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Dynamics of Mg+ + H2O + He: Capture, Collisional Stabilization and Collision-Induced Dissociation Emilio Martı´nez-Nu´n˜ez,*,† Charlotte L. Whalley,‡ Dmitry Shalashilin,‡ and John M. C. Plane*,‡ Departamento de Quı´mica Fı´sica, UniVersidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain, and School of Chemistry, UniVersity of Leeds, UK LS2 9JT ReceiVed: March 18, 2010; ReVised Manuscript ReceiVed: May 6, 2010
A laser flash photolysis technique and quasi-classical trajectory (QCT) calculations have been used to determine the rate coefficients for the title process. The experimental high-pressure-limiting rate coefficient is 7.0 × 10-11 cm3 s-1 at T ) 300 K, which compares with the computed QCT value for the Mg+ + H2O capture rate of 2.75 ( 0.08 × 10-9 cm3 s-1 at the same temperature. The 39-fold difference between the experimental and simulation results is explained by further QCT calculations for the He + Mg+ · H2O* collision process. In particular, our simulation results indicate that collision-induced dissociation (CID) of the Mg+ · H2O* excited adduct is very likely compared with collisional stabilization (CS), which is an order of magnitude less likely. Including the relative rates of CID and CS in the calculation and assuming that those Mg+ · H2O* complexes that perform only one inner turning point in the dissociation coordinate are unlikely to be stabilized by CS, the computed rate coefficient compares well with the high-pressure experimental value. Mg+ + H2O(+He) f Mg+ · H2O
Introduction Metallic ions play important roles in planetary ionospheres, where their major source is meteoric ablation,1-3 and in combustion processes, where metals occur either as fuel contaminants or are added as flame inhibitors.4,5 Mg+ and Fe+ ions are the main constituents of sporadic ion layers, so far observed in the atmospheres of Earth,6 Mars,7 and Venus.8 Sporadic layers are thin layers of enhanced plasma that have a significant impact on radio communications by enabling overthe-horizon radio transmission and limiting ground-to-space communication. The lifetimes of these layers are largely controlled by the reactions of metallic ions with species such as O3 and O2 or by clustering with ligands such as CO2 and H2O; the resulting molecular ions then undergo dissociative electron recombination.9 In the past few years, we have developed a laser flash photolysis technique10,11 for studying the kinetics of recombination reactions involving metallic ions at significantly higher bath gas pressures than can be achieved in a traditional discharge flow apparatus.12 We have found that recombination (or association) reactions of metal ions can exhibit unexpected falloff behavior. For example, the recombination of Ca+ with H2O shows clear falloff from third- to second-order kinetics at moderate pressures (20-40 Torr), with a high-pressure-limiting rate coefficient that is only about 5% of the Langevin capture frequency.11 We proposed that this unusual behavior was caused by collision-induced dissociation (CID) with the third body and that CID was likely to occur in ion-molecule recombination reactions in which, during capture, the ligand orbits the metal ion at relatively large distances.11 In this paper, we will examine in much greater detail the role of CID in ion-molecule association reactions, taking as an example the reaction * Corresponding author. E-mail:
[email protected] (E.M.-N.);
[email protected] (J.M.C.P.). † Universidad de Santiago de Compostela. ‡ University of Leeds.
(1)
We will first describe measurements of the (bimolecular) recombination rate coefficient, krec, over a large enough range of He pressures for the reaction to exhibit significant falloff. The low-pressure-limiting (termolecular) rate coefficient, krec,0, and the high-pressure-limiting (bimolecular) rate coefficient, krec,∞, will then be estimated by fitting Rice-RamspergerKassel-Markus (RRKM) theory to the experimental data. The bulk of the paper will then be devoted to providing a fundamental understanding of the capture of H2O by Mg+ to form an energized adduct, Mg+ · H2O*, and the competing processes of dissociation, collisional stabilization (CS), and CID:
Capture: Dissociation:
Mg+ + H2O f Mg+ · H2O* Mg+ · H2O* f Mg+ + H2O*
Collisional stabilization (CS):
(1a) (1b)
Mg+ · H2O* + He f Mg+ · H2O + He (1c)
Collision-induced dissociation (CID):
Mg+ · H2O* +
He f Mg+ + H2O + He (1d) These processes will be examined using quasi-classical trajectory (QCT) calculations on a new potential energy surface that characterizes the interactions among Mg+, H2O, and He. The relative importance of the CID vs CS was first pointed out in a QCT study of H + O2 by Schatz and co-workers.13 If CID is important in comparison with CS, then at high pressures of the bath gas, the overall second-order recombination rate coefficient (krec) will be considerably reduced with respect to the capture rate, k1a.
10.1021/jp102454j 2010 American Chemical Society Published on Web 05/19/2010
Dynamics of Mg+ + H2O + He Experimental Section Pulsed Photolysis/Laser Induced Fluorescence (PLP/LIF). The application of this technique to study ion-molecule reactions has been described in detail previously.11 Mg+ ions were produced in an excess of He bath gas and H2O by the pulsed multiphoton photolysis of magnesium acetyl acetonate (MgAcAc or Mg(C5H7O2)2) vapor using an ArF excimer laser at 193 nm (typical pulse energy ) 95 mJ, pulse rate ) 5 Hz). The Mg+ ions were then probed by LIF at 279.6 nm (Mg+(32P1-31S0)) using a frequency-doubled Nd:YAG-pumped dye laser (pulse energy ) 10 µJ). The excimer and dye laser beams were aligned to counterpropagate collinearly through the stainless steel reactor. Powdered MgAcAc was placed in a tantalum boat located in a heat pipe connected to the reactor and warmed to between 433 and 463 K, maintained to within (2 K during a particular experiment. The resulting MgAcAc vapor was entrained in a flow of He and transported into the reactor, where it mixed with larger flows of a He and H2O/He mixture. The LIF signal was measured through an interference filter centered at 280 nm (fwhm ) 15 nm) and collected by a gated integrator. The delay between the excimer and dye laser pulses was scanned under computer control. Reaction 1 was studied at 299 K and over a pressure range of 5-30 Torr. Materials: He (99.9999%, BOC Gases). H2O was purified by freeze-pump-thawing deionized H2O for three cycles, and then used to make up mixtures of between 0.4 and 0.6% H2O vapor in He. MgAcAc (98%, Alpha) was further purified by being pumped on in the heat pipe at between 433 and 463 K for about 30 min prior to the experiments. Flow Tube/Mass Spectrometry (FT/MS). The FT/MS technique has been used previously to study the ion-molecule reactions of Fe+ and Ca+.10,11 Mg+ ions were produced via laser ablation of a piece of magnesite (MgCO3) using a Nd:YAG laser at 532 nm (pulse energy ∼ 10 mJ, repetition rate ) 10 Hz), which was loosely focused onto the magnesite target. The target was mounted on a rotary feedthrough powered by a DC motor so that a fresh surface was presented to each laser pulse to maintain a uniform Mg+ signal. The Mg+ ions were entrained in a flow of He that entered upstream of the ablation target. The flow velocity ranged from 35 to 50 m s-1, which produced a Reynolds number 5 × 1017 cm-3. To model this behavior, we now apply RRKM theory using a solution of the master equation (ME) based on the inverse Laplace transform method.14 The reaction is assumed to proceed via the formation of the energized adduct (Mg+ · H2O*), whose
J. Phys. Chem. A, Vol. 114, No. 23, 2010 6473 TABLE 1: Experimental Determination of Second-Order Rate Coefficients for the Recombination of Mg+ with H2O at 299 Ka krec/10-12 cm3 molecule-1 s-1
Pressure/Torr
0.90 ( 0.09 1.40 ( 0.13 3.76 ( 0.41 4.69 ( 0.49 6.30 ( 0.71 6.27 ( 0.45 8.52 ( 0.93 7.51 ( 0.82 10.2 ( 1.2
1.2b 1.7b 5 10 10 15 20 20 30
a Quoted uncertainty is the 1σ error from the kinetic plots and the systematic experimental errors. b Measurements made with the FT/ MS. All other measurements made were with the PLP/LIF technique.
Figure 1. Plot of krec(Mg+ + H2O) versus [He] at 299 K, comparing measurements (solid points), RRKM theory (solid line) with krec,0 and krec,∞ indicated.
internal energy was divided into a contiguous set of grains (width 25 cm-1), each containing a bundle of rovibrational states. Each grain was then assigned a set of microcanonical rate coefficients for dissociation, which were determined using inverse Laplace transformation to link them directly to krec,∞, the high-pressure-limiting recombination coefficient. In the case of reaction 1, the upper limit to krec,∞ can be estimated from Langevin theory modified to include the ion-dipole interaction between Mg+ and H2O. For instance, using the formalism of Su and Chesnavich15 with the polarizability R(H2O) ) 1.46 × 10-30 m3 and dipole moment µ(H2O) ) 6.2 × 10-30 Cm gives krec,∞(Mg+ + H2O) e 2.0 × 10-9 e100/T cm3 molecule-1 s-1. In the procedure for fitting to the experimental data, this capture frequency was then multiplied by a scaling factor. The density of states of the Mg+ · H2O* adduct was calculated with the Beyer-Swinehart algorithm for the vibrational modes (without making a correction for anharmonicity), and a classical densities of states treatment for the rotational modes.16 The molecular parameters for the Mg+ · H2O and binding energy were taken from a recent high-level ab initio calculation (Table 2).17 The rotational constants are 413.0, 10.69, and 10.42 GHz, and the vibrational frequencies are 348, 381, 510, 1661, 3717, and 3794 cm-1. The out-of-plane and in-plane rocking modes of the H2O (381 and 510 cm-1) were treated as a two-dimensional free rotor. The ME describes the evolution with time of the grain populations of the adduct. The probability of collisional transfer between grains was estimated using the exponential down
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TABLE 2: Vibrational Frequencies and Dissociation Energies of the Mg+ · H2O Complex Calculated at the Various Levels of Theory Employed in This Study in Comparison with Previous Theoretical and Experimental Results MP2/SB
MP2/BB
vibrational frequencies 351, 380, 522, 1662, 3737, 3829 345, 382, 502, 1663, 3740, 3833 (cm-1) 30.6 29.6 D0 (kcal/mol)
CCSD(T)/BBa
previous workb 348, 381, 510, 1660, 3717, 3795
30.1
31.3b, 30.4c, 24.4d
a CCSD(T)/BB single point calculations at the CCSD/BB optimized geometries with MP2/BB zero-points vibrational energies. B3LYP/6-311+G(2d,p) and RCCSD(T)/aug-cc-pVQZ results from ref 17. c UCCSD(T)/aug-cc-pVQZ results from ref 17. d Experimental results from ref 20.
b
model, in which the average energy for downward transitions is designated 〈∆E〉down.16 The probabilities for upward transitions were calculated by detailed balance. To use the ME to simulate irreversible stabilization of the adduct, an absorbing boundary was set 15 kJ mol-1 below the energy of the reactants so that collisional energization from the boundary to the threshold was highly improbable.14 The ME was expressed in matrix form14 and then solved to yield krec. To fit to the experimental data in Table 1, two adjustable parameters were allowed. These were a scaling factor, f, to reduce krec,∞ below the Langevin upper limit and the average energy for downward transitions, 〈∆E〉down. A least-squares fit to the data yields 〈∆E〉down ) 120 cm-1 (a sensible value for He as third body16), and f ) 0.025. The rate coefficient for reaction 1 can then be fitted to the Lindemann expression modified by a broadening factor, Fc:17
krec )
krec,0[M] FK krec,0[M] c 1+ krec,∞
where K )
1 krec,0[M] 1 + log10 krec,∞
{ [ (
)] } 2
(I)
where krec,0 ) 2.9 × 10-29 cm6 molecule-2 s-1, krec,∞ ) 5.0 × 10-11 exp(829/RT) cm3 molecule-1 s-1, and Fc ) 0.52. The RRKM fit to the experimental data is illustrated in Figure 1. In the high-pressure limit, the energized Mg+ · H2O* complex can either stabilize or dissociate by collisions with He, so that
krec,∞ )
Figure 2. Geometry of the Mg+ · H2O complex optimized at the MP2 and CCSD levels of theory. For the MP2 calculations, the SB and BB were used, whereas for the CCSD calculations, only the BB was employed. Previous DFT (B3LYP/SB) results17 are also shown for comparison.
k1ak1c ) fk1a k1c + k1d
(II)
where k1a, k1c, and k1d are the rate coefficients for the capture, CS, and CID processes, respectively. The small value of f obtained in the RRKM fit implies that CID is more important than CS in this reaction. Ab Initio Calculations of the Potential Energy Surface. The Capture Process. Several ab initio calculations were carried out for the Mg+-H2O system to find a suitable level of theory for the construction of the potential energy surface (PES) of the capture step (1a). In particular, the geometry of the Mg+ · H2O complex was optimized with MP2 and CCSD using the 6-311+G(2d,p) and aug-cc-pVTZ basis sets, hereinafter SB (small basis) and BB (big basis), respectively. All the ab initio calculations were carried out using Gaussian03.18 Figure 2 shows the geometry of the Mg+ · H2O complex with the main geometrical features optimized at the various levels of theory, in comparison with previous DFT calculations.17 As seen in the Figure, the major discrepancy corresponds to the Mg+-O distance, for which the difference between the CCSD/BB and
Figure 3. Potential energy profile along the Mg+-O distance calculated at the MP2 and CCSD(T) levels of theory. For the MP2 calculations, the SB and BB were used, whereas for the CCSD(T) calculations, only the BB was employed.
MP2/SB calculations amounts to 0.016 Å. Table 2 compares the dissociation energies and vibrational frequencies of the Mg+ · H2O complex with previous theoretical17,19 and experimental results.20 Both the vibrational frequencies and the dissociation energies calculated in this work at the various levels of theory are in excellent agreement with each other and compare very well with previous theoretical results. It should be noted that the experimental value20 for the dissociation energy is ∼6 kcal mol-1 lower than those obtained in this study and in a previous theoretical work. The potential energy profile for a collinear orientation of the water dipole moment, and the Mg+-O distance is shown in Figure 3 at the levels of theory employed in this study. The three calculations provide potential energy curves that agree very well with each other. To build a full dimensional PES for the capture step, the interpolation method of Collins and co-workers21-24 was employed. The method involves the calculation of energies, gradients, and Hessians for a large set of points in the configuration space. According to the above results, the MP2/ SB level of theory provides a good compromise between
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Figure 5. Contour plot for Mg+ moving around the equilibrium H2O molecule. The four atoms are in the same plane.
Figure 4. Convergence of the capture rate coefficients at the three temperatures studied in this work as a function of the number of points in the interpolated PES.
accuracy and CPU time. This level of theory was therefore selected for the construction of the global PES to study the Mg+ + H2O capture reaction. The PES has been grown using the iterative methods implemented in the GROW script.21-24 A total of 2480 MP2/SB points, including energies, gradients, and Hessians, were used to interpolate the PES. The ab initio points added to the data set are selected by running trajectories to sample the configurational space of the system. In these trajectory calculations, the Mg+-H2O relative translational energy and H2O internal energies were sampled from Boltzmann distributions at temperatures up to 2000 K. The impact parameter, b, was set to zero, and the initial separation of the reactants, 35 Å to ensure no initial interaction. Although, as will be seen below, the maximum impact parameters, bmax, used in the quasi-classical trajectory calculations with the converged surface can be as high as 26 Å, building the surface, the value of b was zero in all trajectories. This is because the initial separation of the reactants, 35 Å, is already higher than the highest value of bmax determined for the converged surface (see below), and therefore, the configurational space will be swept from very short to very large Mg+-H2O distances while growing the surface. The convergence of the PES was checked every time 400 new points were added to the data set by running batches of 1000 trajectories. The convergence of the rate coefficients (the calculation of this quantity is described below) is shown in Figure 4 for the three temperatures studied here: 200, 300, and 2000 K. After 2400 points, the rate coefficients for all temperatures are essentially converged as seen in the figure. A contour plot of the potential energy surface for planar configurations is shown in Figure 5. The deep well at a Mg+-H2O distance of ∼2 Å is clearly visible in the plot, as well as the repulsive part of the PES (yellow area). Collisional Stabilization and Collision Induced Dissociation. To study the dynamics of the CS and CID processes, the potential energy surface has to incorporate the interaction between He and Mg+ · H2O:
V ) VMg+ · H2O + Vinter
(III)
where VMg+ · H2O is the Mg+ · H2O ab initio interpolated PES described above, and Vinter is the interaction potential between Mg+ · H2O and He. Ab initio potentials were calculated for
Figure 6. Different orientations used in this work for the He complex intermolecular potential. The circles in the plots represent the MP2/ BB calculations, and the solid line is the fit to the ab initio results.
Mg+ · H2O + He to model Vinter. Intermolecular curves at the MP2/BB level of theory were calculated for four different orientations with the geometry of the complex fixed at its equilibrium geometry. The ab initio curves (circles) are shown in Figure 6, as well as the different configurations emphasizing a different two-body interaction (for O-He, two configurations were included). The ab initio results were fit with the following analytical function, written as a sum of two-body Mg+-He, O-He, and H-He Buckingham potentials
V)
C
∑ Ai-Heexp(-Bi-HeRi-He) + RDi-He i
i-He
(IV)
i-He
where i is each of the atoms of the complex. The potential function was fit up to a maximum energy of 4 kcal mol-1. Higher energies do not need to be included in the fitting because the collisional dynamics study was carried out at 300 K. A genetic algorithm combined with a nonlinear least-squares program was used for the fitting,25 which produced a root-mean square error of 0.12 kcal mol-1. The curve through the ab initio points in Figure 6 is the fitted potential function. Quasiclassical Trajectory (QCT) Calculations. The capture rate coefficients were calculated at three different temperaturess200, 300, and 2000 Ksrunning batches of 104 trajectories. The vibrational quantum numbers of H2O and the relative Mg+-H2O translational energies were taken from the corresponding Boltzmann distributions, and 1/2kT was given to each
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TABLE 3: Computed Capture Rate Coefficients in Units of 10-9 cm3 s-1
a
T (K)
kQCT
ka
200 300 2000
3.32 ( 0.09 2.75 ( 0.08 1.61 ( 0.04
3.30 2.79 1.42
Theoretical model of Su and Chesnavich.15
rotational degree of freedom of the water molecule. Before the trajectory integration, the fragments were randomly rotated about the Euler angles, and the maximum impact parameters bmax were 26, 25, and 10 Å for T ) 200, 300, and 2000 K, respectively. The values of bmax were optimized running separate batches of 100 trajectories for different fixed impact parameters. The initial separation between Mg+ and H2O was 30 Å to ensure no initial interaction. The integration of the trajectories was done using the Velocity Verlet algorithm with a fixed step size of 0.1 fs as implemented in the program Venus05.26 The trajectories were followed up to a maximum time of 100 ps. From the QCT results, the cross sections can be calculated as
σ(T) ) πbmax2
Nc Nt
(V)
where Nc and Nt are the number of trajectories that lead to capture and the total number of trajectories, respectively. A trajectory was considered to fulfill the capture criterion when the inner turning point (ITP) in the Mg+-H2O distance is less than 4 Å. The thermal rate coefficient can be calculated from the above cross sections
k1a(T) )
(
8kT πµMg+ · H2O
)
1/2
Figure 7. Temperature dependence of the QCT capture rate coefficients (circles) calculated in this work. The solid line is the fit to the QCT rates.
σ(T)
(VI)
This rate coefficient is often scaled by an electronic factor, which is the ratio between the number of electronic states that become attractive at short ion-molecule distances and the total number of electronic states at long Mg+-H2O distances.27 Since the electronic ground state of Mg+ is 2S, if one neglects the spin-orbit interaction, the electronic factor for the Mg+ + H2O capture rate is 1. The dynamics of He colliding with several Mg+ · H2O* complexes formed in the capture step was also studied here. The complexes were selected according to their lifetimes to avoid those dissociating before the collision with He. Therefore, 26 complexes with lifetimes longer than 10 ps were selected from those obtained in the simulations of the capture step, and batches of 103 trajectories were run for each complex with different initial conditions to study the Mg+ · H2O* + He collision dynamics. The initial separation between He and the complex was randomly selected between 20 and 30 Å to sample different configurations of the complex at the instant of collision with He. The maximum impact parameter was 15 Å, for which energy transfer was negligible. The collision energy was selected from a 300 K Boltzmann distribution. Theoretical Results. The Capture Process. The computed QCT capture rate coefficients are shown in Table 3 for the three temperatures considered in this study. The Table also collects the capture rates obtained using the modified Langevin model of Su and Chesnavich.15 The comparison between both QCT
Figure 8. Distribution of the number of ITPs in the Mg+-H2O centerof-mass distance for the capture step at 300 K.
and the Su and Chesnavich model results is very good except for the highest temperature considered here, where the QCT result is 13% higher. The typical negative temperature dependence of the capture rate coefficients is depicted graphically in Figure 7. Using a simple model for the temperature dependence of the type k ) A + B/Tm gives a value for m of 0.82, which agrees very well with previous QCT results on the related Si+ + H2O capture reaction.28 It is worth noting here that the shortrange anisotropy of the PES (Figure 5) does not significantly affect the capture rate. The theoretical result at 300 K is, however, ∼40 times higher than the experimentally determined capture rate (krec,∞). Figure 8 shows the distribution of ITPs for the Mg+ · H2O* complexes formed in the capture step. The distribution has a long tail with some complexes being very stable and having several hundreds of ITPs in the Mg+-H2O center-of-mass distance, corresponding to lifetimes of 50-80 ps. However, the figure clearly shows that more than 65% of the complexes formed in the capture step at 300 K undertake only one ITP before dissociation. As will be discussed below, these very short-lived complexes will be hardly stabilized in collisions with He. To investigate in more detail the origin of the 40-fold difference between the capture rate obtained in the simulations and the high-pressure rate coefficient determined experimentally, we now consider competition between collisional stabilization and collision-induced dissociation. Collisional Stabilization and Collision-Induced Dissociation. As mentioned below, if CID were very important in comparison with CS, the value of the actual rate coefficient would be considerably reduced with respect to the computed value for the capture rate. This could explain the difference between the experimental and simulation results. The competition between the two processes (CS and CID) is studied in this section. Figure 9a (solid black line) shows the variation of the Mg-O distance for a Mg+ · H2O* complex that survived ∼12 ps in the
Dynamics of Mg+ + H2O + He
Figure 9. (a) Lifetime distribution (red and blue histograms) of a Mg+ · H2O* complex formed in the capture step after collisions with He (at 300 K). The solid black line represents the vibrations in the Mg+-H2O center-of-mass distance for the isolated complex. (b) Distribution of inner turning points (ITPs) in the Mg+-H2O centerof-mass distance for the complex colliding with He. The vertical dashed line corresponds to the number of ITPs in the Mg+-H2O center-ofmass distance for the complex in the absence of He.
absence of He. The red and blue histograms in Figure 9a represent the lifetime distribution of the same complex after collisions with He at 300 K. As seen in the figure, when He is present, the vast majority of the dissociations have lifetimes much smaller than 12 ps. Those events with lifetimes >12 ps correspond to the negligible tail of the lifetime distribution (shown in blue in Figure 9a). In addition, there is a huge maximum in the lifetime distribution at 1.8 ps, which corresponds to the first ITP in the Mg+-H2O center-of-mass distance in the absence of He. This means collisions of the Mg+ · H2O* adduct with He promote dissociation rather than stabilization. Qualitatively, the same behavior was observed for the lifetime distributions of the remaining 25 Mg+ · H2O* complexes in collision with He. Quantifying the importance of CID vs CS or, in other words, calculating a value for f in eq II is not straightforward because both processes need to be distinguished in a single He collision. Trajectories that dissociate after only 1 ITP can be undoubtedly defined as CID trajectories. However, for the remaining trajectories, the complex survives more ITPs, and further collisions with He could lead to either CID or CS. However, from a qualitative point of view, the following criterion was adopted in this study to define CS and CID trajectories: A trajectory was considered to undergo CID if both the number of ITPs in the Mg+-H2O center-of-mass distance and the lifetime (τ) of the complex after colliding with He are lower than those obserVed in the absence of He. A collision between He and the complex was regarded as CS if, on the contrary, the number of ITPs and τ are higher than in the absence of He. With the above definition, the numbers of CID and CS events are depicted graphically in Figure 9b by the red and blue areas, respectively. The value of the factor f in eq II obtained for the example of Figure 9 is 0.019. For this particular case, according to our definition, CID is ∼52 times more likely than CS. All 26 complexes studied here qualitatively follow the same pattern; that is, a large number of complexes perform only 1 ITP in the Mg+-H2O center-of-mass distance after the collision with He. However, the height of the peak at 1 ITP and the width of the lifetime distribution (see Figure 9a) depend on the particular case. Figure 10 shows the distribution of the values of f found for the 26 batches of trajectories in the CID/CS dynamics study. As seen in the figure, the P(f) distribution
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Figure 10. Distribution of the value of f, which represents the relative importance of CID vs CS, for the 26 complexes employed in the CS/ CID study. The average value of the distribution is 0.105 and is indicated as a dashed vertical line in the figure.
extends up to f values of 0.4 and has an average value of 0.105. In addition, the value of f was found to be independent of the lifetime of the complexes in the absence of He and of their internal energies. The somewhat arbitrary classification of our trajectories as CS and CID precludes a quantitative calculation of the rate coefficient for reaction 1. However, an estimated value of the rate coefficient can be determined by assuming (1) that f is equal to its average value of 0.105 and (2) that those Mg+-H2O* complexes that perform only 1 ITP will not be stabilized in collisions with He. With these two assumptions, a value of 9.7 × 10-11 cm3 s-1 is obtained for the rate coefficient at 300 K, which is in close agreement with the RRKM extrapolation of the experimental data that yielded a value of 7.0 × 10-11 cm3 s-1. The importance of CID in our study is similar to that found by Schatz and co-workers in their He + H + O2 QCT study.13 In particular, they found a reduction of about 7 in the capture rate when CID is taken into account, which compares with a reduction of about 9.5 found in our study. It is important to mention at this point that classical trajectory calculations suffer from the well-known problem of zero-point energy (ZPE) leakage,29-45 which may be particularly important at energies close to the dissociation threshold. If the QCT results were corrected to account for those dissociations that violate the ZPE, the relative number of CID with respect to CS would decrease. In other words, the value of f obtained in our study could be considered as a lower bound due to the ZPE problem of QCT calculation. On the other hand, the calculated dissociation energy is ∼6 kcal mol-1 higher than the reported experimental value. Bringing the dissociation threshold down by 6 kcal mol-1 would increase the dissociation rate, decreasing the value of f. No attempt has been made in the present study to correct either the ZPE problem or the dissociation energy, but both may affect the computed values of the recombination rate coefficients. Figure 11 shows the CID mechanism for a typical trajectory. Before collision, Mg+ and H2O orbit around each other, reaching Mg+-O distances of 10 Å. The trajectory depicted in Figure 11 shows a Mg+ · · · H2O* complex with an important excitation of its orbital angular momentum as a consequence of the very large impact parameters of the capture step (the maximum impact parameter at 300 K was 25 Å). The collision with He promotes rotational to vibrational energy transfer. In particular, part of the rotational energy of the complex is released as translational energy of the Mg+ and H2O fragments. For the trajectory of Figure 11, the collision with He takes place after 2-3 ps, inducing the dissociation of the complex, which
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Figure 12. Distributions of the vibrational energy gain or loss in Mg+ · H2O* collisions with He at 300 K. The average vibrational energy gain for the CID trajectories is 2115 cm-1, and that for the CS trajectories is 1700 cm-1.
Figure 11. Representative trajectory leading to CID at 300 K. The upper plot shows the various interatomic distances as a function of time, and the bottom plots show several snapshots of the trajectory. There is only one inner turning point in the Mg+-O distance after the collision with He.
performs only 1 ITP in the Mg+-H2O center-of-mass distance. The example shown in Figure 11 is followed by most of the CID trajectories, as was mentioned above. However, there is a small fraction for which the He complex collision does not induce immediate dissociation of the complex. The rotational energy distribution of the complexes formed in the capture step (for simplicity, not shown here) extends up to 20 kcal mol-1, the average value being ∼7 kcal mol-1. This is a consequence, as mentioned above, of the very large impact parameters of the capture process. The rotational energy, R, of the complex is transferred, upon collision, to vibrational energy, V. This result contrasts with a previous CID study of Ar + CH4, in which the collision process induces V f R rather than R f V tranfer.46 Although CH4 was, like Mg+ · · · H2O*, vibrationally excited, the initial rotational energy of methane was taken from a Boltzmann distribution at 300 K,46 that is, much less than the initial rotational energy of the Mg+ · · · H2O* complex, as indicated at the beginning of this paragraph. The differences in the initial rotational energy of CH4 and Mg+ · · · H2O* might explain the different energy transfer pathways found for Ar + CH4 and He + Mg+ · · · H2O*. The distribution of ∆Evib ) Evib,f - Evib,i for a typical complex, where Evib,f (Evib,i) is the vibrational energy of the complex after (before) the collision with He, is shown in Figure 12 for the two mechanisms (CS and CID). For this particular complex, most of the collisions lead to an increase in the vibrational energy of the complex, irrespective of the type of mechanism. However, the P(∆Evib) distributions for the CID and CS trajectories are different, as shown in the figure. In particular, the P(∆Evib) distribution for CS trajectories is much broader with an average vibrational energy of 1700 cm-1, a much lower
Figure 13. Distributions of the difference in the average vibrational energy gain between CID and CS trajectories for the 26 excited complexes collided with He in this study. The average difference is 216 cm-1.
value than that found for the CID trajectories (2115 cm-1). The distribution of the CID trajectories is, in turn, narrower, peaking at a vibrational energy close to 2500 cm-1. In addition, only the distribution of the CS trajectories enters the negative region, corresponding to a net loss of vibrational energy in the collision process. In summary, both CID and CS trajectories lose their initial rotational energy: CID trajectories lose more rotational energy than CS trajectories do, and this energy is transferred to the Mg+-O dissociation coordinate. CS trajectories gain less vibrational energy, keeping more of their initial rotational excitation. The difference in the average vibrational energy gain between CID and CS trajectories is depicted graphically as a distribution in Figure 13. Although the number of values (26) to plot the distribution is clearly insufficient to extract quantitative conclusions, the average value is
