J. Phys. Chem. 1996, 100, 19227-19240
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FEATURE ARTICLE Rotational and Vibrational Energy Effects on Ion-Molecule Reactivity As Studied by the VT-SIFDT Technique A. A. Viggiano* and Robert A. Morris Phillips Laboratory, Geophysics Directorate, Ionospheric Effects DiVision (GPID), 29 Randolph Road, Hanscom AFB, Massachusetts 01731-3010 ReceiVed: July 12, 1996; In Final Form: September 18, 1996X
A method is described for measuring internal energy dependences of gas phase ion-molecule reactions in a variable temperature-selected ion flow drift tube (VT-SIFDT) instrument. Numerous studies have been conducted to examine the effects of both rotational and vibrational excitation on rate constants and branching ratios. Rotational and translational energy are found to be equally efficient at driving endothermic reactions. For exothermic reactions, large rotational effects are found only when one or both of the reagents have a large rotational constant. This indicates that changing from a low to moderate J value can affect reactivity but that changing from moderate to high J has little influence on reactivity. Vibrational effects are more varied. In some reactions, vibrational excitation in the anticipated reaction coordinate strongly affects reactivity, while in other cases it does not. Vibrational effects are often observed in charge transfer reactions, presumably due to energy resonances and Franck-Condon arguments. For the SN2 reactions studied to date, vibrations play no role in governing reactivity for halide ions reacting with methyl halides, while vibrations are equivalent to other types of energy in influencing the reactivity of non-methyl halide systems.
Introduction The flowing afterglow and its successors have proven highly versatile for studying a large variety of ion-molecule reactions under many conditions. Since its introduction to this field in the early 1960s,1 the flowing afterglow technique2 has been used to examine literally thousands of reactions,2 and a large number of variations of the technique now exist with a wide range of capabilities. Good historical papers are those of Graul and Squires3 and Ferguson.4 Of particular interest for this review is the advent of the variable temperature flowing afterglow,5 the flow drift tube,6-8 and the selected ion flow tube.9 These three capabilities were combined for the first time into a variable temperature-selected ion flow drift tube (VT-SIFDT) by Adams and Smith.10 This allowed kinetic energy dependences to be measured at several temperatures, thus allowing the effects of temperature and kinetic energy on reactivity to be measured independently. Smith and Adams used the information obtained to relate kinetic energy to temperature simply as KE ) nkT, where n was a parameter to be derived from the data.10 Upon introduction of a VT-SIFDT in our laboratory, we realized that one could obtain more detail from the data, namely, that information on the effects of translational, rotational, and vibrational energy could be separated.11 A key to separating the effects of individual types of energy was the ability to reduce the relative error limits in the kinetics data by measuring all key parameters such as velocity and end corrections for every data point.12 Since that time we have used the VT-SIFDT to study dozens of reactions as a function of internal energy. In some instances we have been able to derive information on individual vibrational levels, but more often we measured the effects of rotational or vibrational temperature on reactivity. We X
Abstract published in AdVance ACS Abstracts, November 1, 1996.
have focused on the effects of internal energy since the effects of translational energy have been studied extensively in beam and drift tube apparatuses. At the NOAA labs, researchers have compared variable temperature and drift tube data obtained in separate apparatuses.13,14 In this paper we summarize our results on internal energy dependences derived from VT-SIFDT data. There is a variety of techniques that have been used to study the effects of rotational and vibrational energy on reactivity. Many of the techniques have been reviewed in an excellent book15 and will not be discussed at any length here. However, we will compare the present technique to those used elsewhere to study internal energy effects. Most other techniques involve photoionization to vibrationally state select the ion. Multiphoton ionization (MPI) has been used by a number of groups.16-23 The most comprehensive study involving MPI has been the recent work of Anderson and co-workers on the [C2H2:OCS]+ system, where they examined the effects of nine different vibrational levels of the two ions as well as studying kinetic energy dependences and differential scattering of the products.18 Two coincidence techniques have been used to study internal energy dependencies, namely, threshold electron secondary ion mass coincidence (TESICO)24 and photoelectron photoion coincidence (PEPICO).25,26 Both of these techniques are wellsuited to study vibrational effects but have difficulty with rotational state selection. Gerlich has used the guided ion beam technique in several different forms to study internal energy effects.27 This is not a comprehensive list but is intended to give a flavor of the techniques used. Aside from the present technique, fast flow systems have been used in a variety of ways to examine vibrational effects. The monitor ion technique determines the state of the ion chemically.28 Varying the identity of the buffer gas in a flow-drift tube allows one to obtain crude information on the effect of the ion internal temperature.14 Vibrationally exciting the
S0022-3654(96)02084-9 This article not subject to U.S. Copyright. Published 1996 by the American Chemical Society
19228 J. Phys. Chem., Vol. 100, No. 50, 1996
Viggiano and Morris
Figure 1. Schematic of the variable temperature-selected ion flow drift tube.
reactant neutral in a microwave discharge has proven useful in certain cases.29 More detailed studies, performed by Leone, Bierbaum, and colleagues, have involved vibrationally exciting the ion by varying the injection energy in a SIFT and monitoring the excitation by laser techniques.30 It is useful to compare the advantages and disadvantages of our technique to those used elsewhere since most of the techniques are complementary; i.e., they study different aspects of the problem. The photon-based techniques have many common features and will be discussed together. The main advantages of the VT-SIFDT technique are the ease of use and the wide variety of accessible systems. Essentially any ion or neutral (with sufficient vapor pressure) can be studied, although for larger systems less detailed information is obtained. In contrast, laser-based studies often provide exquisite detail, at the expense of ease and versatility, as to how vibrations and sometimes rotations affect reactivity. For instance, MPI excitation schemes are difficult to devise, and signal levels are often low. Neutral photoexcitation is very difficult to control, and complex schemes such as stimulated emission pumping are needed. For this reason few studies outside of the VT-SIFDT work reported here focus on the excitation of the neutral reagent. Some of the laser-based methods (e.g., MPI) are capable of measuring rotational effects, but few such studies have been made. The information obtained on rotational effects in the VT-SIFDT is not at all detailed but has provided considerable insight into how rotations affect reactivity. Product state detection in a flow tube without lasers is possible but extremely difficult.31 Laser-based techniques have provided a wealth of data on product states. Experimental Technique The technique employs a variable temperature-selected ion flow drift tube (VT-SIFDT) instrument, originally developed by Smith and Adams.32 This type of apparatus is a product of the development and improvement of the earlier fast flow techniques for ion chemistry, namely, the flowing afterglow (FA)33 and conventional selected ion flow tube (SIFT)9 instruments. All of these techniques involve kinetics measurements in a fast flow of inert buffer gas under pseudo-first-order conditions (large excess of neutral reactant) with mass spectrometric ion detection. The VT-SIFDT instrument at Phillips Laboratory has been described previously12 and is shown schematically in Figure 1.
Since internal energy effects are studied by making measurements as a function of drift tube electric field at several different flow tube temperatures, we will emphasize that aspect of the experiment. Only a brief discussion of the standard part of the technique is given. The reactant ions are prepared from appropriate precursors in a high-pressure ion source which is external to the flow tube. The ions exit the source and enter a quadrupole mass filter which transmits the selected reactant ion of interest and excludes all other ion masses. The reactant ions then pass through a Venturitype inlet into a fast flow of He buffer gas (∼10 000 cm s-1 at ∼0.4 Torr) in a 1 m flow tube. The buffer gas transports the ions along the flow tube and also serves to thermalize the ions via thousands of collisions upstream of the reaction region. In the downstream half of the flow tube the reactant neutral gas is introduced through one of two ring-shaped inlets. The inlets are 4 cm diameter rings fabricated from 1/8 in. o.d. stainless steel tubing, with eight 0.4 mm diameter holes pointing upstream. Two inlets at different reaction distances are used in order to measure the end effect correction which takes account of the finite distance for mixing of the reactants. This procedure is followed for every measured data point since the end correction varies slightly with experimental conditions. At the downstream end of the flow tube, a fraction of the gas is sampled through a 0.2 mm diameter orifice in a blunt nose cone, while most of the gas is pumped by a Roots-type pump. The sampled reactant and product ions are mass analyzed by a second quadrupole and detected with a channeltron particle multiplier. Rate constants are obtained from the slope of a linear leastsquares fit of the logarithm of the reactant ion signal as a function of reactant neutral concentration. The experiment can be operated over the temperature range 85-550 K. A copper heat exchanger invaginating the flow tube houses both resistive heaters and liquid nitrogen cooling lines. The He buffer gas is preheated or precooled as it passes through a copper line in the heat exchanger. Direct temperature measurements made along the reaction region of the flow tube have shown us that additional precooling of the He is necessary for low-temperature measurements; this is accomplished by cooling the Venturi inlet injector flange with liquid nitrogen. The entire temperature-controlled region is contained within a large vacuum box which acts as a Dewar. The flow tube contains a drift tube for varying the ion kinetic energy. The drift tube is constructed of 60 identical stainless
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steel rings of 6.0 cm i.d., 6.3 cm o.d., and 0.9 cm length. The rings are separated from one another by 0.1 cm ceramic insulators and are connected together electrically by a series of resistors external to the vacuum system. A voltage from a stabilized power supply applied to the resistance chain produces a uniform electric field in the drift tube. The two reactant neutral ring inlets pass through small gaps in two corresponding drift tube rings, and each inlet is connected electrically to the ring through which it passes. Ion flight times are measured by applying retarding pulses to each of two drift tube rings 20 cm apart in the reaction region. The arrival times of the ion signal perturbations caused by the pulses are measured using a digital time-of-flight unit connected to a multichannel analyzer. By pulsing two rings, end effect errors in the time-of-flight measurements are canceled, and the ion velocity is obtained from the distance between the two rings divided by the difference in the two flight times. Drift velocity is calculated by subtracting the ion velocity measured at zero drift electric field from the ion velocity measured at the drift field of interest. This procedure is followed for each experimental condition, i.e., at each temperature and each drift electric field strength. The average kinetic energy of collision in the ion-neutral center-of-mass reference frame (〈KEcm〉) is calculated from the drift velocity using the Wannier expression.6-8,34 The Wannier expression has been shown to be a good approximation, especially for monatomic ions drifting in monatomic gases.35,36 The reproducibility of the rate constant values is typically (4% but can be as poor as (8% for worst-case situations such as low reactant ion signal or small extent of ion decay. A standard error propagation analysis was carried out12 using the following sources of measurement error: reproducibility, 8%; temperature, 2%; pressure, 1%; ion flight time, 3%; He flow rate (relative, 1%; absolute, 2%); reactant neutral gas flow rate (relative, 3%; absolute, 15%). These errors lead to overall uncertainties of (10% for relative error and (18% absolute error; relative error is the uncertainty in the ratio of two data points. We report as final relative and absolute uncertainties (15% and (25%, respectively, to account for the possibility of systematic errors not treated in the above analysis. Experimental evidence37 presented later in this section, however, indicates that the above error limits are in fact conservative and that there is little additional systematic error. A convenient form12 of the Wannier expression34 for describing the 〈KEcm〉 in a VT-SIFDT is
〈KEcm〉 )
(mi + mb)mn 2 3 V + kT 2 2(mi + mn) d
(1)
where mi, mb, and mn are the masses of the reactant ion, buffer gas, and reactant neutral, respectively, Vd is the reactant ion drift velocity, and T is the temperature. The first term describes the component of the collision energy imparted by the drift electric field, while the second term is the thermal component due to the real gas temperature. This expression shows that a particular 〈KEcm〉 can be obtained with varying contributions from the drift field component and the real temperature component, i.e., various combinations of electric drift field strength and gas temperature. By measuring rate constants (or branching ratios) as a function of drift field at several temperatures, we obtain a separate 〈KEcm〉 dependence curve (rate constant or branching ratio plotted versus 〈KEcm〉) for each temperature. If these curves do not fall on top of one another, then at a given 〈KEcm〉 the difference between rate constants (or branching ratios) measured at different temperatures results from the effect of
the corresponding different internal temperatures of the reactants (since the kinetic energy of collision is fixed). Graphically, this corresponds to taking a vertical slice through the set of 〈KEcm〉 dependence curves at a given 〈KEcm〉 to obtain the dependence on the reactant internal temperature. For the above analysis to be valid, the velocity distributions of the ions must be similar at the different applied drift fields. The use of a He buffer ensures that the velocity distributions are adequately approximated by a Maxwellian distribution,38,39 which in turn ensures that the kinetic energy distributions are similar, whether electric field or temperature is used to increase the kinetic energy. This has been predicted40 and demonstrated38,39 previously to be the case. The ability to approximate the kinetic energy distributions as Maxwellian means that the kinetic energy dependence of ion-molecule reaction kinetics measured in a He buffer does not differ within experimental uncertainty from what would be found for a Maxwellian distribution.36,38,41-43 For example, in the case of the reaction of N+ + NO where there is only a weak kinetic energy dependence, less than a 2% correction is needed to convert the rate constants measured in a He-buffered drift tube to what would be found for a Maxwellian distribution.42 An example of a reaction which is very sensitive to kinetic energy is the Si+ + O2 system, the rate constant for which varies by a factor of 30 over the energy range from thermal to 1 eV at 300 K, but here a correction of less than 10% is needed despite the high sensitivity of the reaction to the kinetic energy distribution.43 The derivation of internal energy dependences from the VTSIFDT data is most straightforward when the reactant ion is monatomic and therefore cannot be internally excited. For reactions of monatomic ions, the internal temperature dependence refers to the internal temperature of the reactant neutral, which is defined by the buffer gas temperature. For diatomic reactant ions, it is often the case that only rotations are excited; i.e., the vibrational frequencies are high enough so that no vibrational excitation occurs at the temperatures and drift electric fields used in the study. (Diatomic reactant ions can be vibrationally excited intentionally by injecting them at high energy into the flow tube.) Often rotations have little effect on reactivity, so in many cases data analysis for diatomic ions is straightforward. For polyatomic ions, the ion internal modes can be excited, making the interpretation of the results significantly more complicated, as shown later in the paper. If we restrict ourselves to cases of monatomic ions reacting with neutrals which have only high-lying vibrational levels, levels which are not populated at the temperatures of the experiment, e.g., diatomics,44 then the internal temperature dependence refers to the dependence on the rotational temperature of the reactant neutral. In cases where excited vibrational levels of the neutral reactant are populated at our experimental temperatures, then the internal temperature dependence relates to a combination of possible effects from both vibrations and rotations. As an early test of the technique, we studied a reaction between a monatomic ion and a monatomic neutral, where there can be no internal excitation of either the ion or the neutral reactant. The system studied37 was the symmetric charge transfer reaction between isotopes of neon, specifically 22
Ne+ + 20Ne f 20Ne+ + 22Ne
(2)
Since there are no internal modes in the reactants, we expect to see 〈KEcm〉 dependences which fall on top of each other to define a single 〈KEcm〉 dependence curve which is independent of temperature at a particular 〈KEcm〉. Figure 2 shows that this is exactly what was found. No difference is observed between
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Viggiano and Morris TABLE 1: Reactions Studied as a Function of Rotational Energy in the VT-SIFDT reaction
Figure 2. Rate constants for the reaction of 22Ne+ with 20Ne as a function of average kinetic energy at several temperatures.37 Relative error bars of 15% are shown.
the 〈KEcm〉 dependence curves measured at different temperatures. The curves coincide with one another to better than 10%, within our quoted relative error of 15%. In order to better understand the present results, it is useful to have a general understanding of “typical” drift tube behavior. Typical behavior can be grouped into two classes, fast and slow reactions. For fast reactions the rate constants either remain constant or decrease slowly with increasing kinetic energy in the low-energy regime. Often at higher energies the rate constants decrease more rapidly. The dependence on kinetic energy for slow reactions is more complicated. At low kinetic energies the rate constants are found to decrease with increasing energy. At some intermediate energy the rate constants level off and then start to increase with kinetic energy. The lowenergy behavior is the result of ion-molecule reactions taking place on a double-minimum potential. The reactants are trapped in a long-lived complex in the entrance channel well and then proceed to products over a central barrier. The temperature dependence comes from a competition between returning to reactants over a loose barrier or going on to products over a tight barrier. Since dissociation back to reactants involves a looser transition state and hence a higher density of states that changes more rapidly than does the forward transformation, the rate constant for the backward reaction increases more rapidly with temperature or kinetic energy than does that for the forward reaction. Consequently, a decreasing fraction of the collision adducts will surmount the central barrier and result in product formation with increasing temperature or kinetic energy. In fast reactions the influence of the central barrier is minimal at low energy, and the reactions remain fast until the lifetime of the collision complex with respect to dissociation into reactants becomes comparable to the lifetime with respect to product formation. The increase in rate constant in slow reactions usually indicates that a new mechanism becomes important. The new mechanism may involve a new vibrational or electronic state becoming energetically accessible or a completely new product. Note that fast reactions at low energy may become slow at higher energy and have the same type of increase as slow reactions at even higher energies. In the two sections which follow, we describe systems for which we have investigated possible rotational and vibrational energy effects. The technique is most sensitive for reactions whose rate constants are in the range from 10-11 to 10-10 cm3 s-1. Reactions which are much faster are close to the collisional limit, and therefore little rate variation is possible. Rate constants much smaller than 10-11 cm3 s-1 are difficult to
ref
+ O2 f O2 + Ar + CO f CO+ + Ar + HCl f HCl+ + Kr + DCl f DCl+ + Kr + HCl f HCl+ + Ar f ArH+ + Cl Ar+(2P3/2) + N2 f N2+ + Ar O+(4S) + HD f OH+ + D f OD+ + H Kr+(2P3/2) + HD f KrH+ + D f KrD+ + H O- + CH4 f OH- + CH3 O2+ + CH4 f products O+(4S) + CO2 f O2+ + CO f CO2+ + O OH- + D2 f OD- + HD OD- + H2 f OH- + HD O- + N2O f NO- + NO O- + SO2 f e- + SO3 f SO2- + O F- + CH3Cl f Cl- + CH3F F- + CH3Br f Br- + CH3F F- + CH3I f I- + CH3F Cl- + CH3Br f Br- + CH3Cl Cl- + CD3Br f Br- + CD3Cl CO2+ + O2 f O2+ + CO2 NO- + CO2 f e- + NO + CO2 NO- + N2O f e- + NO + N2O O2- + SF6 f SF6- + O2 Ar+(2P3/2) Ar+(2P3/2) Kr+(2P3/2) Kr+(2P3/2) Ar+(2P3/2)
+
107 107 12 12 12 12 72 72 82, 108 81 67 68 68 104 101 83 83 83 84 84 91 106 106 98
measure, and their accuracy suffers as a result. These and other considerations were used to choose systems for study. Rotational Energy Effects The effects of reagent rotational excitation on reactivity have not received a great deal of attention by experimentalists, apparently due to several factors including the relatively small amount of energy stored in individual rotational levels and the experimental difficulty of preparation of usable concentrations of rotationally state-selected reagents. In the chemical literature, discussions of internal energy effects on neutral reactions often ignore rotational effects, and the same is generally true of the literature covering ion-molecule reactions. Recent theoretical work on rotational effects has greatly added to the available literature on the subject,45-56 but contributions by experimental researchers remain scarce. Much of the experimental work has involved H2, both because of its large rotational constant and because it is relatively easy to change the rotational population by making measurements with both normal H2 and para-H2.57-62 The previous work has shown that, for many reactions, rotational energy has little effect on reactivity. The VT-SIFDT technique described in this article has been used to investigate the possible influence of rotational temperature on ion-molecule reactivity for a variety of systems. The results can be divided into three categories: (1) most reactions, where we find what has been observed previously, namely, that rotational temperature has little or no influence on reactivity, (2) endothermic reactions, where rotational energy contributes to the total energy used to overcome the endothermicity, and (3) reactants with large rotational constants, where we have observed rotational excitation to affect measurably the reaction kinetics. Table 1 lists the results for all of the systems to date for which we investigated the role of rotational excitation using the VT-SIFDT technique. In some cases the role of rotations can only be inferred since some excitation of low-lying vibrations does occur.
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+ 2
Figure 3. Rate constants for the reaction of Ar ( P3/2) with CO as a function of average kinetic energy at several temperatures.107
Most Systems. For the majority of reactions studied in this laboratory and elsewhere, rotations have been found to have little or no effect on reactivity. For our technique this means that at a fixed kinetic energy the differences in reactivity at different temperatures are less than or equal to our 15% relative uncertainty. This is illustrated in Figure 3 for the reaction of Ar+ with CO. In this case both temperature and kinetic energy are found to decrease the reactivity to the same extent, indicating that internal energy has no effect on the reactivity. Since this is a reaction of a monatomic ion with a diatomic neutral of high vibrational frequency, any internal energy effect must be due to rotations. A number of systems we have studied have been this clean, i.e., the effects of vibrations can be completely ruled out. Other systems, such as the reactions of O- with N2O and SO2, also show no internal energy dependence despite some bending mode vibrational excitation. In these systems two possibilities exist, namely, (1) that a rotational dependence and vibrational dependence exactly balance each other over the entire kinetic energy range or (2) neither rotational nor vibrational excitation has a large influence on reactivity. The latter is much more likely, especially since we have observed this behavior in a number of systems, and it seems extremely unlikely that rotational and vibrational effects cancel so often. In some systems, such as those involving CH4, vibrational and rotational effects can be separated. For CH4 no vibrational modes are significantly populated at temperatures below 300 K. In the reactions of both O- and O2+ with CH4 little internal dependence is found below 300 K, and it is concluded that rotational energy has little effect on the reactivity. At higher temperatures, internal energy dependences are found and can be attributed to vibrational excitation by assuming that the lack of a rotational temperature dependence found at low temperature applies to higher temperatures as well. The vibrational effects in these reactions will be discussed later. All told, we have found 16 reactions where rotational energy does not have a pronounced effect on reactivity. Endothermic Reactions. The reaction between Ar+(2P3/2) and N2 proceeds by charge transfer reaction in which the N2+ product is formed mainly in the first vibrationally excited level.63,64
Ar+(2P3/2) + N2 f N2+(V)1) + Ar ∆H ) 8.9 kJ mol-1 65 (3) This process is endothermic by 0.092 eV. The VT-SIFDT technique was used to measure 〈KEcm〉 dependences of the rate
Figure 4. Rate constants for the reaction of Ar+(2P3/2) with N2 as a function of average kinetic energy at several temperatures.12
Figure 5. Rate constants for the reaction of Ar+(2P3/2) with N2 as a function of average total energy at several temperatures.12
constants at 298, 428, and 552 K,66 shown in Figure 4. The three 〈KEcm〉 dependence curves do not coincide with one another in the lower part of the 〈KEcm〉 range but begin to merge at higher energies. By comparing rate constants at a given 〈KEcm〉 in the lower portion of the energy range, i.e., where the curves are separated, it is evident that in this case higher rotational temperature increases the reactivity. It should also be pointed out that the pure temperature dependence, i.e., the leftmost point in each of the three 〈KEcm〉 dependences (zero drift field applied), yields an activation energy of 0.07 eV in approximate agreement with the reaction endothermicity. Thus, increases in true temperature, rotational temperature, and kinetic energy all act to promote the reaction. Since the reaction proceeds via an endothermic pathway, it seems plausible that these different forms of temperature/energy promote reactivity simply by overcoming the mild reaction endothermicity. As a simple test of this idea, the rate data are replotted in Figure 5 as a function of average total energy,66 which is defined as the sum of the average rotational and translational energies. (Excited vibrational levels of N2 are not populated at the temperatures of the experiment.44) Figure 5 illustrates that the three distinct 〈KEcm〉 dependence curves collapse into a single curve which depends only on average total energy, independent of the type of energy. This implies that rotational and translational energy have the same effect on reactivity, promoting reaction by supplying energy to overcome the endothermicity. The larger rotational dependence at lower 〈KEcm〉 is simply a consequence of the rotational energy being a larger fraction of the total energy at low 〈KEcm〉. To confirm that the Ar+ velocity distributions are essentially Maxwellian under the experimental conditions, solution of the
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Figure 6. Rate constants for the reaction of Kr+(2P3/2) with HCl as a function of average kinetic energy at several temperatures.12
Boltzmann kinetic equation was performed36 using potentials based on measured mobility data for Ar+ drifting in He. Ar+ velocity distributions in a He-buffered drift tube were calculated and combined with cross sections for the Ar+ + N2 reaction in order to determine the corrections necessary to convert the measured rate constants for Ar+ + N2 to those which would be found for Maxwell-Boltzmann distributions. The calculations addressed two types of possible error: (1) a deviation of the average kinetic energy derived from the Wannier expression compared with the true average kinetic energy in the experiment and (2) error resulting from the rate constant being more sensitive to the details of the distribution function than through the average energy alone. The calculations indicate that the Wannier expression is very accurate at low energies and is not in error by more than 10% even at energies approaching 1 eV (0.5 eV at 82 K). The largest deviations were found at very low temperature (82 K) and high drift electric field. The calculations also show that the dependence on gas temperature at fixed 〈KEcm〉 is not due to the difference between the experimental distribution function and a Maxwell-Boltzmann distribution. Thus, the calculations confirm that the rate constants show a dependence on the rotational temperature of N2 and not upon the velocity distributions at fixed 〈KEcm〉. We and others have studied the effect of rotational excitation on a number of other reactions that are endothermic. In each case the same conclusion is reachedsthat kinetic energy and rotational excitation are equally efficient in supplying the energy to drive the reaction. The reactions studied to date are the reactions of O+ with CO2,67 OD- with H2,68 N+ with H2,60 and C+ with H2.59,69 No exceptions to this generality have been found. Reactions with Large Rotational Effects. Kr+ + HCl, DCl. The charge transfer reaction
Kr+(2P3/2) + HCl f HCl+ + Kr ∆H ) -121 kJ mol-1 65 (4) was investigated12 over a range of 〈KEcm〉 from thermal to several tenths of an electronvolt at each of the temperatures 173, 298, and 486 K. In addition, the experiments were repeated using DCl. The results for HCl are shown in Figure 6 where the rate constants are plotted versus 〈KEcm〉 on a log-log scale. The 〈KEcm〉 dependences measured at the three temperatures do not coincide with one another; rather, they define three distinct curves which are separated by more than the relative error bars. Increased rotational temperature leads to a decrease in the reaction rate constant. The magnitude of the effect is approximately independent of 〈KEcm〉 and is similar for HCl
Viggiano and Morris and DCl, although fewer data points were obtained for DCl. The measurements were repeated using another VT-SIFDT instrument, at the University of Birmingham, and the results are in good agreement with the data from the Phillips Laboratory VT-SIFDT. The rotational temperature dependence can be quantified by taking a vertical slice through the curves in Figure 6 at a particular 〈KEcm〉 and comparing the rate constants. (Interpolation between points is often necessary, depending on the choice of 〈KEcm〉.) The different rate constants so obtained then relate to the different rotational temperatures of HCl, defined by the bath gas temperatures in the experiments. Thus, the rate constant for reaction 2 depends on HCl rotational temperature (Tr) approximately as Tr-0.37 at most 〈KEcm〉. At least part of this negative dependence on rotational temperature can be explained by the rotational temperature dependence of the collisional or capture rate constant due to a decrease in the effectiveness of the locking of the HCl permanent dipole to the ionic charge at higher rotational temperatures.12 Classical trajectory methods70,71 which include an ion-dipole locking term were used to calculate the capture rate constant for this reaction.12 The trajectory calculations yield a Tr-0.17 dependence of the capture rate constant for reaction 2 on the HCl rotational temperature. HCl has both a high dipole moment and a high rotational constant, which lead to the sensitivity of the capture rate constant to the HCl rotational temperature. The rotational dependence of the capture rate constant is weaker than that of the reaction rate constant, indicating that increased rotational temperature of HCl reduces not only the capture rate but also the efficiency of reaction. The cause of the rotational effect has not been investigated theoretically, but the data suggest that the charge transfer process is facilitated by a collinear configuration. This is based on the fact that the dipole of HCl will lock to the positive charge better at lower rotational temperature. It is interesting to note that we observe no rotational temperature dependence of the rate constant for the analogous reaction Ar+ + HCl, for which the capture rate constant also has a Tr-0.17 rotational dependence.12 In the Ar+ case, however, an atom transfer channel is involved in addition to charge transfer. OH- + D2 and OD- + H2. The isotope exchange reactions OH- + D2 and OD- + H2 were investigated with the VT-SIFDT technique,68 and effects attributable to both rotational and vibrational excitation were observed; the vibrational effects were observed by injecting the ions into the flow tube at high energy and monitoring a curved decay plot. We discuss only those data for which the reactant ions are in the V ) 0 level. The reaction enthalpies given here,
OH- + D2 f OD- + HD
∆H ) -1.8 kJ mol-1 44 (5)
OD- + H2 f OH- + HD
∆H ) +2.5 kJ mol-1 44 (6)
are based on vibrational zero-point energies44 and differ by only 0.1-0.2 kJ mol-1 from those based on heats of formation.65 Since these reactant ions are diatomic, the internal modes of the ions can be excited in the drift field. The effective internal temperature, Tint, of the reactant ions is given by the Wannier formula by substituting the buffer mass (4 amu) for the reactant neutral mass so that 〈KEcm〉buffer ) (3/2)kTint. The vibrational frequencies44 of OH- and OD- are sufficiently high that no thermal vibrational excitation will occur; i.e., Tint is too low for populating V > 0.
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Figure 7. Rate constants for the reaction of OH- with D2 as a function of average kinetic energy at several temperatures.68 Rate constants for vibrational ground state of OH- in solid points and for vibrational excited OH- in open points. The vibrational excited data were obtained from curvature in the decay plots when OH- was injected at high energy into the flow tube and cannot be assigned to any particular vibrational level.
Figure 8. Rate constants for the reaction of OD- with H2 as a function of average kinetic energy at several temperatures.68 Rate constants for vibrational ground state of OD- in solid points and for vibrational excited OD- in open points. The vibrational excited data were obtained from curvature in the decay plots when OD- was injected at high energy into the flow tube and cannot be assigned to any particular vibrational level.
Since the reactant ions are not vibrationally excited, Tint refers to the rotational temperature of the OH- or OD- ions and is given by 〈KEcm〉buffer ) (3/2)kTint. Fortuitously, for the reaction of OH- with D2 (reaction 5), the rotational temperature of the OH- is equal to 〈KEcm〉 because D2 and the He buffer have the same mass; i.e., 〈KEcm〉buffer ) 〈KEcm〉. Therefore, at a fixed 〈KEcm〉, the dependence of the rate constant on temperature represents the dependence on the rotational temperature of D2; the ion rotational temperature as well as the kinetic energy of collision are both fixed. The data for reaction 6 are not as simple to interpret since the OD- ion rotational temperature is not constant at a fixed 〈KEcm〉. (The masses of H2 and He are different, and therefore 〈KEcm〉buffer * 〈KEcm〉.) At a fixed 〈KEcm〉, the OD- ions will have increasing rotational temperatures as the buffer gas temperature is raised, so that both the neutral and ionic reactants will have higher rotational temperatures at higher gas temperature and fixed 〈KEcm〉. As mentioned above, in the case of OH- + D2, the dependence on temperature at fixed 〈KEcm〉 is due solely to the dependence on the rotational temperature of D2. The data are shown in Figure 7, and here a large negative influence on reactivity is found. At a 〈KEcm〉 of 0.064 eV, the rate constant measured at 129 K is a factor of 2.2 larger than that measured at 507 K, with an intermediate value at 300 K. This represents a strong negative dependence on the rotational temperature of D2 of Tr-0.58 for reaction 4. This can be compared with the pure temperature dependence for reaction 4 of T-0.92. In contrast to reaction 5, the reaction of OD- with H2 (reaction 6) exhibits a pure temperature dependence which is positive, shown in Figure 8. This is qualitatively understandable in terms of the reaction being slightly endothermic, since increasing temperature can help to overcome the endothermicity. However, the activation energy derived from the pure temperature dependence of reaction 6, 0.3 kJ mol-1, is much less than the reaction endothermicity of 2.5 kJ mol-1. The strong negative temperature dependence for the exothermic reaction 5 may help to explain this: an underlying strong negative temperature dependence could weaken the increase in rate constant expected from overcoming the endothermicity. As mentioned above, in reaction 6 both the ion and the neutral reactant will have higher rotational temperatures at fixed 〈KEcm〉 as the temperature is raised. Nevertheless, it is clear from the data that reaction 6 shows a weaker rotational dependence than
does reaction 5. The smaller rotational dependence in reaction 5 could be due to a cancellation of opposing effects of rotations of the ion and neutral, i.e., a negative dependence on H2 rotations as in reaction 4 offset by a positive dependence on ODrotations. We believe a more likely explanation is that a strong negative dependence as in reaction 5 is offset by a positive component of the dependence associated with the endothermicity, i.e., an activation energy component where rotations help to overcome the activation barrier, as in the Ar+ + N2 case.66 According to this explanation, the two effects offset each other but do not cancel, leading to the weaker negative rotational dependence in reaction 6 than in reaction 5. Support for this explanation is found in the “intrinsic” activation energy for reaction 6, obtained by adjusting the rate constants for reaction 6 by the decrease with temperature found for reaction 5. By normalizing for the negative temperature dependence of reaction 5, we derive an activation energy for reaction 6 of 1.9 kJ mol-1, which is in good agreement with the reaction endothermicity of 2.5 kJ mol-1. This lends support for the idea that the difference in reactivity between reactions 5 and 6 is due to the endothermicity of the latter. The reason for the strong negative rotational dependence is not clear, and we eagerly encourage theoretical studies of this system to help explain the dynamics. O+ and Kr+ + HD. We now turn to an example where rotational excitation of the neutral reactant influences the product branching ratio.72 The reaction is the atom transfer
O+ + HD f OH+ + D
∆H ) -52 kJ mol-1 65 (7a)
f OD+ + H
(7b)
where two isotopic products are formed. The rate constant for this reaction is independent of temperature and 〈KEcm〉.72 The O+ reactant ion is monatomic, and the neutral reactant HD has no vibrationally excited levels populated in the experiment. Thus at fixed 〈KEcm〉, differences in branching ratios measured at different temperatures are due to the differing rotational temperatures of HD. Such differences were predicted theoretically by Dateo and Clary73 and confirmed experimentally by Sunderlin and Armentrout,74 who used a variable-temperature collision cell in a guided ion beam (GIB) instrument. Thus, this reaction provided an opportunity for us to compare our data not only with theoretical predictions but also with experimental data from a different technique.
19234 J. Phys. Chem., Vol. 100, No. 50, 1996
Figure 9. Fraction of OH+ produced in the reaction of O+ with HD as a function of average kinetic energy.72 Theoretical predictions are from Dateo and Clary.73
The fraction of OH+ formed in reaction 6 measured in the VT-SIFDT, along with the associated error bars, is shown as functions of 〈KEcm〉 in Figure 9. The theoretical predictions73 are shown as lines. At fixed 〈KEcm〉, the fraction of OH+ decreases with increasing temperature. This is in contrast to the effect of increasing kinetic energy, which leads to an increase in OH+ formation relative to OD+. Thus, rotational and kinetic energy have opposite effects on the branching ratio. The GIB data74 show a similar effect although they are not as pronounced as the VT-SIFDT results because the energy distribution variations in the GIB experiment are less than those in the VTSIFDT work. Theoretical predictions confirm this. The reason for the dependence of the OH+/OD+ ratio on HD rotational temperature is explained in the theoretical work73 and may be understood in terms of simple physical ideas. The preference observed for the OH+ product results from the fact that the center-of-mass (nearer to D than H) and the center-ofpolarizability (the center of the H-D bond) are at different positions. This difference creates a torque on the molecule as the ion approaches that tends to orient the H end of the molecule toward the O+ ion. The rotational temperature dependence then arises from rotational averaging of the anisotropic potential as the HD rotational velocity increases. As expected from this argument, the largest enhancement in OH+ formation should be for low J levels, and in fact the theory73 predicts the largest effect for J ) 0 and smaller effects for large J. This is reflected in the data as a larger difference between the 93 and 300 K OH+ branching fractions than between the 300 and 509 K fractions. The reaction of Kr+ with HD shows similar but smaller rotational effects.75 This reaction is different in that the rate constant is smaller than collisional. We have speculated that the differences between the O+ and Kr+ results have to do with the position in the reaction coordinate that determines reactivity. In the O+ case, the critical position is the centrifugal barrier and in the Kr+ it is a curve crossing. Other Results and Conclusions. By studying normal and para-H2, Sbar and Dubrin58 found that the ratio of the cross sections for the reaction of Ar+ with H2 for the rotational levels J ) 0 and J ) 1 was 0.95 ( 0.025 at 〈KEcm〉 ) 0.13 eV. Marquette et al.60 studied the difference in reactivity of N+ with normal and para-H2 and found a large positive dependence on rotational excitation. The effect, which is greater than a factor of 10 at 20 K, is the result of the reaction being slightly endothermic; the increased rotational energy helps to overcome the endothermicity.
Viggiano and Morris Gerlich and co-workers have used guided ion beam (GIB) and ion trap techniques to study rotational effects in several reactions. By operating a supersonic beam of D2 at two temperatures in the GIB experiment, they demonstrated that rotational and translational energy are equally effective in driving the N+ + D2 reaction.76 A rotational effect in the reaction of C+ + H2 was found59 by using alternatively a variable-temperature scattering cell or different mixtures of ortho- and para-H2; at low translational energies, the reactivity of H2(J)1) is less than that of J ) 0. Greater reactivity of H2(J)0) compared with j ) 1 has been found in several other reactions using ortho/para-H2 mixtures in an radio-frequency ion trap. Reactivity is enhanced for H2(J)0) in the hydride transfer reaction D+ + H2,27 in the association reactions of CH3+ and CD3+ with H2,61 and in the association and fragmentation reactions of the hydrogen cluster ions (H5+ to H23+) with H2.62 Some of this effect is explained by the anisotropy of the potential caused by the quadrupole moment of H2, which increases the capture rate for the nonrotating j ) 0 level. An additional effect is the extra energy available in j ) 1 which affects the complex lifetime with respect to either dissociation or stabilization. Gerlich has also used laser excitation in combination with GIB to prepare and study CO+ ions in particular rovibronic states; for the charge transfer reaction CO+(A2Π,V)2,J) + Ar, no rotational dependence was found.27 Taken together the rotational effects studied to date lead to the following conclusions. For endothermic reactions, rotational and translational energy are similarly effective in overcoming the endothermicity. There have been no exceptions in the five reactions studied to date. For exothermic reactions, rotational temperature has little effect on reactivity for molecules with small rotational constants. For systems with large rotational constants (HCl, H2, HD, D2), large rotational effects are possible but not guaranteed. This is in spite of the fact that the amount of rotational energy varied in our experiments is roughly independent of the rotational constant since the energy is simply (1/2)k∆T per rotational degree of freedom. These facts lead to the following picture. Changing J from a low value (large rotational constant, low temperature) to a moderate value (large rotational constant, high temperature) can lead to the possibility of a large rotational effect. In contrast, changing from a moderate (small rotational constant, low temperature) J value to a large one (small rotational constant, high temperature) is likely to have at most a small effect on reactivity. The reason for this is often related to the fact that more averaging of the intermolecular forces occurs as the molecule rotates faster. In several examples simple classical arguments have shown that multipole forces allow locking of the neutral to the ion when J is low,27,73 i.e., when the rotational period is greater than the interaction time. Vibrational Effects There have been numerous studies on the effects of vibrations on ion-molecule reactivity, although most of the studies have centered on the effects of vibrations in the ion, due in large part to the advent of ionization schemes which prepare ions in particular vibrational levels. Additionally, monitor ion techniques have allowed the differentiation of vibrational levels through their differences in chemical reactivity. The VT-SIFDT studies reported here are complementary to work done elsewhere in that we can study the effects of vibrations of the reactant neutral, at least those with vibrational levels that can be excited at buffer gas temperatures. In the past we have been limited to the upper temperature range of the VT-SIFDT of 550 K. However, we have recently developed a high-temperature
Feature Article
J. Phys. Chem., Vol. 100, No. 50, 1996 19235
TABLE 2: Reactions Studied as a Function of Vibrational Energy in the VT-SIFDT reaction ++
ref
CO2 CO2 + O2 f O2 NO- + CO2 f e- + NO + CO2 NO- + N2O f e- + NO + N2O NO- + C3H8 f e- + NO + C3H8 Br- + WF6 f WF6Brf WF6- + Br F- + WF6 f WF7f WF6- + F O2+ + CH4 f products O+(4S) + CO2 f O2+ + CO f CO2+ + O O2- + SF6 f SF6- + O2 F- + CF3Br f Br- + CF4 f F-‚CF3Br F- + CF3I f I- + CF4 f F-‚CF3I Ar+(2P3/2) + N2 f N2+ + Ar OH- + D2 f OD- + HD OD- + H2 f OH- + HD 37 Cl + 35ClCH2CN f 35Cl- + 37ClCH2CN O- + CH4 f OH- + CH3 O- + N2O f NO- + NO O- + SO2 f e- + SO3 f SO2- + O F- + CH3Cl f Cl- + CH3F F- + CH3Br f Br- + CH3F F- + CH3I f I- + CH3F Cl- + CH3Br f Br- + CH3Cl Cl- + CD3Br f Br- + CD3Cl +
91 106 106 106 102 102 80, 81 67 98 86 Figure 10. Rate constants for the reaction of O- with CH4 as a function of effective kinetic temperature, 〈KEcm〉 ) 3/2kTeff including both the VT-SIFDT and high-temperature flowing afterglow data. The pure temperature data from the VT-SIFDT experiment are connected to aid in viewing the data.82
86 103 68 68 85 82, 108 104 101 83 83 83 84 84
flowing afterglow capable of studying reactions to at least 1800 K,77 opening up a new realm of vibrational frequencies by combining drift tube studies with data taken from the hightemperature flowing afterglow. Reactions with CH4. Methane is a particularly good example illustrating how the effects of vibrations can be derived from the VT-SIFDT measurements. At low temperature (
