Guided ion beam study of collision-induced dissociation dynamics: integral and differential cross sections

The low energy collision-induced dissociation (CID) of Cr(CO)6+ with Xe is investigated using a recently modified guided ion beam tandem mass spectrometer, in the energy range from 0 to 5 eV in the center-of-mass (CM) frame. The additions to the instrument, updated with a double octopole system, and the new experimental methods available are described in detail. Integral cross sections for product formation are presented and analyzed using our standard modeling procedure.

JOURNAL OF CHEMICAL PHYSICS VOLUME 115, NUMBER 3 15 JULY 2001 Guided ion beam study of collision-induced dissociation dynamics: integral and differential cross sections Felician Muntean and P. B. Armentrout Chemistry Department, University of Utah, SaltLake City, Utah 84108 (Received 22 January 2001; accepted 26 March 2001) The low energy collision-induced dissociation (CID) of Cr(CO)6 with Xe is investigated using a recently modified guided ion beam tandem mass spectrometer, in the energy range from 0 to 5 eV in the center-of-mass CM frame. The additions to the instrument, updated with a double octopole system, and the new experimental methods available are described in detail. Integral cross sections for product formation are presented and analyzed using our standard modeling procedure. A slightly revised value for the bond dissociation energy of (CO)5Cr+-CO of 1.43 ± 0.09 eV is obtained, in very good agreement with literature values. Axial and radial velocity distributions for primary and product ions are measured at 1.3, 2.0, and 2.7 eV, in the threshold region for product formation. The resulting velocity scattering maps are presented and discussed. Evidence of efficient energy transfer is observed from angular scattering of CID products. Experimental distributions of residual kinetic energies are derived and extend to zero, the point of 100% energy deposition. This indicates that energy transfer is nonimpulsive and probably associated with transient complex formation. For the first time, the experimental residual kinetic energy distributions are compared with the predictions of the empirical model used in integral cross section analyses. Good agreement is observed within experimental uncertainties. A model for the distribution of deposited energy during collisional activation is derived on the basis of these experimental observations. © 2001 American Institute of Physics. [DOI: 10.1063/1.1371958] I. INTRODUCTION Low-energy or threshold collision-induced dissociation CID has currently established itself as a powerful experi­mental technique for providing thermodynamic information for a large variety of molecular ions.1-16 Its main strengths are the relatively direct way of obtaining bond energies from dissociation thresholds, its broad dynamic range, and its abil­ity to treat a diverse set of chemical species. Despite the increasing use of the threshold CID method and its wider applications today, there is still limited experi­mental evidence to provide fundamental information about the energy transfer dynamics in threshold CID. Understand­ing the energy transfer dynamics is of prime importance for modeling CID data, in order to extract correct dissociation threshold values. Indeed, the ability to obtain thermodynamic information from CID thresholds requires that complete en­ergy transfer is possible. In addition, the internal energy dis­tribution of molecules energized by collisions plays an im­portant role in determining their dissociation lifetime, thereby controlling the kinetic effects on thresholds obtained from CID. As detailed further below, the model describing the distribution of deposited energy represents the main em­pirical part of our CID threshold modeling. In the absence of any direct experimental measurements of the energy transfer, this empirical model has only been tested in an indirect fash­ion, by comparing final threshold determinations with values available from other experiments, although these tests have provided remarkably good results.17-24 Current understanding of the CID dynamics25-29 in the low energy (< 100 eV region is that the energy is transferred to rovibrational states of the ground electronic state of the energized molecule and occurs as a result of one or a com­bination of several main mechanisms. There are two limiting mechanisms observed for energy transfer, with different sys­tems following a range of behaviors in between. Which mechanism dominates depends on energy and on the charac­teristics of the two collision partners. One limit involves a direct mechanism, occurring via impulsive collisions. This mechanism is dominant at energies high above the thresh­olds, where conditions are investigated most thoroughly.28,29 Different variations of the impulsive model30-33 all assume a binary interaction, mainly elastic, between the neutral target and an atom or group of atoms of the molecule. The maxi­mum energy transfer is determined simply by a mass ratio, always less than unity, such that complete energy transfer is not possible. Thus, obtaining thermodynamic information from a CID experiment that follows this mechanism at threshold cannot be achieved. The other limit involves complex formation between the projectile molecular ion and the neutral target. The complex must survive for many vibrational periods, such that internal energy randomization takes place, thereby allowing all of the collision energy to be available for dissociation. Note that efficient energy transfer does not require that the complex survive for rotational periods. Complex formation is favored for highly polarizable neutral targets and for low collision energies, conditions less easily studied in the past. Although the complex formation mechanism is currently believed to occur in CID at the lowest energies and although there is a significant amount of implicit experimental evidence for it,28 © 2001 American Institute of Physics 0021-9606/2001/115(3)/1213/16/$18.00 1213 Downloaded 11 Aug 2009 to 155.97.13.46. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp 1214 J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 F. Muntean and P. B. Armentrout FIG. 1. Schematic diagram of the guided ion beam tandem mass spec­trometer, double octopole configura­tion. there is currently no direct dynamics experiment to prove it. This is mainly because differential scattering experiments are usually performed using crossed beam instruments,34'35 which are limited to laboratory frame energies of at least several electron volts. Attaining low energies (in the center- of-mass frame) with these instruments requires the use of low mass neutral targets like He, which has a low polariz- ability. The use of a highly polarizable target like Xe limits these experiments to minimum energies that tend to be higher than those required to observe efficient complex for­mation behavior. Guided ion beam experiments can also provide differen­tial scattering information with a substantially increased sen­sitivity, as has been demonstrated before.36-39 Although they provide lower angular resolution than crossed beam studies, the resolution is sufficient for investigating typical CID dy­namics experiments. In addition, guided ion beams are able to explore a much lower energy range, covering the thresh­old region and filling the gap in our understanding of the dynamics of CID at low energies. In this paper, we present a comprehensive study of the dynamics of a low energy CID process, applied to the Cr(CO)6+ system. Cr(CO)6+Xe^Cr(CO)5++CO+Xe (1) -»Cr(CO)4+2CO+Xe (2) ->Cr(CO)3+3 CO+Xe. (3) This system is representative of a large class of organome- tallic systems and has a significant kinetic shift,19 making it suitable for a test of the CID model. Also, its thermochemi­cal information is well established19,40,41 and the onsets of the sequentially dissociating products (1)-(3) provide fairly well-defined markers for the energy dependence of the CID. In this work, we present results of integral and differential CID cross section measurements on this system for a range of collision energies in the threshold region. Collision dy­namics and energy transfer information are obtained from the differential cross sections and the angular and kinetic energy distributions derived from them are discussed and compared to available theoretical models. Distributions of residual kinetic energy are obtained for the threshold region and compared with the empirical function used in modeling. A model for the energy deposition function is also derived. II. EXPERIMENTAL SECTION A. Instrumentation The instrument used for this work is a recently modified guided ion beam tandem mass spectrometer, presented in Fig. 1. Because most of the instrument has been described in detail previously,42 only a brief description will be given here, emphasizing the changes we have recently made. Briefly, the instrument comprises an ion source, a mass selector, a reaction region surrounding an octopole ion guide, a second mass selector, and a detector. The ion source used in the experiments described here is a microwave discharge, followed by a flow tube, with He as a buffer gas at about 0.7 Torr. Cr CO 6 vapors are introduced in the flow tube, about 0.5 m downstream from the ion source. Chromium carbonyl crystals are volatile enough at room temperature to provide a good signal without any additional heating. Sample ions are formed by collisions with He ions and metastables, then ther- malized by many collisions (> 104) with He in the flow. We assume that sample ions beyond the flow tube are in their ground electronic state with an internal energy distribution well characterized by a Maxwell-Boltzmann distribution of rovibrational states at the flow tube temperature room tem­perature . This assumption is supported by many years of experimental evidence in our laboratory.19-24,43,44 Sample ions drift out of the flow tube, are focused through two regions of differential pumping, accelerated, fo­cused into a magnetic mass selector, decelerated using an exponential retarder, and focused into the double octopole ion guide region. This latter region has been recently modi­fied and is described in detail further below. The energy spread of the Cr(CO)6 ion beam in this region is about 0.23 eV full width at half maximum (FWHM, as measured by Downloaded 11 Aug 2009 to 155.97.13.46. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 Ion beam study of dissociation dynamics 1215 retarding potential analysis. The reaction cell is placed around the first octopole and CID with Xe takes place here. Typical Xe pressures in the cell vary between 0.05 and 0.2 mTorr. Product and unreacted primary ions drift out of the octopoles, are focused into the second mass selector, a quad- rupole mass filter, then detected by a Daly type detector.45 Formerly,42 the collision region of our instrument con­tained a single octopole, 27.9 cm long. This has now been replaced by a series of two octopoles, 22.9 and 63.5 cm long, which offer a higher resolution for the time-of-flight (TOF) and differential cross section measurements described below. This arrangement also provides a means of studying kinetic shifts by varying the time ions spend in the instrument, among other possible applications. The two octopoles have the same cross-sectional dimensions (3.2 mm diam molyb­denum rods on a 8.6 mm diam inscribed circle, which are the same as the replaced octopole. An injection lens (3.2 mm diam aperture, which pro­trudes 4 mm inside the first octopole has been installed to help inject ions close to the axis of the octopole and to re­duce rf fringing field effects. The first octopole, 22.9 cm long, has the reaction cell placed around it. The new reaction cell has identical dimensions as the old one: 5.1 cm long central part with two 3.2 cm long extension tubes, yielding a 8.3 cm effective length. The new cell and its extension tubes can be easily taken off, for cleaning or replacing with a dif­ferent length, without disassembling the octopoles. The sec­ond octopole is 63.5 cm long and it is placed inline and 1 mm apart from the first octopole. A cylindrical lens covers the gap between the two octopoles to control the fringing fields. A separate vacuum chamber houses the second octo- pole, pumped by a 700 1/s diffusion pump. The two octo- poles are powered in phase, by the same rf power supply,46 at a frequency around 5 MHz and a maximum amplitude around 150 V, zero to peak, for complete radial trapping of primary ions and products. Different dc voltages can be ap­plied on the two octopoles. Typically, the second octopole is set to float at a slightly more negative 0.3 V dc voltage than the first one to help collect slow products and to over­come local potential barriers in the long octopole. When the second octopole is floated at a much lower dc voltage than the first octopole, low energy tails are observed in the integral cross sections of CID processes, Fig. 2. These tails result from reactant ions being accelerated in the second octopole, where they collide with residual target gas mol­ecules and dissociate. The magnitude of the tails is in good agreement with the calculation of total cross sections, when considering the second octopole length as the interaction re­gion and the residual pressure in the octopole chamber as the interaction pressure. For example, the ratio of 7.7 between the lengths of the second octopole and the collision cell and the ratio of about 0.001 between the pressures in the second octopole chamber and the collision cell, give a ratio of 0.008 for the intensities of product ions produced in the two octo- poles. This ratio is in good agreement with the ratio of cross section magnitudes for the tail at 10 V offset of the second octopole and the total cross section at 10 eV, lab frame Fig. 2 . Collision energy (eV, lab) 0 2 4 6 8 10 ---■---1---1__I__i__I__.__I__I__.__.__I__.__.__i__I__.__.__.__L- Cr(CO)6 + Xe -*■ atota| ^ 0 12 3 4 Collision energy (eV, CM) FIG. 2. Total cross sections for the CID of Cr(CO)6 with Xe as a function of collision energy in the center-of-mass frame (lower x axis) and laboratory frame (upper x axis). Results are shown for different dc offset voltages between the first and the second octopoles: 0 V (solid circles), 2.0 V (open circles), 3.5 V (solid triangles), 5.0 V (open triangles), and 10 V (solid squares . B. Experimental methods Both integral and differential cross section measure­ments can be performed on the instrument described above. The method of measuring integral cross sections on this in­strument has been previously described in detail.42 Briefly, ion intensities for reactant and all products are measured as a function of the interaction energy and target gas pressure in the collision cell, then converted to cross sections. Interaction energy calibration can be done by retarding voltage analysis42,47 RET in the first octopole or by TOF measurements, as described below. The two methods give comparable results Fig. 3 , within the uncertainty of our measurements, ±0.05 eV laboratory frame. The RET 0.0 0.5 1.0 1.5 Ion energy (eV, lab) FIG. 3. Kinetic energy distribution of the Cr CO 6 ion beam. Comparison of the distributions obtained using the TOF method open triangles and the retarding voltage analysis, RET solid circles . The line represents a Gauss­ian fit to the RET distribution with a mean of 0.67 eV and a FWHM of 0.21 eV. Downloaded 11 Aug 2009 to 155.97.13.46. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp 1216 J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 F. Muntean and P. B. Armentrout method is more sensitive to local potential barriers, such that when the octopole rods become dirty, this method tends to shift the absolute zero to slightly higher energies. On the other hand, the TOF calibration depends on the values of the effective octopole lengths, which are difficult to know accu­rately because they depend on the fringing fields of the oc- topoles, which depend on the particular focusing of the ad­jacent lenses. Because of this, we use the RET method as our standard procedure for calibration when performing integral cross section measurements. When a significant discrepancy between the results of the RET and TOF methods is ob­served, a check of the system is indicated. In order to determine differential cross sections, we mea­sure ion velocity distributions. To accomplish this, the in­strument is operated in a TOF mode, using the octopoles as the free flight region. A pulsed primary ion beam is prepared by applying a pair of pulsed voltages one positive, the other negative on a split cylindrical lens, in the focusing region immediately before the first octopole. The pulses float on the dc voltage of the split lens, with amplitudes comparable to this voltage, typically between 5 and 25 V. Pulse widths, typically between 5 and 20 /xs, are selected by trading be­tween considerations of TOF resolution and sensitivity. Times of flight for ions are measured using a multichannel scaler triggered by the deflecting pulse. TOF distributions are then converted into axial velocity distributions as described in Appendix A. The radial components of the velocity distributions are measured following a procedure described in detail elsewhere.36 The principle of the method is that the maxi­mum radial velocity of an ion transmitted by a rf octopole is determined by the amplitude of the rf field, i.e., weak fields permit ions with large radial velocities to escape the trapping potential. Axial velocity distributions are measured for a se­ries of increasing rf voltages. Each of these distributions cor­responds to ions that have radial velocities lower than a limit set by the rf voltage used. These distributions are then sub­tracted from one another to give intensities that correspond to ions having radial velocities between two limits. These two procedures provide both axial and radial ve­locity distributions of ions for the scattering process investi­gated. It is worth noting that these distributions reflect the cylindrical symmetry of the scattering process in the octo- pole field. Thus, the radial scattering intensity is a function of the cross sectional area in velocity space. To obtain the densities of scattering flux distributions also called Carte­sian velocity maps or doubly differential cross sections , those that usually describe scattering experiments in the lit­erature, we divide our experimental radial distributions by the annular area corresponding to each radial velocity incre­ment in velocity space . Maximum radial velocities of ions transmitted by the octopole are related to the rf voltage applied following an­other calibration procedure, detailed elsewhere.36 In short, differential dc voltages are applied to the two sets of four octopole rods, positive on one set and negative on the other, by the same amount U. As a result the ions will be acceler­ated toward the negatively biased rods with a radial energy roughly equal to qU. In order to transmit the ions through the RF amplitude (V) Sf J, 1.5 >> o 0 S> 1.0 "S T3 CD ^ 0.5 D E X 1 0.0 0 50 100 150 RF amplitude (V) FIG. 4. Radial energy calibration. (a Octopole rf voltage scans of transmit­ted Cr(CO)B ion intensity for different values of the differential dc voltage applied on the two sets of four octopole rods. The maximum radial energy of the ions is set by the values of the differential dc voltages. Insert: example of finding the rf cutoff voltage corresponding to a 0.15 V differential dc applied on the rods by differentiating the rf scan in (a and fitting the peak obtained solid circles with a Gaussian function solid line . b The cali­bration curve: maximum radial velocity of the transmitted ions as a function of the rf voltage applied on the octopoles. The points deviate from the linear dependence in the region of very low radial velocities 0.2 km/s because in this region, radial ion energies 50 meV become comparable to local potential barriers on the octopole rods. octopole, a rf voltage has to be applied on the rods such that the effective potential of the octopole field V* is at least equal to this radial energy. Practically, cutoff curves are re­corded by monitoring transmitted ion intensity as a function of rf voltage, for a series of values of the differential dc voltage U applied, as shown in Fig. 4 a . The dependences between the rf voltage applied and the maximum radial en­ergy of the ions are then obtained by differentiating the cut­off curves and fitting the resulting peaks with Gaussian func­tions, as shown in the insert of Fig. 4 a . An example of a calibration curve obtained this way is presented in Fig. 4 b . Notice the deviation from linearity in the region of very low radial velocities, where the applied fields are comparable to the local potential distortions on the octopole rods. For this reason, experimental curves, rather than the linear fits, are used for the radial velocity calibration in that region. Conversion of velocity distributions from the laboratory to the center-of-mass CM system is straightforward in our beam-cell experiment, because the average laboratory veloc­ity of the neutral target is zero. This leads to Eqs. (4)-(6) u axial- IV axial- V CM ,4 Downloaded 11 Aug 2009 to 155.97.13.46. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 Ion beam study of dissociation dynamics 1217 a(E) = g^E+E-E0)7E, 7 FIG. 5. Normalized axial energy distributions for the products of Cr CO 6 CID with Xe at a pressure of 0.1 mTorr for a collision energy of 2.7 eV in the center-of-mass frame. Symbols represent distributions ob­tained by retarding potential analysis (RET in the second octopole and lines represent distributions obtained from time-of-flight (TOF measurements. u radial ^radial, i>cm = /(Mi + mJ, where is the cross section, E is the relative collision en­ergy, E0 is an adjustable parameter representing the reaction threshold at 0 K, cr0 is another adjustable but energy inde­pendent parameter that acts as a scaling factor, and the sum­mation is over the rovibrational states of the reactant ion having energies Ei with populations gi . The expression in Eq. 7 is further convoluted over the kinetic energy distri­butions of the two reactants before comparison with the data. Parameter n is yet another adjustable parameter that de­scribes the energy deposition during collision, dependent on the characteristics of the two colliding reactants. For ex­ample, n 1 indicates that all of the kinetic energy allowable by angular momentum conservation is transferred into inter­nal excitation, the case of maximum energy deposited. A recent review of theoretical models applied to the kinetic energy dependence of ion-molecule reactions is presented elsewhere.53 For a CID process, n typically takes values be­tween 1 and 2, although some systems can only be fit with n values as low as 0.5 or as high as 3. Among the significant (5) theories, the ‘‘line-of-centers'' (LOC) model54 predicts a (6) where u represents laboratory velocities and u represents CM velocities, CM is the velocity of the CM of the system, i and mi are the average primary ion velocity and mass, and mn is the neutral reactant mass. Axial kinetic energy distributions for reaction products can also be obtained by performing a retarding potential analysis in the second octopole, without the need to pulse the ion beam and without any conversion procedure. An ex­ample of such distributions for Cr CO 6 CID products at 2.7 eV CM is presented in Fig. 5, compared to the same dis­tributions obtained by TOF measurements. Care must be taken when performing such measurements for at least two reasons. First, the absolute energy scale calibration using a retarding analysis in such measurements is better performed in the first octopole. The second octopole, because of its much greater length, is more susceptible to local potential inhomogeneities. Second, the retarding analysis in an octo- pole does not give reliable results for largely off-axis or di­vergent ion beams, as the reaction product ions can be. Di­vergent and energetic products may reach the high fields close to the octopole rods where they may gain energy from the rf field. An example of an artifact resulting from this effect is seen in the high energy tail of the Cr CO 5 distri­bution in Fig. 5. Still, this technique can be used as a rapid method to obtain preliminary information about the energy distributions of product ions. C. Data analysis Thermodynamic information provided by the low energy CID experiment is extracted from the energy dependence of the integral cross sections in the threshold region by fitting the data with an empirical model. The model19,20,48-53 used with best results is represented by the expression value of 1, the Langevin model48 predicts 0.5, and the ‘‘translationally driven'' model of Chesnavich and Bowers55 predicts a value between 1 and 3.5, depending on the prop­erties of the transition state. The model of Eq. 7 has been found to reproduce the energy dependence of cross sections for a large variety of ion-molecule reactions.53,56 As has been demonstrated by previous work in our laboratory,20,49,57 reliable results de­pend on a careful consideration of a number of factors that can affect threshold energy determinations. Among these, the kinetic and internal energy distributions of reactants, and the number of collisions between them are straightforward to consider, as described previously.20,42,49,57 Inclusion of these effects in our modeling provides accurate reproduction of data for relatively simple systems (less than 5-10 heavy at­oms). For more complex systems, dissociation can become slower than the TOF of the dissociating molecule through the instrument. As a result, products are not efficiently observed until energies higher than the real dissociation threshold, yielding what is called a kinetic shift. No matter how good the experimental sensitivity, there is a minimum rate of prod­uct formation necessary to enable detection above back­ground noise. To account for kinetic shifts, the CID model has been complemented19,50,51 with a statistically calculated probability of dissociation. Briefly, we use Eq. 8 , in which our CID model Eq. 7 incorporates an integration over a unimolecular dissociation probability a(E) = (na0/E)2 g< f [1 -e~k{E+E>)T] l JEn-E, x(E-e)n~ 'de. (8) Here, is the deposited energy, is the average experimental time available for dissociation the ion time-of-flight from the collision cell to the quadrupole mass analyzer, on aver- Downloaded 11 Aug 2009 to 155.97.13.46. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp 1218 J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 F. Muntean and P. B. Armentrout age 500 /us in the present configuration, and k(s + Et) = k(E*) is the unimolecular dissociation rate constant, cal­culated using Rice-Ramsperger-Kassel-Marcus (RRKM) theory.58 In the limit that k(E*) is faster than the time-of- flight of the ions, this integration recovers Eq. (7). It is worth emphasizing the energy deposition distribu­tion according to our model. As detailed in Appendix B, the distribution of residual kinetic energy the energy that re­mains in translation after collision and the distribution of deposited energy, according to our model are P(AE) = <r0n( AE)B_ 1/E , (9) P(e) = a0n(E-e)n- 1/E, (9') where E is the residual kinetic energy the energy that remains in translation after collision and is related to the energy transferred by energy conservation, namely E E . This represents the main empirical part of the CID model in Eq. 8 , and is controlled by only one adjustable parameter n. When n= 1, the deposited energy per collision has the maximum value allowed by angular momentum con­servation and the distributions Eqs. 9 and 9 become uni­form functions. Uncertainties in CID threshold measurements are calcu­lated considering a series of sources of error: the variation of the optimized fit parameters 0 , n, and E0 among different data files, the range of parameters that allow reasonably good reproduction of a given set of data, the uncertainty in the vibrational frequencies (±10%-20%), the uncertainty of the experimentally available time for dissociation a factor of 2), and the uncertainty in the collision energy measurement (±0.05 eV, lab. The confidence level of the final uncertain­ties reported is two standard deviations. III. RESULTS A. Integral cross sections The experimental integral cross sections as a function of energy from 0 to 5 eV in the CM frame for the CID of Cr CO 6 with Xe are presented in Fig. 6. The present data are in very good agreement with previous experiments19 on this system performed on the same instrument, in the con­figuration with only one octopole ion guide. CID results in the sequential loss of CO molecules, as in reactions 1 - 3 , with no other products observed in the energy range investi­gated. Even though the integral cross sections on this system have been analyzed previously,19 we perform a complete analysis on the current data as well as on the old data be­cause our methods of analysis with respect to kinetic shifts have become more sophisticated51 in the interim. There are two main differences between the methods of analysis used now versus the ones used at the time of the first CID study reported on the Cr CO 6 system. The first is related to the fact that we generally obtain the primary threshold from fit­ting the total cross section the sum of all product cross sec­tions , whereas in the old analysis, we fit the individual pri­mary cross section. The old procedure involved using an additional model59 to fit the decline in the primary cross section resulting from subsequent loss of another ligand. Collision energy (eV, lab) 0 2 4 6 8 10 12 Cr(CO)6+ + Xe-* ato:a ZrlC.Ci\S _ . 0 1 2 3 4 5 Collision energy (eV, CM) FIG. 6. Integral cross sections for the CID of Cr CO 6 with Xe at a pressure of 0.1 mTorr as a function of collision energy in the center-of-mass frame lower x-axis and laboratory frame upper x-axis . The symbols represent the product cross sections: Cr(CO)5 (open circles), Cr(CO)4 (solid tri­angles), Cr(CO)3 (open squares), and Cr(CO)J (solid diamonds). The solid line represents the total cross section and the vertical lines show the energies investigated in the velocity distribution measurements. This model introduces two additional empirical parameters, increasing the uncertainty of the overall result. The second main difference is related to modeling the kinetic shift. Now we utilize a procedure that provides a more rigorous assign­ment and treatment of rotational modes of the transition state, which are integrated over a statistical distribution, as recently described in detail.51 The vibrational frequencies used in the present analysis are the same as the ones previ­ously assumed and rotational constants have been calculated on the basis of the structures presented in the same reference.19 A representative fit of the total cross section is presented in Fig. 7. A summary of the modeling results is compared to the previous results in Table I. The present analysis yields a 0 K bond dissociation en­ergy for the first CO loss of 1.43 ± 0.09 eV. This is 0.08 eV higher then the value previously reported,19 although within the experimental errors of either measurement. Most of the difference, about 0.07 eV, comes from the different treat­ment of kinetic shift effects as demonstrated by the similar results for old and new data obtained when performing the basic analyses using Eq. 7 Table I . Reanalysis of the Cr CO 5 system using the current procedure yields results within 0.01 eV of the previously reported threshold. Re­analysis of the x 1 -4 systems will not change the thresh­olds reported as these exhibit no kinetic shifts. B. Axial velocity distributions Axial velocity distributions for the primary and product ions were recorded for a series of collision energies: 1.3, 2.0, and 2.7 eV (in the center-of-mass frame and are presented in Figs. 8 and 9. The energies of investigation have been cho­sen to be slightly higher than the apparent thresholds of each of the first three products, as shown by the vertical lines in Fig. 6. A low neutral gas pressure has been used (0.1 mTorr) to minimize multiple collisions that distort the information Downloaded 11 Aug 2009 to 155.97.13.46. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 Ion beam study of dissociation dynamics 1219 Collision energy (eV, lab) 0 2 4 6 8 10 0 12 3 4 Collision energy (eV, CM) FIG. 7. Total cross section for the CID of Cr(CO)6 with Xe, extrapolated to zero pressure, as a function of collision energy in the center-of-mass frame lower x-axis and laboratory frame upper x-axis . The solid line shows a representative fit to the data using the model of Equation 8 with parameters indicated in Table I, convoluted over the energy distributions of the two reactants. The dashed line shows the same model in the absence of energy convolution, for reactants with an internal temperature of 0 K. A 50 times magnification of the threshold region of the cross section is presented in the upper left side of the figure. about collision dynamics. Figure 8 presents velocity distribu­tions for the incident and residual primary Cr CO 6 ions, obtained without and with Xe in the collision cell, respec­tively. It also presents distributions for the sum of all product ions and for the sum of the product and scattered reactant ions. The latter are estimated as described in detail below. Residual primary ion distributions show a high velocity part, which is similar to the incident ion distribution, and tails extending to low velocities. This correspondence at high ve­locities is reasonable because, at this pressure and at these energies, less than 25% of the ions undergo any collisions. As the collision energy increases, the tails decrease in inten­sity, until intensity is completely missing from the low ve­locity part of the tail. Concomitantly, product ion intensity starts to build up around the CM velocity of the system, then shifts toward higher velocities as the collision energy in­creases. Clearly, the product intensity replaces the intensity missing from the tails of the residual primary ions, such that the sum of the two gives smooth, similar looking distribu­tions for all energies investigated. Individual product axial velocity distributions are pre­sented in Fig. 9 for the same series of interaction energies. At TABLE I. Optimized parameters for modeling primary CO loss.a Species 00 n E0 (eV, RRKM)b E0 eV, basic c (CO)5Cr+-CO 46 (9)d 1.7 0.4 d 1.43 (0.09)d 1.59 0.09 d 39 (10) 1.9 (0.5) 1.35 0.08 1.58 0.12 (CO)4Cr+-CO 53 (8) 0.8 0.1 0.64 0.03 0.67 0.04 (CO)3Cr+-CO 72 (12) 1.2 0.2 0.53 0.08 0.53 0.08 "Uncertainties in parentheses. Values from Ref. 19 except as noted. bEquation 8 . cEquation 7 . dPresent results. |1.3 eV | f\ ■ ■ ■ ^............ .>............ ' 3 c 0.0 0.5 1.0 1.5 2.0 CD no 0.5 1.0 1.5 2.0 2.5 Axial velocity (km/s) FIG. 8. Axial velocity distributions for the CID of Cr CO 6 with Xe at a pressure of 0.1 mTorr at 1.3 upper plot , 2.0 middle plot , and 2.7 eV lower plot in the center-of-mass frame. The lines represent primary inci­dent ions, obtained without gas in the collision cell (dotted lines); primary residual ions, obtained with gas in the collision cell (dashed lines); and sums of product ions dash-dot-dot lines . The distribution of scattered ions before dissociation solid line is obtained by adding the sums of the product ions to the residual scattered ions, obtained by scaling down the distribution of primary incident ions dotted lines and subtracting from the distribution of primary residual ions dashed lines . The vertical lines represent the posi­tions of the velocities of the center-of-mass of the system. energies close to their respective thresholds, all products show distributions that are centered around CM , with some tendency for backscattering peaking at a velocity lower than the CM velocity and tails extending to low velocities. As the collision energies increase above their threshold, product ion distributions shift to being forward scattered peaking at a velocity higher than the CM velocity . At higher energies, the forward scattering becomes pronounced, like for Cr(CO)5+ at 2.7 eV. The details of the axial velocity distributions are sensi­tive to collision gas pressure, as presented in Fig. 10. Product ions at their threshold are the most affected, showing a large apparent shift to lower velocities as the Xe pressure in­creases, as with Cr CO 4 in Fig. 10. The apparent back- scattering is thus a result of multiple collisions in the cell. As the pressure decreases, the distributions become more and more symmetric around the CM velocity of the system. At higher energies well above their thresholds, the shape of the product ion velocity distribution is less affected by pressure. Partly because of their larger magnitude, the intensity of slow ions does increase but this only appears as a small tail on the distribution, as with Cr CO 5 in Fig. 10. Downloaded 11 Aug 2009 to 155.97.13.46. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp 1220 J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 F. Muntean and P. B. Armentrout tions are presented along with a detail of the residual reactant ion distributions, focusing on the region around the CM ve­locity of the system. Residual reactant ion distributions do not exhibit signifi­cant large angle scattering, so all observations made from examining the axial velocity distributions still apply. How­ever, the velocity maps show that the depletion at low axial velocities is approximately isotropic around the CM velocity of the system. At 1.3 eV, there is a slight depletion close to the CM velocity in the Cr CO 6 distribution. At 2.0 eV, intensity is missing from a wider region, and is fairly isotro­pic; while at 2.7 eV, the tail of the distribution is almost completely depleted around the CM velocity. Most of the features of the product Cartesian velocity maps are also observed in the axial velocity distributions. In addition, the velocity maps show that, as the collision energy increases, product distributions not only shift to higher axial velocities but also to higher radial velocities, so they peak away from the collision axis. This is most obvious in Fig. 13 in the Cr CO 4 and Cr CO 5 data and will be discussed in Sec. IV. Also, primary product distributions are depleted around the CM velocity as the collision energy increases, most apparent on the Cr(CO)5 distribution at 2.7 eV. FIG. 9. Axial velocity distributions for the products of CID of Cr CO 6 with Xe at a pressure of 0.1 mTorr, at 1.3 (upper plot), 2.0 (middle plot), and 2.7 eV (lower plot) in the center-of-mass frame. The vertical lines represent the positions of the velocities of the center-of-mass of the system. Dotted lines represent normalized distributions of the incident primary ions. C. Cartesian velocity maps Cartesian velocity maps for the same series of energies are presented in Figs. 11, 12, and 13. Product ion distribu- FIG. 10. Axial velocity distributions for the products of CID of Cr CO 6 with Xe at a pressure of 0.05 mTorr solid symbols and 0.20 mTorr open symbols at a collision energy of 2.0 eV in the center-of-mass frame, nor­malized with respect to the magnitudes of Cr CO 5 distributions. The ver­tical line represents the position of the velocity of the center-of-mass of the system. IV. DISCUSSION A. Thermodynamics A detailed discussion of the thermodynamics of the Cr(CO)6+ system has already been published,19 so we will only comment here on the changes made by the present study. The present value for the (CO)5Cr+ - CO bond energy at 0 K is 1.43 ±0.09 eV, 0.08 eV higher than the CID value previously reported, although within experimental uncer­tainty. In order to compare to other available literature values,40,41 we convert our number to a 298 K enthalpy. Fol­lowing the procedure previously explained,19 this results in the addition of 0.052 eV to the 0 K value, yielding a 298 K bond dissociation energy (BDE of 1.48 ± 0.09 eV. The agreement is very good with the appearance energy measure­ments of Michels et al.40 (1.43± 0.04 eV) and with the threshold photoelectron-photoion coincidence measure­ments of Meisels and co-workers41 (1.49 ±0.25), values that are the most reliable, as previously discussed.19 A better check of the thermochemistry is to compare the sum of the BDEs of all six Cr(CO)X(x = 1-6) systems with the known value for the enthalpy of reaction for losing all six CO ligands from Cr(CO)6+ at 298 K,5.23 ± 0.09 eV.19 Our experi­mental value is now 5.25 ± 0.09 eV, where we use our new value for the BDE of Cr CO 6 and previous values for BDEs of Cr(CO)X (x = 1-5).19 Clearly, the agreement is very good, suggesting that the reassigned bond energy is reliable. B. CID dynamics Reactant and product ion velocity distributions provide a thorough picture of the scattering and energy deposition pro­cess in this CID experiment. Because collision dynamics in­formation is distorted when multiple collisions between the primary ions and the neutral target occur, we performed the experiments at a low Xe pressure of about 0.1 mTorr. For Downloaded 11 Aug 2009 to 155.97.13.46. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 Ion beam study of dissociation dynamics 1221 FIG. 11. (Color) Cartesian velocity maps for the CID of Cr(CO)6 with Xe at a pressure of 0.1 mTorr and a colli­sion energy of 1.3 eV in the center-of- mass frame showing: a a detail of the residual primary ion distribution em­phasizing the low velocity tail and its slight depletion around the center-of- mass velocity of the system and b the Cr(CO)5 product distribution. The fill colors represent the intensity scale of data from blue zero to red maxi­mum, 7500 for part (a) and 1000 for part b in arbitrary units . The solid dots represent the position of the ve­locity of the center-of-mass of the sys­tem and the solid line circles ESC represent the expected velocities of elastically scattered reactant ions. The dashed line circles represent the maxi­mum expected product velocity calcu­lated from E+E;-E0, where E, is taken as the average internal energy of the reactant at room temperature 0.35 eV . such a low pressure and at the collision energies investi­gated, we expect most of the Cr(CO)6 primary ions (more than about 75% pass through the collision cell without en­countering any Xe atom. Among the ones that do collide, almost all suffer only single collisions and many of these are grazing collisions. Indeed, Fig. 8 shows that most of the intensity of residual primary ions resembles the distribution of incident ions. It is possible to scale down this latter dis­tribution and to subtract it from the residual primary ion distribution to obtain the distribution of ions that suffered collisions, the scattered reactant ions. An example of this is presented in Fig. 8. The distribution of scattered ions is still bimodal with a peak at velocities very close to the incident ions, although the magnitude of this peak is highly depen­dent on the subtraction procedure. Here, scaling factors of 0.75, 0.73, and 0.73 were used at 1.3, 2.0, and 2.7 eV, re­spectively. The presence of this forward-scattered peak can be explained by grazing collisions. Because these occur at large impact parameters, they are the most abundant type of collision and do not result in appreciable changes in velocity. Among the scattered ions, we expect to see elastic and inelastic scattering. Elastically scattered ions preserve their velocity in the CM frame so they would appear in the ve­locity maps on a circle with radius u;- uCM, centered on CM . The contribution of elastic scattering collisions at large deflection angles is minor for this system, as observed from the residual primary ion distributions in Figs. 11(a), 12(a), and 13 a . Inelastic scattering results in kinetic energy being trans­ferred into internal energy of the scattered ion. As a result, the residual kinetic energy the energy remaining in transla­tion after collision is smaller than the incident energy. These ions will appear as low velocity tails in the residual primary ion distributions. Some of these ions gain enough internal energy to dissociate into products, so they disappear from the primary ion distributions, creating the depletion around CM shown in Figs. 8 and 11-13. The residual reactant ion veloc­ity maps show that primary ion depletion is most pronounced in the region around CM and that it has an isotropic evolu­tion around this point. The fact that the most energized ions are scattered symmetrically in the CM system is characteris­tic of complex formation between the Cr CO 6 ion and the Xe atom. We can extract more information about the dynamics of the CID process by examining the product velocity distribu­tions in Figs. 9 and 11-13. At energies close to their thresh­olds, the products, Cr(CO)5+ at 1.3 eV, Cr(CO)4 at 2.0 eV, and Cr(CO)3 at 2.7 eV, are scattered close to and isotropi- cally around CM . The isotropic behavior is a sign of a com­plex formation mechanism, the most efficient for depositing energy in the threshold region, as also concluded from the depletion of the residual reactant ion distributions. The slight backscattering observed in product distributions at thresholds is mainly a result of multiple collisions, as seen in Fig. 10 and discussed in Sec. III. As the collision energy increases above the dissociation thresholds, the products appear more forward and slightly sideways scattered, as seen for Cr(CO)5 at 2.0 eV, Cr(CO)4 at 2.7 eV, and Cr(CO)5+ at 2.7 eV, in Figs. 9, 12, and 13. The Downloaded 11 Aug 2009 to 155.97.13.46. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp 1222 J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 F. Muntean and P. B. Armentrout FIG. 12. (Color) Cartesian velocity maps for the CID of Cr(CO)6 with Xe at a pressure of 0.1 mTorr and a colli­sion energy of 2.0 eV in the center-of- mass frame showing: a a detail of the residual primary ion distribution em­phasizing the low velocity tail and its visible depletion around the center-of- mass velocity of the system, b the Cr(CO)5 product distribution showing a slight depletion around the center-of- mass velocity, and (c) the Cr(CO)4 product distribution. The filled colors represent the intensity scale of data from blue zero to red maximum, 14 000 for parts a and b , and 5000 for part c in arbitrary units . The solid dots represent the position of the velocity of the center-of-mass of the system and the solid line circles ESC represent the expected velocities of elastically scattered reactant ions. The dashed line circles represent the maxi­mum expected product velocity calcu­lated from E+E;-E0, where E, is taken as the average internal energy of the reactant at room temperature (0.35 eV). trend of the most probable scattering angle is better observed by examining product angular distributions (differential cross sections in the CM frame, Fig. 14. These are obtained by azimuthal and radial integration of the CM velocity maps, which are obtained from the laboratory frame velocity maps by the simple conversions in Eqs. (4)-(6). The most prob­able product scattering angle decreases with collision energy and increases with the order of the product in the sequence. Care should be taken when examining the products formed just above their thresholds at each kinetic energy, because the intensity of these species at large scattering angles is mainly an artifact of multiple collision effects, as discussed above. The trends in the product angular scattering distributions can be rationalized by considering angular momentum con­servation during the collision. In order to observe a product, a minimum amount of energy has to be deposited, the thresh­old energy for that product. Angular momentum conserva­tion limits the amount of energy that can be deposited to the kinetic energy along the radial direction, the LOCs of the two reactants, in the CM frame. Consequently, there is a maximum impact parameter that can deposit the threshold energy E 0 for formation of a particular product. The maxi­mum is attained when the energy along the LOCs equals E0 and this LOC energy is deposited with 100% efficiency. As demonstrated in Appendix C, the maximum impact param­eter translates into a minimum scattering angle min defined by Eq. 10 cos2(/3min) = (E+E;-E0)/E, (10) where E is again the relative collision energy and E i is the average internal energy 0.35 eV for Cr CO 6 at room tem­perature]. Note that the energy term in Eq. (10 is the same as that for Eq. (7) when ra= 1, i.e., the LOC cross section. The predictions of relation 10 , using the threshold val­ues of Table I, are represented in Fig. 14 by vertical bars. The most probable angle of the experimental distributions is in reasonable agreement with the trend predicted by relation Downloaded 11 Aug 2009 to 155.97.13.46. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 Ion beam study of dissociation dynamics 1223 FIG. 13. Color Cartesian velocity maps for the CID of Cr CO 6 with Xe at a pressure of 0.1 mTorr and a colli­sion energy of 2.7 eV in the center-of- mass frame showing: (a) a detail of the residual primary ion distribution em­phasizing the depletion of its low ve­locity tail around the center-of-mass velocity of the system, b the Cr CO 5 product distribution, also showing depletion around the velocity of the center-of-mass, c the Cr CO 4 product distribution, and d the Cr CO 3 product distribution. The filled colors represent the intensity scale of data from blue zero to red maximum, 75 000 for parts a and (b), 37 500 for part (c), and 7500 for part d in arbitrary units . The solid dots represent the position of the ve­locity of the center-of-mass of the sys­tem and the solid line circles (ESC) represent the expected velocities of elastically scattered reactant ions. The dashed line circles represent the maxi­mum expected product velocity calcu­lated from E+E;-E0, where Et is taken as the average internal energy of the reactant at room temperature 0.35 eV . 10 . In addition, the fact that the angular distributions peak close to the minimum angle set by angular momentum con­servation indicates that energy is deposited with high effi­ciency. It is also worth mentioning that this efficient energy transfer is observed for all energies investigated, covering the entire energy range over which integral cross sections are usually modeled. C. Residual kinetic energy distribution The residual kinetic energy E is the kinetic energy of primary ions after collision before dissociation and it is a function of the energy deposited into internal modes during collision. Its empirical distribution in our model is given by expression 9 . The energy range in which we are interested Downloaded 11 Aug 2009 to 155.97.13.46. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp 1224 J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 F. Muntean and P. B. Armentrout FIG. 14. Angular distributions in the center-of-mass frame for the products of Cr(CO)6+ CID with Xe at a pressure of 0.1 mTorr at collision energies of 1.3 (upper plots), 2.0 (middle plots), and 2.7 eV (lower plots), obtained from the experimental velocity maps. The vertical lines represent the cutoff angles predicted by angular momentum conservation, Eq. (10, calculated using the product threshold values in Table I. The scatter of the data points is a result of the different procedures used to obtain the distributions and is a measure of the experimental uncertainties. is from 0, where all the collision energy is deposited, to E + Et - E0, the limit for inducing dissociation. This distribu­tion is the most empirical part of our modeling and it con­trols all kinetic shift effects in our model. The complete ex­perimental velocity maps for the CID process enable us to obtain experimental distributions of the residual kinetic en­ergy for the first time in the threshold energy range. This provides a test of our model and potentially the means to improve it. Because CID involves the interaction of more than two particles, we have to make an approximation in order to be able to extract energy transfer information from the mea­sured velocity distributions. A common28 approximation is to assume that the velocity distributions of product ions are similar to the ones of the energized ions from which they derive. This is supported, first, by the fact that in the thresh­old energy region of a CID process, as in any endoergic reaction, the kinetic energy release to products is necessarily small. Second, for a complex system like Cr(CO)6 at the low energies investigated here, the kinetic energy release to prod­ucts appears as an isotropic broadening of the velocity dis­tribution of the scattered primary ions Fig. 8 indicating that dissociation is generally slower than one rotational period of the complex. Finally, for this system, the mass ratio between the investigated product ions, Cr(CO)X (x = 3-5) and prod­uct neutrals, CO, is fairly big, which means that most of the kinetic energy release goes to the product neutral and not to the product ion, because of momentum conservation. Indeed, Fig. 8 shows nicely that the depletion of the primary ion distribution is filled smoothly by the sum of product ion distributions at all energies investigated. As a result, the re­sidual kinetic energy distributions can be obtained with good fidelity by adding up the kinetic energy distributions of scat- tered primary ions and those of the products. Experimental kinetic energy distributions are obtained from the velocity maps. The lab-frame velocity maps are first transformed into CM velocity maps using relations (4)-(6). Next, we obtain CM velocity distributions P (u) for the scat­tered ions. This is done by integrating the intensity of the CM velocity maps Pm(u) corresponding to every particular CM velocity u, over all space: "2tt CTT C2 TT f TT P„,(u)u{ 0)sin OdOdip Jo Jo = 2it Pm(ii)u(0)sin 0d0, (1D where 0 is the CM scattering angle and <p is the azimuthal angle. Because the collisions are cylindrically symmetric, u has no <p dependence and the latter integral is just 2tt. Fi­nally, we convert the above distributions into CM kinetic energy distributions using the relation between the CM ve­locities and CM kinetic energies E= H miimt + mj / mju2, (12) where indices i and n stand for reactant ion and neutral, respectively. This conversion requires an intensity transfor­mation (Jacobian) that has been included. Residual kinetic energy distributions for the same set of energies analyzed above, are presented in Fig. 15. The dis­tributions shown are sums of distributions of residual reac­tant and product ions, as discussed above. We observe a high energy peak and a tail extending to zero kinetic energy. The high energy peak (not fully shown in Fig. 15 is mainly a result of unscattered and slightly scattered primary ions, which are part of the measured residual primary ion distri­butions. Although we could isolate out the unscattered ion distributions with some degree of accuracy, as exemplified in Fig. 8, this is not worthwhile here because this procedure affects only the magnitude of the high energy peak, which is outside the energy range over which dissociation is possible. The arrows in Fig. 15 emphasize this energy range. All of the information about collision energy deposition that is relevant for CID is contained in the low energy tails of the distributions in Fig. 15. A very important observation is that the intensity extends to zero residual energies, within experimental error, for all of the collision energies investi­gated. This signifies that the energy deposition the differ­ence between the collision energy and the residual energy E-AE) reaches the point of 100% of the energy being de­posited. Of course, the probability of E 0 is zero, because this can occur only for zero impact parameter collisions, which have no orbital angular momentum. Thus, the fact that the experimental residual kinetic energy distribution extends to zero is a necessary condition for thermodynamic determi­nations using CID. Figure 15 also shows the energy limits predicted by an impulsive model32,33,60 according to which only one atom or group of atoms of the molecule interacts with the neutral gas atom, and the interaction is totally elastic. This model 0 Downloaded 11 Aug 2009 to 155.97.13.46. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 Ion beam study of dissociation dynamics 1225 1.0 FIG. 15. Residual kinetic energy distributions of Cr(CO)6 ions as a result of collisions with Xe at a pressure of 0.1 mTorr at collision energies of 1.3, 2.0, and 2.7 eV, obtained from the experimental velocity maps. The high-energy peaks of the distributions, containing the contribution of unscattered primary ions, are off scale in the figures. The energy region over which dissociation is possible is represented by the arrows. The impulsive model Eq. 13 predicts that there should be no residual energy below the limits indicated by the vertical lines. Solid lines represent the best fits to the data using the model of Eq. (9) with parameters n indicated in the figures. The different sets of points are the result of the different procedures performed to the Cartesian velocity maps before converting into CM energy distributions: no procedure circles , linear extrapolation to zero radial velocity triangles , and linear extrapolation of the raw velocity distributions representing azi­muthally integrated Cartesian velocity maps to zero radial velocity. predicts an upper limit to the energy deposition that is always less than unity. In terms of the residual energy, the lower limit predicted is given by 1 4 mnma(mn + mi)(mi-ma) (Mn + mJ 2m 2„„2 E, (13) where ma is the mass of the atom (or group that interacts with the neutral, and the rest of the quantities have been defined before. In the present system, we consider the CO group as the interacting part and obtain a 19% minimum residual energy (81% maximum energy deposited. These limits are clearly exceeded by the experimental distributions, Fig. 15, indicating nonimpulsive behavior for this system. Finally, we compare the experimental residual energy distributions with the predictions of our empirical model Eq. (9. The best fits and the corresponding values of parameter n are presented in Fig. 15. Clearly, the experimental distribu­tions are reproduced by the empirical model Eq. (9 over the entire region of interest, within experimental uncertainties. Although the scatter in the data accommodates a range of cn ns E 0.5 a> > as a) a. o.o \ Energy deposition function 2.7 eV \ \ \ V 0.0 0.5 1.0 1.5 2.0 Energy (eV, CM) 2.5 3.0 3.5 FIG. 16. Deposited energy distribution model (solid line); a plot of Eq. (14) convoluted over a Gaussian energy distribution of reactant ions. The param­eters used in the plot are A = 0.46, B = 0.71, n= 1.75, E = 2.7 eV, and FWHM=0.5 eV. The first term (dash-dot line and the second term (dashed line of the model of Eq. 14 are also represented in the figure. parameters, the model predicts the correct energy depen­dence. Further, the best values of parameter n in the fits in Fig. 15 are in good agreement with the values found from fitting the integral cross sections Table I , within uncertain­ties. Although model 9 has been indirectly verified before, as explained in Sec. I, this is the first direct experimental test of the energy transfer model 9 used in CID integral cross section modeling. D. Deposited energy distribution The above analysis of the experimental distributions of residual kinetic energy allows us to derive a simple model for the distribution of energies deposited by collisions in CID f(s)=Ae -4 ln2(e/FWHM) + B(E-s)n^1/E. 14 A plot of the model distribution is presented in Fig. 16 for a set of parameters typical to the present CID experiment. The model assumes that the deposited energy distribution has the form of Eq. 9 . This yields the second term in Eq. 14 , which represents the bulk of the energized ions. The energy dependence of this tail is controlled by the exponent n, and its magnitude by the parameter B. The tail extends to a de­posited energy equal to the incident energy E, where the distribution has zero magnitude. The first term in Eq. 14 represents the ions that suffer grazing collisions, the most abundant type of collisions, which deposit little amounts of energy. The peak is centered on zero deposited energy, the most probable value, and approximated by a Gaussian with an amplitude given by parameter A and a FWHM roughly equal to that of the incident kinetic energy distribution CM frame . The Gaussian dependence has been chosen for sim­plicity, because this part of the deposited energy distribution cannot lead to dissociation and is therefore less interesting for most applications. The relative magnitude of the two scaling factors, pa­rameters A and B, is difficult to evaluate from the present experimental data. This is especially because we cannot mea- Downloaded 11 Aug 2009 to 155.97.13.46. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp sure velocity distributions of ions scattered at small angles, so we cannot quantitatively determine the magnitude for the grazing collision term in the model of Eq. 14 . The choice of scaling factors in the model plot of Fig. 16 is representa­tive of the data for the scattered ion axial velocity distribu­tions Fig. 8 . The model in Eq. 14 corresponds to monoenergetic incident reactant ions. When compared to experimental re­sults, Eq. 14 needs to be further convoluted42,61 over the experimental kinetic energy distribution of the incident reac­tant ions. The main effect of the convolution is observed as an extended tail of the distribution, beyond the incident en­ergy E. An example of the convoluted model is also pre­sented in Fig. 16. 1226 J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 transfer at threshold, while a high value, above 2, is the sign of a poor energy transfer in the threshold region. F. Muntean and P. B. Armentrout ACKNOWLEDGMENTS The authors thank D. Gerlich for enlightening discus­sions, S. L. Anderson for supportive advice throughout, and K. M. Ervin and R. A. Dressler for very helpful hints related to the implementation of differential scattering measure­ments on our instrument. K. M. Ervin is also thanked for a very helpful review and for focusing the discussion in Ap­pendix B. This work is supported by the National Science Foundation. V. CONCLUSIONS The threshold energy region of the CID of Cr(CO)6 is investigated by both integral and differential cross section measurements on a recently modified guided ion beam tan­dem mass spectrometer. The instrument has been updated with a double octopole system that offers significantly better resolution for TOF measurements, allows studies of dissocia­tion lifetime effects, and rapid measurements of product en­ergy distributions, among other uses. Integral cross sections for sequential CO losses are ana­lyzed as a function of energy using our recently devised sta­tistical model.51 A revised value for the (CO)5Cr+-CO bond dissociation energy of 1.43 ± 0.09 eV shows very good agreement with known literature values.40,41 Double differential scattering is investigated at a series of energies (1.3, 2.0, and 2.7 eV, CM covering the entire range of modeling for the total integral cross sections. Scat­tering velocity maps for reactant and product ions reveal a detailed picture of the collision and dissociation dynamics. No significant elastic or superelastic scattering is observed in the reactant ion maps. Product velocity maps show peaks at scattering angles that are close to the limit set by angular momentum conservation, indicating an efficient energy transfer at all energies investigated. Quantitative information concerning energy deposition in the collision event is obtained from the residual kinetic energy distributions that are derived from the scattering ve­locity maps. Residual kinetic energy distributions extend to zero, corresponding to 100% energy deposition, clearly be­yond the limit set by an impulsive mechanism for this sys­tem. A direct comparison between the experimental residual energy distributions and the predictions of the CID threshold model is performed for the first time. The agreement is very good within experimental uncertainties. On the basis of this analysis, a model for the distribution of energy deposited by collisions is derived, Eq. 14 . Further studies may be performed to gain a complete description of the energy transfer in the threshold region of the CID process. Other systems envisioned include ones that exhibit very different energy transfer efficiencies. Candidates may be selected according to the optimum value of param­eter n obtained in integral cross section modeling. A very low value of n, below 1, signifies a highly efficient energy APPENDIX A: TOF TO AXIAL VELOCITY CONVERSION Primary ion TOF distributions are converted into axial velocity distributions using: tt=t0 +11h i+l 2^v 2 + 2 q;A V/ (A1) where the first term 10 represents the TOF outside the octo- poles basically from the end of the second octopole to the detector , the second term is the TOF spent in the first octo- pole, and the third term is the TOF spent in the second oc- topole. Indices i refer to primary ions, t is the total TOF measured, are axial velocities, q and m are the charge and mass of ions, l1 and l2 are effective lengths of the two octo- poles, and V is the dc offset between the two octopoles. The parameter t0 is a constant of the experiment, determined during a calibration procedure, as shown below. Product TOF distribution are converted into axial veloc­ity distributions using: tp = t0Vqmp/qpmi+lp /vp±l2/^ + 2q^AV/mp + (l 1- lp)/{v i), (A2) where the significance of the first three terms is similar to the ones in Eq. A1 . The fourth term represents the TOF spent by primary ions in the first octopole, before collision. Indices p refer to product quantities and lp is the distance from the middle of collision cell to the end of the first octopole 11.8 cm . In order to determine the parameter t0, we perform a calibration following a procedure previously described.36 Briefly, we first measure average times of flight t for a series of octopole dc floating voltages, then we use Eq. A3 to determine starting values for parameters t0 and V0 U = t 0 +11/V2 qAV-V „)/mt+l 2/V2 qAV+AV-V„)/mt. i i i i iA3 Here, V is the dc floating voltage of the first octopole and parameter V0 represents the difference between the dc volt­age set and the actual potential inside the first octopole with respect to the ion source, due to field effects in the ion source, contact potentials, surface charge, etc. Finally we perform an iterative calculation according to the procedure previously described36 to obtain the final values of the three parameters. Downloaded 11 Aug 2009 to 155.97.13.46. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp All of the conversions described above require intensity (Jacobian) transformations that have been included in our data reduction procedures. APPENDIX B: DEPOSITED ENERGY DISTRIBUTION Consider the expression Eq. (7) of the cross section de­pendence of energy in our model. For simplicity, we assume the case of no internal energy of the reactants <r(E) = o-0( E-E„)7E. (BI) Usually, the cross section is expressed as a function of the impact parameter b f ^Iiki \ ■ ! (t{E) = 2tt P{b)db, (B2) Jo where for a collision between structureless particles (n = 1), the reaction probability, P(b), equals b for 0<b bmax and zero for b bmax. In this case, the maximum energy that can possibly be transferred into internal degrees of freedom is the energy along the line of centers between the two reactants: e = E(1- b2/d2), where d is the sum of the radii of the two reactants and <x0= ird2. Because of the one-to-one correspondence between the impact parameter and the deposited energy in our model, the cross section can also be expressed in terms of as <r(E) = \E P(e)de, (B3) JE o where P( ) is the energy transfer function. To recover Eq. B1 , it is straightforward to show that P(s) = <r0n{E-e)n~ 1/E. (B4) Previously,19 we derived this function in terms of the energy left in translation after collision E, which is related to by energy conservation E E such that P( ) = P(AE) = a0n(AE)n~1/E. For collision-induced dissocia­tion reactions, we also need to introduce into this integration the probability for dissociation PD(e). This is given by sta­tistical unimolecular rate theory and has previously19 been identified as PD(s)= 1-exp[-k(e)r\ where k(e) = k(E*) and are defined in the text and this quantity is zero except when E0<e<E. This gives the equation originally derived elsewhere19 in terms of AE and reproduced as Eq. (8) in terms of . We also comment on an alternative energy deposition function suggested without justification by Anderson and co-workers,62 namely P(e) = (1-e/E)n_ 1, (B5) although normalization constants needed to substitute di­rectly into Eq. (B3) are not specified. Nevertheless, this form of the deposition function will eventually yield a cross sec­tion form comparable to <x(E) = <x0(1 - E0/E)n, even though Anderson and co-workers also utilized Eq. B1 to reproduce their data. However, the distribution function of Eq. B5 is also capable of reproducing the data shown in Fig. 15, with the only distinction being different scaling fac­tors. Hence, the present experiments cannot distinguish be- J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 Ion beam study of dissociation dynamics 1227 FIG. 17. Vector diagram describing the velocity components for a two-body collision reduced to the interaction between a particle of mass /i. and veloc­ity and a radial field centered at CM. The incident and scattering velocities are and , respectively. The incident and scattering angles are and , respectively. LOC indicates the radial direction, which corresponds to the line-of-centers of the two particles, whereas t refers to the transverse direc­tion, i.e., the velocity associated with the orbital angular momentum. r in­dicates the fraction of the LOC velocity that is elastically scattered. tween the functions Eqs. (B4) and (B5). Our preference for (B4) lies in the cross section form, as discussed in detail elsewhere.53 APPENDIX C: INELASTIC SCATTERING Consider the collision of two particles with masses m j and m 2 and a relative velocity u. This problem can be treated as the motion of a particle with the reduced mass = m 1 m2/(m^m2) and velocity u in a radial potential cen­tered at the CM of the two particles Fig. 17 . Velocity can be broken down into two components: one radial, lying along the line-of-centers of the two particles, uLOC cos , and one perpendicular to the line-of-centers, t sin . The latter velocity defines the orbital angular mo­mentum of the system and is approximately conserved, as­suming that rotational excitation of the particles is minor compared with the orbital angular momentum. We now con­sider that part of the line-of-centers energy is deposited into internal modes of the particles, such that only a fraction r is retained in translation. r can vary from 1 for a totally elastic collision hard spheres approximation to 0 for a totally in­elastic collision, i.e., 100% efficient energy deposition. The relative velocity of the scattered particles is now described by , which is the vectoral sum of t t and LOC = -rv LOC. The angle between v and uLOC is a and the scattering angle is . For elastic collisions, r 1, 2 = 180°, whereas for inelastic collisions, r= 0, a + /3 = 90°. Note that for grazing collisions, where 90° , 0° for both elastic and inelastic collisions. However, for head-on collisions, where a = 0°, /? reaches a different limit, back­ward scattering for elastic interactions, ^ = 180°. For inelas­tic collisions, there is sideways scattering, 90° , but with zero magnitude because all the energy has been deposited into internal modes. The general relationship between a and is defined by Eq. C1 tan 1 r tan / tan2 r . C1 Note that when r 0, tan cot . Dissociation cannot occur unless the deposited energy s plus the reactant internal energy Ef exceeds the threshold energy E0, therefore, e 3= E0 - E{. The deposited energy Downloaded 11 Aug 2009 to 155.97.13.46. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp 1228 J. Chem. Phys., Vol. 115, No. 3, 15 July 2001 F. Muntean and P. B. Armentrout equals s = ijl\_(1 - r)ucosa]2/2, and in the limit where r 0, it is simply E cos2 Esin2 . 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