Quantum Manifestation of Roaming in H + MgH â Mg + H2: The Birth

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Quantum Manifestation of Roaming in H + MgH # Mg + H: The Birth of Roaming Resonances 2

Anyang Li, Jun Li, and Hua Guo J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp4049988 • Publication Date (Web): 28 May 2013 Downloaded from http://pubs.acs.org on June 1, 2013

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The Journal of Physical Chemistry

Submitted to JPCA, 5/21/2013

Quantum Manifestation of Roaming in H + MgH → Mg + H2: The Birth of Roaming Resonances Anyang Li, Jun Li, and H. Guo* Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, NM 87131 Abstract The dynamics of the H + MgH → Mg + H2 reaction at low collision energies is analyzed with both the quasi-classical trajectory and quantum wave packet methods on an improved potential energy surface for the ground electronic state of MgH2. Three microscopic reaction channels, namely direct abstraction, roaming via a loose roaming transition state, and complex decaying via a tight transition state, are identified. It is shown that the reaction is dominated by the direct abstraction channel, while the roaming channel is responsible for about 20% of reaction flux. On the other hand, the pathway via the tight transition state plays almost no role at the energy of study. The two dominant channels produce similar highly excited vibrational distributions for the H2 product. Finally, it is shown that roaming is manifested quantum mechanically by a large amplitude vibration, which emerges just below the reaction threshold, guided by the roaming transition state. Its continuation into the continuum leads to roaming resonances. Key words: transition state, roaming, reaction dynamics *: corresponding author: [email protected]

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I. Introduction Since its recent discovery,1 the roaming reaction mechanism has been shown to operate in many chemical systems.2-12 Instead of following the minimum energy path over a conventional transition state, highly energetic systems may react via the roaming, or frustrated dissociation, mechanism, in which an atom or a group of atoms attempts unsuccessfully to break apart, typically facilitated by a high energy radical dissociation channel.12 Such a reaction mechanism departs significantly from the minimum energy path associated with the conventional transition state, thus representing an alternative reaction mechanism that produces drastically different product distributions from those via the conventional transition state. The roaming mechanism can be quite significant and sometimes dominant. Interestingly, roaming transition states have been found in many of the roaming systems, which allow statistical and dynamic treatments.13-16 However, the roaming saddle point is often very loose because of its location in the flat region of the potential energy surface (PES) just below dissociation limit and the corresponding transitionstate treatment can be quite different from a conventional tight saddle point. For instance, recrossing can be quite significant due to the large amplitude motion in roaming. While the roaming dynamics has been extensively investigated theoretically and the agreement with available experiment has been quite good, nearly all theoretical studies have been classical in nature,1, 3, 12, 17-20 due apparently to the large size of the roaming systems. These classical models based on trajectories on accurate global PESs are intuitive and instrumental for advancing our understanding of this interesting phenomenon. Given the quantum mechanical nature of molecular systems, however, it is also highly desirable to understand how roaming manifests quantum mechanically. Unfortunately, most known roaming systems are too large or too energetic for an accurate quantum mechanical characterization. 2 ACS Paragon Plus Environment

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The H + MgH → Mg + H2 reaction represents an ideal testing ground to understand the quantum mechanical face of roaming dynamics. As shown in Fig. 1, this bimolecular reaction proceeds either directly via hydrogen abstraction or indirectly via a highly energetic MgH2 complex.21 Unlike most known roaming systems, the energetic complex is prepared here by collision, rather than photoabsorption.10-11 Because of the tight saddle point leading to the products is close in energy with the reactant channel, the MgH2 intermediate can in principle decay via two possible mechanisms.22 The first is via the tight transition state (labeled as t-TS in Fig. 1), while the other through roaming near the reactant asymptote. The situation here is quite similar to the H + HCO → CO + H2 reaction, which has been investigated by several authors.20, 23-24

Indeed, the MgH2 potential energy surface (PES) is qualitatively similar to that of H2CO,25

and roaming in the H + MgH reaction has already been suggested by Takayanagi and Tanaka.22 However, the previous dynamical study22 was carried out on a PES designed for spectroscopic studies of MgH2,21 thus inaccurate in the dissociation limits. Furthermore, no cross sections were computed as only the J=0 partial wave was considered in their study.22 More recently, a loose roaming transition state (denoted as r-TS in Fig. 1) near the H + MgH asymptote has been identified by Harding et al.,16 thus allowing a statistical treatment of the roaming channel. However, its role in roaming dynamics has not been investigated. In this work, we report an improved ab initio PES for the H + MgH reaction and carry out both quasi-classical trajectory (QCT) and quantum mechanical (QM) wave packet calculations of the reaction dynamics. In addition, the wave functions for both bound states and resonances near the reaction threshold were extracted and analyzed. The aim is to quantitatively examine the role played by roaming in this simple bimolecular reaction and to better understand the quantum manifestations of roaming dynamics.



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II. Potential energy surface In 2004, Li, Xie, and Guo (LXG)21 reported a global PES for the ground (11A') electronic state of the MgH2 system using the internally contracted multi-reference configuration interaction method with the Davidson correction (icMRCI+Q) with the cc-pVnZ (n = 3, 4, 5) basis sets extrapolated to the complete basis set limit. This electronic state correlates with both the Mg(1S0) + H2 and MgH(X2+) + H asymptotes, thus facilitating the reaction. Recent quantum dynamics calculations by Takayanagi and Tanaka22 have been carried out on this PES. Subsequently, Li and Le Roy reported an improved PES using the larger aug-cc-pVnZ (n = 3, 4, 5) basis sets, but aimed at a better description of the vibrational spectrum.26 Unfortunately, neither of these PESs is suitable for dynamical studies because the distance between the Mg atom and H atom ( rMgH ) was limited to 9.0 a0, which is not enough to accurately describe the MgH + H asymptotic region. To remedy the deficiency, additional ab initio calculations were carried out at the same level of theory as in the LXG work.21 In particular, we added additional points at rMgH = 4.2, 6.0, 10.5, 12.0, and 15.0 a0 with the entire grid in the other two coordinates. This is necessary to describe the long-range asymptotic region for the reaction. Tests showed that the energy at rMgH = 20.0 a0 is only less than 1.0 cm−1 higher than that at rMgH = 15.0 a0. Finally, the global PES was obtained by a spline fit to 5406 symmetry-unique ab initio points, which are much more than the 3330 points used in the LXG PES. The additional ab initio points raised the energy of the MgH + H asymptote by about 70 cm−1, relative to the HMgH minimum. Importantly, it lowered the asymptotic angular anisotropy


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from more than 300 cm-1 at 9.0 a0 to less than 1 cm-1 at 15.0 a0, which is necessary for accurate state-to-state calculations. In addition, an accurate description of the asymptotic region is vital for a reliable characterization of the roaming pathway, which can reach large H-MgH distances. III. Quantum dynamics The state-to-state reactive scattering calculations were performed using the Chebyshev real wave packet method,27 which has been presented in detail in our previous work.28-30 Specifically, the Hamiltonian in the reactant Jacobi coordinates (R, r, γ) can be written as (   1 ) ˆj 2 1 2 1  2 ( Jˆ  ˆj ) 2 Hˆ       V ( R, r ,  ) , 2 R R 2 2 r r 2 2 R R 2 2 r r 2

(1)

where the radial coordinates R and r are defined as the H'-MgH and Mg-H distances with  R and

 r as the corresponding reduced masses, respectively, and γ is the angle between R and r. Jˆ is the total angular momentum and ˆj is the diatomic MgH angular momentum operator. The last term in Eq. (1) represents the PES for MgH2. The wave function were discretized in a mixed representation,28 consisting of a direct product discrete variable representation (DVR)31 for the two radial degrees of freedom and a finite basis representation (FBR) for the angular degrees of freedom. A Gaussian wave packet associated with the MgH (vi=0, ji=0) internal state was launched in the reactant channel and propagated using the modified Chebyshev recursion relation:

 k  2DHˆ s  k 1  D2  k 2 ,

k  2,


(2)


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where 1  DHˆ s  0 and  0   i . To avoid divergence, the Hamiltonian was scaled to the range [–1, 1]. During the wave packet propagation, the fast Fourier transform method was employed for the radial degrees of freedom on a L-shaped grid,32-33 which saves grid points in the calculations. For the angular degrees of freedom, the wave function was converted from FBR to DVR by using a pseudo-spectral method.34 The action of the potential energy operator was evaluated in the DVR grid where it is diagonal. Finally, the wave packet is damped by D which is the (real) damping function defined at the edges of the grid to impose outgoing boundary conditions. The parameters used in the QM calculations are listed in Table I. The S-matrix elements ( SvJf j f K f vi ji Ki ( E ) ) were obtained using a reactant coordinate based (RCB) method,33, 35 Once these elements are obtained, the state-to-state integral and differential cross sections (ICSs and DCSs) are calculated by summing over all partial waves:

v

f

j f vi ji

(E) 

 (2 ji  1)k

d  v f j f vi ji ( , E ) dΩ



2 vi ji

 (2 J  1) S

 (2 ji  1)

Ki K f

J v f j f K f vi ji Ki

2

(E) ,

(3)

J

2

 Ki K f

1 2ik vi ji

 (2 J  1)d

J K f Ki

( ) S

J v f j f K f vi ji Ki

(E) ,

(4)

J

where  is the scattering angle and d KJ f Ki ( ) is the reduced rotational matrix.36

In addition to the quantum reactive scattering calculations described above, we have also investigated both the bound and resonance state wave functions near the reaction threshold. In these calculations, the propagation was initiated at R = 6.0 a0 with the same wave packet form, which is already inside the MgH2 well. The Chebyshev autocorrelation function was computed


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and the energy-dependent wave functions for both the bound and resonance states were reconstructed using the following equation:37 K

 ( E )   (2   k 0 ) cos(k arccos E )  k

(5)

k 0

IV. QCT calculations Standard QCT calculations for the H + MgH reaction were carried out based on the newly improved PES described above, using VENUS.38 The MgH reactant is in its ro-vibrational ground state, and sampled using the classical action-angle variables.39 The maximal impact parameter (bmax) was determined using small batches of trajectories with trial values. The trajectories were initiated with a reactant separation of 7.0 Å, and terminated when products reached a separation of 6.0 Å, or when reactants are separated by 6.0 Å for non-reactive trajectories. During the propagation, the gradient of the PES was obtained numerically by a central-difference algorithm. The propagation time step was selected to be 0.02 fs, which conserves the energy better than 0.04 kcal/mol for most trajectories. A few trajectories which failed to converge energy to 0.04 kcal/mol or were nonreactive after 2.0 ps were discarded. The reactive integral cross section (ICS) for the reaction was computed according to the following formula: 2  r  Ec    bmax ( Ec ) Pr  Ec  ,

(6)

where the reaction probability at the specified collision energy Ec is given by the ratio between the number of reactive trajectories (Nr, r can be abstraction, exchange or their sum) and total number of trajectories (Ntotal): 7 ACS Paragon Plus Environment


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Pr  Ec   Nr / Ntotal .

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(7)

The standard error is given by:   ( Ntotal  Nr ) / Ntotal Nr .

To determine the final state distributions of the products we have used the both the traditional histogram binning (HB) and Gaussian binning (GB) methods,40 which enforce the vibrational quantization of the products. The GB approach weights the contribution of a trajectory by a Gaussian function centered at the vibrational quantum number of the diatomic product, thus requires a large number of trajectories to achieve reasonable statistics. The reactive differential cross section (DCS) was computed by

d r  P ( )  r r , d  2 sin( )

(8)

where Pr(  ) is the normalized probability for the scattering products at the scattering angle  , which is given by

  i  f  .  i  f   

  cos 1 

(9)

Here,  is the relative velocity vector, and the subscripts ‘i’ and ‘f’ denote ‘initial’ and ‘final’, respectively,  i   H  MgH ,  f   H2  Mg . The signs of the relative velocity vectors were chosen such that  =0° corresponds to forward scattering and  =180° corresponds to backward scattering.


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In addition to the reactive scattering calculations, trajectories have also been run from the tight transition state (t-TS) to identify the signature of that pathway. In this case, micro-canonical sampling of the initial conditions41 was performed using a modified version of VENUS (courtesy of Bill Hase and Swapnil Kohale) and the final state distributions were determined the same way as in bimolecular collisions. V. Results Figure 2 displays the two-dimensional PES with the Mg-H distance fixed at its equilibrium value (r=3.23 a0). The deep H-Mg-H well near =180o is apparent while the Mg + H2 channel near =0o is also visible. The H + MgH collision near =0o is likely to lead to direct abstraction, while the collision near =180o would experience attractive forces toward the HMgH well. The resulting complex may return to the reactant asymptote, overcome the tight transition state (t-TS) to the Mg + H2 product asymptote, or roam to the same products via the roaming transition state (r-TS), as depicted in Fig. 1. The tight transition state (t-TS, R=3.36 a0, r=3.44 a0, =55.4o) and roaming transition state (r-TS, R=8.78 a0, r=3.29 a0, =58.2o) are also indicated in the figure. On our PES, t-TS has a C2v symmetry and is tight (1= 2160 cm-1, 2= 253 cm-1,3= 1516i cm-1), while r-TS is very loose (1= 1487 cm-1, 2= 77 cm-1,3= 87i cm-1), which is consistent with the finding of Harding and coworkers.16 In addition to the H + MgH → Mg + H2 abstraction reaction, the PES also allows the H + MgH' → MgH + H' exchange reaction, which is thermoneutral. The QM excitation functions for both the abstraction and exchange reactions are shown in Fig. 3 as a function of the collision energy. The reactive ICSs have no threshold, consistent with the absence of an intrinsic barrier in the entrance channel. Some oscillations are present, suggesting involvement of resonances, which dominate the reaction probabilities, particularly at 9 ACS Paragon Plus Environment


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low energies, as shown by the J=0 reaction probability in the inset. The ICS for the thermoneutral exchange channel is much smaller than that for the exothermic abstraction channel. In the main abstraction channel, the excitation function is large at low collision energies, but levels off as energy increases. The QCT ICSs at Ec = 1 and 3 kcal/mol are also included for comparison and the agreement with the QM results is quite good. To understand the reaction dynamics, we focus on the results at 1 kcal/mol of collision energy. 5×104 trajectories were calculated at this energy, resulting 7794 reactive trajectories with the energy converged within 0.04 kcal/mol. The vibrational state distributions of the H2 product obtained from both the QM and QCT calculations are shown in Fig. 4. The quantum-classical agreement is quite good, so is the agreement between the results obtained with the two different binning approaches in the QCT calculations. This is presumably due to the large exothermicity of the reaction that deposes much energy into the H2 vibration. In the same diagram, the H2 vibrational state distribution obtained from the micro-canonical sampling of t-TS at the same total energy is also included. The much less excited H2 distribution suggests that this pathway plays a relatively minor role in the reaction, as confirmed below. In Fig. 5, the rotational state distributions in various vibrational channels are displayed. Apparently, the rotational states of H2 are populated up to the highest accessible ones, and the rotational excitation decreases with increasing vibrational excitation. The observed correlation between the rotational and vibrational distributions is similar to that reported in the earlier work of Takayanagi and Tanaka.22 Again the quantum-classical agreement is satisfactory. In Fig. 6, DCSs obtained from both the QCT and QM calculations are shown, and they all predict a forward bias and significant sideway scattering. These product angular distributions suggest that the reaction is dominated by a stripping mechanism, in which the incoming H atom strips the other H atom away from Mg. 10 ACS Paragon Plus Environment

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VI. Reaction mechanisms The good agreement with QM results suggests that the QCT model provides a reasonable description of the reaction dynamics. Thus, it is used to examine mechanistic issues in this reactive system. To analyze the reaction mechanism, we plot in Fig. 7 the distribution of the reaction lifetime in the QCT calculations, which is simply defined as the length of each reactive trajectory with a bin of 50 fs. It is shown that the reaction is dominated by fast trajectories via mostly direct hydrogen abstraction. However, there is a long tail in the distribution, clearly suggesting longer lived complex-forming trajectories. In the inset, the cumulative vibrational state distribution obtained in the QCT calculations is plotted for different time periods. It is clear that the initial flux, which corresponds to direct abstraction, preferably populates the highly excited vibrational levels of H2. Interestingly, the subsequent flux also prefers highly excited vibrational levels. The direct abstraction trajectory can be readily identified by the following criterion: the H-H distance is less than 2.3 Å after the first turning point. As discussed above, the MgH2 complex might decay either through t-TS or via roaming. To distinguish these two channels, the following metrics were used. A trajectory is considered passing through t-TS if it enters the t-TS region ( rMgH =1.82±0.3 Å, and rHH =1.64±0.6 Å) and reaches the product asymptote within 100 fs. On the other hand, it can be argued that the roaming trajectories are guided by the roaming transition state (r-TS). However, they typically undergo large amplitude motions that pass through a large configuration area near r-TS. Hence, it is difficult to define these trajectories solely based by the geometry of r-TS. In this work, a roaming trajectory is identified as a reactive one in which its HH distance wonders beyond 4.5 Å after the first turning point. These criteria, which are similar to



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those used by Christoffel and Bowman in identifying various types of trajectories in the H + HCO reaction,20 are of course not unique. However, they are sufficient for a reasonable division of these microscopic reaction channels. An alternative, perhaps more precise, way to distinguish these two types of trajectories is to take advantage of the second-order saddle point between t-TS and r-TS.16, 42 Figure 8 displays three representative trajectories and they are striking different. With these metrics, it was found that at Ec = 1 kcal/mol the direct abstraction accounts for about 75% of the reaction, while the roaming channel 18%. There are about 7% of trajectories that fit to none of the categories. These numbers become 82, 13, and 5% at 3 kcal/mol. In addition, our QCT analysis showed that both the direct and roaming channels yield very similar vibrational state distributions, which are shown in Fig. 4. This is understandable as the roaming trajectories are essentially frustrated non-reactive scattering events and the reaction is also via abstraction. Furthermore, both the direct abstraction and roaming channels are dominated by forward scattering, as shown in Fig. 6, due to the same stripping mechanism. These observations here are very similar to those in the H + HCO reaction, in which the H2 products from the roaming and direct channels are both vibrationally hot and difficult to distinguish and the latter dominates.20 Interestingly, there are only 11 trajectories going through t-TS, which indicate a negligible role to this pathway, in good accord with the earlier J=0 finding of Takayanagi and Tanaka.22 This is readily understood: the centrifugal potential raises the already high barrier at this tight saddle point further to block this pathway effectively. The above analysis confirms that there is significant roaming in the H + MgH reaction, at least at low collision energies. However, it is still unclear how roaming manifests quantum mechanically. Since resonances above the reaction threshold is contaminated by non-reactive scattering wave functions, we explore the bound states (J=0) just below the threshold. In Fig. 9, 12 ACS Paragon Plus Environment

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several such bound state wave functions are shown along with several resonances in twodimensional contour plots where the Mg-H bond is fixed at 3.23 a0. It is clear from the first panel, the vibrational wave function of the low-lying bound state at -2.63 kcal/mol is quite regular with a clear nodal structure. As energy increases, a striking large-amplitude structure starts to emerge and it corresponds to an H atom swinging between the collinear H-Mg-H and T-shaped configurations. In the latter case, the H reaches the relatively flat region of the PES significantly away from the potential well, thus corresponding to the roaming motion. This feature grows steadily as the energy increases, eventually reaches to product asymptote near =180o, and becomes dominant just below the reaction threshold (E=-0.02 kcal/mol). Interestingly, this largeamplitude roaming feature, guided by the roaming transition state (r-TS) at E = -0.05 kcal/mol, skirts the tight transition state (t-TS). This is presumably due to the higher second order saddle point between the two first order saddle points, which has found in both H2CO16, 42 and MgH2 systems.16 We have also included in Fig. 9 two resonances near 1 kcal/mol of collision energy, as indicated in the inset of Fig. 3. As expected, the resonance wave functions above the reaction threshold become much less structured. Much of the amplitude in large R values is simply the non-reactive scattering part of the wave function from and back to the reactant asymptote. However, the roaming structure is still discernible and there is still no amplitude near t-TS. In the last panels, two roaming trajectories (b~0 Å) are superimposed on the roaming wave function. The quantum-classical correspondence for the roaming part of the trajectories is apparent, which allows the unambiguous assignment of the large-amplitude H swing motion in these wave functions to roaming.



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The gradual emergence of this large-amplitude roaming vibration is apparently dictated by the global feature of the PES near the dissociation threshold, where the PES becomes very flat. It is clear that the roaming transition state (r-TS) seems to present a focal point that shapes up the roaming vibration, which differs significantly from the regular HMgH vibration and only becomes viable near the reaction asymptote. The continuation of this roaming vibration into the continuum leads to the formation of roaming resonances, which are the quantum mechanical manifestation of roaming. It is also apparent that the roaming vibration in the resonances is more complex than that below the reaction threshold. In particular, we note that there are multiple branches in the roaming vibrational wavefunction, which spread out in a large configuration space, underscoring the loose nature of the roaming transition state. Although our analysis is based on J=0, the conclusions should be general. VII. Conclusions The quantum and classical dynamics of the H + MgH reaction is investigated on an improved potential energy surface based on high-level ab initio calculations. At low collision energies, the reaction is dominated by a direct abstraction channel, but a significant portion proceeds via a roaming channel through the MgH2 reaction intermediate. Both microscopic reaction channels lead to the H2 product with similar high internal excitations. A tight transition state between the MgH2 well and the product channel is found to play a negligible role in the reaction. The quantum mechanical manifestation of roaming in this reaction is investigated and identified as a large-amplitude vibrational feature that emerges just below the reaction threshold and persists at higher energies in the continuum. This roaming vibrational feature is guided by the roaming transition state on the potential energy surface near the entrance channel, underscoring the importance of the roaming transition state in roaming dynamics. Indeed, our 14 ACS Paragon Plus Environment

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results presented here suggest that roaming is not, as the word might imply, aimless and chaotic. Rather, it is manifested in quantum mechanics as a large amplitude but regular vibration organized by the roaming transition state. This observation in the current triatomic system might have important implications for larger roaming systems, particularly the H2CO system, which has qualitatively the same potential energy surface. While a full quantum mechanical characterization may still be difficult for some time, classical analysis based on periodic orbits 43 might shed valuable lights on roaming vibration.

Acknowledgements: This work was supported by the Department of Energy (DE-FG0205ER15694). Parts of the computation were carried out at the National Energy Research Scientific Computing (NERSC) Center. We thank Bill Hase and Swapnil Kohale for sharing with us an updated version of VENUS, Joel Bowman and Larry Harding for several useful discussions on roaming, and Hui Li for sending us the potential routines.



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TABLE I. Numerical parameters used in the QM wave packet calculations. (Atomic units used unless stated otherwise.)

Grid/basis ranges and sizes*

R  [2, 17.0], N R1  134, N R2  107 r  [2, 13.0], N r1  107, N r2  31

  [0,180], j  0 ~ jmax  160, N j  161 R  7.5

Projection** Initial wave packet

exp(( R  R0 )2 / 2 2 ) cos(k0 R), k0  2 R E0

R0 = 12.0,  = 0.3, E0 = 0.15 eV Damping function

R  12.5 2   exp[ 0.02(17.0  12.5 ) ], 12.5  R  17.0  r  12.6 2  exp[ 0.2( ) ]  0.01, 12.6  r  13.0 D 13.0  12.6  r  10.8 2 ) ], 10.8  r  12.6 exp[ 0.01( 12  1, otherwise.6  10.8 

Spectral range

Potential energy cutoff: 6.0 eV Rotational kinetic energy cutoff: 6.0 eV 40000

Propagation steps

* N R1 / r is the number of grid points in R/r, and N R2 / r is the number of R/r grid points in products/reactants region. ** R is the Mg + H2 product Jacobi coordinates.


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References: 1. Townsend, D.; Lahankar, S. A.; Lee, S. K.; Chambreau, S. D.; Suits, A. G.; Zhang, X.; Rheinecker, J.; Harding, L. B.; Bowman, J. M., The roaming atom: Straying from the reaction path in formaldehyde decomposition, Science 2004, 306, 1158-1161. 2. Houston, P. L.; Kable, S. H., Photodissociation of acetaldehyde as a second example of the roaming mechanism, Proc. Natl. Acad. Sci. USA 2006, 103, 16079-16082. 3. Heazlewood, B. R.; Jordan, M. J. T.; Kable, S. H.; Selby, T. M.; Osborn, D. L.; Shepler, B. C.; Braams, B. J.; Bowman, J. M., Roaming is the dominant mechanism for molecular products in acetaldehyde photodissociation, Proc. Natl. Acad. Sci. USA 2008, 105, 12719-12724. 4. Goncharov, V.; Herath, N.; Suits, A. G., Roaming dynamics in acetone dissociation, J. Phys. Chem. A 2008, 112, 9423-9428. 5. Kamarchik, E.; Koziol, L.; Reisler, H.; Bowman, J. M.; Krylov, A. I., Roaming pathway leading to unexpected water + vinyl products in C2H4OH dissociation, J. Phys. Chem. Lett. 2010, 1, 3058-3065. 6. Sivaramakrishnan, R.; Michael, J. V.; Harding, L. B.; Klippenstein, S. J., Shock tube explorations of roaming radical mechanisms: The decompositions of isobutane and neopentane, J. Phys. Chem. A 2012, 116, 5981-5989. 7. Sivaramakrishnan, R.; Su, M. C.; Michael, J. V.; Klippenstein, S. J.; Harding, L. B.; Ruscic, B., Shock tube and theoretical studies on the thermal decomposition of propane: Evidence for a roaming radical channel, J. Phys. Chem. A 2011, 115, 3366-3379. 8. Hause, M. L.; Herath, N.; Zhu, R.; Lin, M. C.; Suits, A. G., Roaming-mediated isomerization in the photodissociation of nitrobenzene, Nat. Chem. 2012, 3, 932-937. 9. Grubb, M. P.; Warter, M. L.; Xiao, H. Y.; Maeda, S.; Morokuma, K.; North, S. W., No straight path: Roaming in both ground- and excited-state photolytic channels of NO3 -> NO+O2, Science 2012, 335, 1075-1078. 10. Suits, A. G., Roaming atoms and radicals: A new mechanism in molecular dissociation, Acc. Chem. Res. 2008, 41, 873-881. 11. Herath, N.; Suits, A. G., Roaming radical reactions, J. Phys. Chem. Lett. 2011, 2, 642647. 12. Bowman, J. M.; Shepler, B. C., Roaming radicals, Annu. Rev. Phys. Chem. 2011, 62, 531-553. 13. Harding, L. B.; Klippenstein, S. J., Roaming radical pathways for the decomposition of alkanes, J. Phys. Chem. Lett. 2010, 1, 3016-3020. 14. Harding, L. B.; Georgievskii, Y.; Klippenstein, S. J., Roaming radical kinetics in the decomposition of acetaldehyde, J. Chem. Theo. Comput. 2010, 114, 765-777. 15. Klippenstein, S. J.; Georgievskii, Y.; Harding, L. B., Statistical theory for the kinetics and dynamics of roaming reactions, J. Phys. Chem. A 2011, 115, 14370-14381. 16. Harding, L. B.; Klippenstein, S. J.; Jasper, A. W., Separability of tight and roaming pathways to molecular decomposition, J. Phys. Chem. A 2012, 116, 6967-6982. 17. Shepler, B. C.; Braams, B. J.; Bowman, J. M., "Roaming" dynamics in CH 3CHO photodissociation revealed on a global potential energy surface, J. Phys. Chem. A 2008, 112, 9344-9351. 18. Fu, B.; Shepler, B. C.; Bowman, J. M., Three-state trajectory surface hopping studies of the photodissociation dynamics of formaldehyde on ab initio potential energy surfaces, J. Am. Chem. Soc. 2011, 133, 7957-7968. 17 ACS Paragon Plus Environment


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19. Bowman, J. M.; Zhang, X., New Insights on reaction dynamics from formaldehyde photodissociation, Phys. Chem. Chem. Phys. 2006, 8, 321-332. 20. Christoffel, K. M.; Bowman, J. M., Three reaction pathways in the H plus HCO -> H2 + CO Reaction, J. Phys. Chem. A 2009, 113, 4138-4144. 21. Li, H.; Xie, D.; Guo, H., An ab initio potential energy surface and vibrational states of MgH2(11A'), J. Chem. Phys. 2004, 121, 4156. 22. Takayanagi, T.; Tanaka, T., Roaming dynamics in the MgH+H -> Mg+H2 reaction: Quantum dynamics calculations, Chem. Phys. Lett. 2011, 504, 130-135. 23. Harding, L. B.; Wagner, A. F., The reaction of atomic hydrogen with the formyl radical, Symp. (Int.) Combust. 1986, 21, 721-728. 24. Troe, J.; Ushakov, V., Classical trajectory study of the reaction between H and HCO, J. Phys. Chem. A 2007, 111, 6610-6614. 25. Zhang, X.; Zou, S.; Harding, L. B.; Bowman, J. M., A global ab initio potential energy surface for formaldehyde, J. Phys. Chem. A 2004, 108, 8980-8986. 26. Li, H.; Le Roy, R. J., Spectroscopic properties of MgH2, MgD2, and MgHD calculated from a new ab initio potential energy surface, J. Phys. Chem. A 2007, 111, 6248-6255. 27. Guo, H., Quantum dynamics of complex-forming bimolecular reactions, Int. Rev. Phys. Chem. 2012, 31, 1-68. 28. Lin, S. Y.; Guo, H., Quantum state-to-state cross sections for atom-diatom reactions, A Chebyshev real wave packet approach, Phys. Rev. A 2006, 74, 022703. 29. Sun, Z.; Lee, S.-Y.; Guo, H.; Zhang, D. H., Comparison of second-order split operator and Chebyshev propagator in wave packet based state-to-state reactive scattering calculations, J. Chem. Phys. 2009, 130, 174102. 30. Ma, J.; Lin, S. Y.; Guo, H.; Sun, Z.; Zhang, D. H.; Xie, D., State-to-state quantum dynamics of the O + OH -> H + O2 reaction, J. Chem. Phys 2010, 133, 054302. 31. Light, J. C.; Carrington Jr., T., Discrete-variable representations and their utilization, Adv. Chem. Phys. 2000, 114, 263-310. 32. Mowrey, R. C., Reactive scattering using efficient time-dependent quantum mechanical wave packet methods on an L-shaped grid, J. Chem. Phys. 1991, 94, 7098-7105. 33. Sun, Z.; Guo, H.; Zhang, D. H., Extraction of state-to-state reactive scattering attributes from wave packet in reactant Jacobi coordinates, J. Chem. Phys 2010, 132, 084112. 34. Corey, G. C.; Tromp, J. W.; Lemoine, D., Fast pseudospectral algorithm curvilinear coordinates. In Numerical Grid Methods and Their Applications to Schroedinger's Equation, Cerjan, C., Ed. Kluwer: Dordrecht, 1993; pp 1-23. 35. Gómez-Carrasco, S.; Roncero, O., Coordinate transformation methods to calculate stateto-state reaction probabilities with wave packet treatments, J. Chem. Phys. 2006, 125, 054102. 36. Zare, R. N., Angular Momentum. Wiley: New York, 1988. 37. Chen, R.; Guo, H., Evolution of quantum system in order domain of Chebychev operator, J. Chem. Phys. 1996, 105, 3569. 38. Hase, W. L.; Duchovic, R. J.; Hu, X.; Komornicki, A.; Lim, K. F.; Lu, D.-H.; Peslherbe, G. H.; Swamy, K. N.; Linde, S. R. V.; Varandas, A., et al., VENUS96: A General Chemical Dynamics Computer Program, Quantum Chemistry Program Exchange Bulletin 1996, 16, 671. 39. Hase, W. L., Classical Trajectory Simulations: Initial Conditions. In Encyclopedia of Computational Chemistry, Alinger, N. L., Ed. Wiley: New York, 1998; Vol. 1, pp 399-402. 40. Bonnet, L.; Rayez, J.-C., Gaussian weighting in the quasiclassical trajectory method, Chem. Phys. Lett. 2004, 397, 106-109. 18 ACS Paragon Plus Environment

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Figure captions Figure 1. Schematic of the PES and the three microscopic pathways for the H + MgH reaction. Figure 2. Two-dimensional contour plot of the PES in Jacobi coordinates with the Mg-H distance fixed at its equilibrium (r=3.23 a0). Both the tight and roaming transition states are indicated. The contours have an interval of 5 kcal/mol. Figure 3. Integral cross sections as a function of the collision energy for the abstraction and exchange channels of the H + MgH reaction obtained by QM and QCT calculations. The J=0 reaction probability in the abstraction channel is shown in the inset and the arrows indicate the resonances investigated. Figure 4. Calculated H2 vibrational state distributions at Ec=1 kcal/mol. The H2 vibrational state distribution from the tight transition state (t-TS) is also shown in gray, which is normalized to the highest population of the distribution. The contributions from the direct and roaming channels are given in dashed lines. Figure 5. Calculated H2 rotational state distributions in different vibrational levels at Ec = 1 kcal/mol. Figure 6. Differential cross sections for the H + MgH reaction obtained from QCT and QM calculations. The contributions from the direct and roaming channels are given in dashed lines. Figure 7. Reaction time distribution of trajectories and evolution of the vibrational distribution of the H2 product as a function of time (inset).


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Figure 8. Time evolution of direct and roaming trajectories. The left column is the three dimensional rendition while the right column is the evolution in three internuclear distances. The orange ball denotes Mg and the two colored lines and white balls are for the two H atoms. Figure 9. Two-dimensional contour plots of wave functions of several bound and resonance states near the reaction threshold. The two transition states are also indicated in the figures. In the last two panels, two roaming trajectories are superimposed on the roaming vibrational wave function.



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Fig 1


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Fig. 2



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Fig. 3


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Fig. 4



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Fig. 5


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Fig.6



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Fig. 7


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Fig. 8



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Fig. 9


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Quantum Manifestation of Roaming in H + MgH â Mg + H2: The Birth

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