOC model. To this end, in our simulations we have fixed E 0 at the experimental value, leaving only the n parameter adjustable 0 is simply a scale factor; it does not affect the threshold or curvature of the cross section. Table III gives the results. For Xe, it is possible to get good fits with only small variations in the n parameter, with all values near unity. As noted above, n 1.0 is consistent with hard sphere scattering. The conclusion is that the effect of E vib on the threshold is identical to that of collision energy, within experimental error. On the other hand, the magnitude of the cross section at fixed total energy is strongly dependent on vibrational state, as shown by the 0 factors given in Table III and the enhancement factors shown in the insets to Fig. 9. These results suggest that while P(b) constant is a reasonable approximation, the constant is not unity and varies with vibrational state. For Ne, larger values of n( ) were required to reproduce the data. The physical significance of an n parameter greater than 1 depends on the CID mechanism assumed. For example, it has been shown that a statistical theory based on reverse three-body recombination in a long-lived complex can lead to n values significantly greater than unity. 51 Such a complex-mediated model is quite unlikely for Ne CID, however, because the binding energy is negligible compared to our collision energies. Chesnavich and Bowers 52 have developed a theory for the energy dependence of translationally driven reactions that involve a rate-limiting transition state TS, and depending on the properties of this TS, different curvatures are possible. Because the limiting factor in Ne CID is T-to-V energy transfer in the initial impulsive collision, rather than passage through the dissociation TS, this approach is also probably not applicable. Levine and Bernstein have shown that assumption of an orientationdependent activation barrier results in a quadratic (n 2) threshold law for endoergic reactions under a LOC-based model. 11 Clearly for CID, the dissociation energy is not angle-dependent, but it would not be surprising if the collisional activation process were, resulting in an angledependent CID probability and n 1. In this scenario, the fact that the n parameter is substantially larger for Ne than for Xe might be accounted for by the fact that the interaction potential is more anisotropic for the smaller and much less polarizable Ne atom. Further insight into the influence of vibrational excitation on Ne CID dynamics is obtained from the velocity dis-

11 5540 J. Chem. Phys., Vol. 116, No. 13, 1 April 2002 Liu, Van Devener, and Anderson tributions. To allow direct comparison of P(b) functions and recoil energies extracted for different vibrational states, we fixed N deg and the energy and angle broadening parameters at the best-fit values for the ground state reaction. The fact that reasonable fits to the data for vibrationally excited H 2 CO are obtained with these parameters frozen, suggests that low levels of vibrational excitation do not grossly change the CID dynamics. The fit results for different H 2 CO vibrational states are included in Table II, and the opacity functions at E col 2.1 ev are compared in the lower frame of Fig. 8. It should be noted that the b max parameter in these opacity functions comes from fitting the velocity distributions, while the magnitude of the constant P(b) comes from the integral cross section, via the requirement that the integral of P(b) b db CID (E). As shown in the bottom frame of Fig. 8, most of the vibrational enhancement in the integral cross section is accounted for by the increase in b max demanded by the fits to the velocity distributions, which are substantially more forward-peaked for vibrationally excited H 2 CO. Note that the b max values for vibrationally excited CID remain below b LOC. It is also necessary to increase the constant in P(b) constant with increasing vibrational energy, suggesting that vibration not only increases the range of b over which CID is efficient, but also increases the efficiency even for low impact parameters. Velocity data for vibrationally excited CID at high E col have not been analyzed because it is unclear how the collection efficiency problem might vary with E vib, however, it is quite clear that a substantially greater fraction of forwardscattered CID products is observed. These forward-scattered products result from collisions at large impact parameters, thus we can conclude that vibrational excitation enhances the CID probability at large impact parameters, even at high E col. This effect also accounts for the large apparent enhancement in CID cross section at high collision energies, particularly for Xe, counter to the expectation that CID should approach HS for all states. In essence, we lose a smaller fraction of the products for vibrationally excited reactants, because forward-scattered products are collected efficiently. IV. DISCUSSION A. Missing channels One issue for interpretation of H 2 CO chemistry is that H 2 CO might isomerize to trans-hcoh prior to reaction and/or in collisions. In the case of CID, the trans-hcoh might then dissociate to both HCO and COH, significantly effecting both the reaction mechanism and energetics. We calculated optimized geometries for both isomers and the isomerization transition state TS at the B3LYP/6-311 G** level of theory, and also calculated single point energies at the CCSD T /6-311 G** level of theory, using GAUSSIAN HCOH is calculated to be 0.35 ev 0.32 ev above H 2 CO at the B3LYP/6-311 G** CCSD T /6-311 G** level, but the isomerization TS is 1.98 ev 1.93 ev above H 2 CO. The isomer energy difference and barrier height are in good agreement with earlier computational studies Clearly with an isomerization TS of 2 ev, we need not worry about isomerization induced by the reactant vibrational excitation. This TS is actually above the dissociation limit, and also is considerably tighter than the TS for the dissociation channel. As a consequence, in collisionally activated H 2 CO, isomerization is both energetically and entropically disfavored compared to dissociation. RRKM calculations were done using the calculated isomerization TS, and an orbiting TS for the dissociation channel, 56 with the result that dissociation is calculated to dominate by at least 2 3 orders of magnitude over the energy range of our experiments. We conclude that the isomerization, and COH H or COH H dissociation channels can be neglected. No CO ( H 2 ) product is observed despite an endoergicity of only 3.22 ev only one-third of our highest collision energy. Bomach et al. reported a ev appearance energy for CO from H 2 CO, 28,29 corresponding to an activation barrier of 0.72 ev in excess of the thermodynamic threshold. Ab initio calculations by Barbier et al. 32 predicted a similar barrier of 0.82 ev associated with H 2 CO CO H 2. We expect the TS for H 2 elimination to be tight compared to that for H elimination, thus CO H 2 is strongly disfavored on both energetic and entropic grounds. Another missing low energy channel is Xe charge transfer CT, with a threshold only slightly above that for CID, and no reason to expect an energy barrier. We propose that CT is suppressed by competition, H 2 CO Xe H 2 CO Xe Xe H 2 CO H 0 H 1.26 ev. As the H 2 CO Xe reactants collide, it is not unlikely that collisional interactions mix the H 2 CO Xe and Xe H 2 CO electronic states, such that there is some charge transfer character in the electronic wavefunction at short intermolecular separations. As the collision partners separate, the electronic states decouple and the system must choose between the charge states. In the separation process, the system must negotiate a series of crossings between vibronic surfaces that connect to the upper and lower electronic state. The probability of remaining in the excited electronic state i.e., CT will depend relative number of accessible vibronic surfaces that belong the two electronic states, as well as on factors relating to the inter-surface coupling strengths and crossing velocities. 57 The densities of vibrational states at fixed total L and E E avail associated with the two electronic states, should be a reasonable approximation to the number of accessible vibronic surfaces. For H 2 CO Xe, the density of states was calculated using the RRKM program of Zhu and Hase, 45 and it turns out that this factor disfavors CT by a factor of 20. When we also consider that the collision velocities are relatively slow favoring adiabatic scattering it is not surprising that no CT products are observed. Indeed, for all the polyatomic ion molecule reactions we have studied with No. atoms 4, we see CT only in cases where the endoergicity is less than 1 ev. 14,34,40,47,58 68 In addition, the maximum endoergicity for which CT is significant appears to decrease with system size, consistent with the density-ofstates argument given above.