^{1,a)}

### Abstract

The dynamics of the isotopic scrambling in the energized and metastable complex has been studied using classical molecular dynamics (MD) trajectories starting from regions of phase space corresponding to an already formed collisional complex. The simulations cover the range of internal energies spanned by gas phase collision experiments. Rate constants for the isotopic exchange and the complex dissociation have been computed; the isotopic branching ratio has also been obtained from MD simulations and found to deviate substantially from an equivalent prediction based on a previously proposed kinetic scheme. This finding suggests the possibility that details of the reactiondynamics play a role in defining the isotopic branching ratio. The analysis of trajectory results indicated a relatively long lifetime for the collisional complex and the presence of multiple time scales for the exchange process, with a large fraction of the exchange events being separated only by a single oxygen-oxygen vibration or half of it. The occurrence of these fast consecutive jumps and their different probabilities as a function of the relative direction between first and second jumps suggest the presence of ballistic motion in the complex following each reactive event. This can be explained on the basis of overlapping regions in phase space and it is used to provide an explanation of the difference between kinetic and MD branching ratios.

The author acknowledges Barry K. Carpenter, Peter J. Knowles, and Fausto Cargnoni for useful comments and Samuel R. Stone for a careful read of the manuscript. The authors also acknowledges financial support from EPSRC (GR/R77803/01).

INTRODUCTION

METHODS AND RESULTS

Calculation of reaction rate constants and branching ratios using MD and statistical theories

Detailed investigation of the Zundel internal dynamics using MD trajectories

The relationship between nonstatistical dynamics and branching ratio

CONCLUSIONS

### Key Topics

- Dissociation
- 19.0
- Monte Carlo methods
- 19.0
- Molecular dynamics
- 15.0
- Statistical analysis
- 15.0
- Protons
- 12.0

## Figures

Process involved during the collision. (a) Potential energy surface (kcal∕mol; MP2∕aug-cc-pVTZ; OSS3, square brackets; OSS2 bracket). (b) Details of the pseudorotation inducing the proton exchange in the Zundel cation and choice of labels for the H atoms involved in the process. The process shown in this panel can be represented using the shorthand notation , where means atom moves in location previously occupied by atom .

Process involved during the collision. (a) Potential energy surface (kcal∕mol; MP2∕aug-cc-pVTZ; OSS3, square brackets; OSS2 bracket). (b) Details of the pseudorotation inducing the proton exchange in the Zundel cation and choice of labels for the H atoms involved in the process. The process shown in this panel can be represented using the shorthand notation , where means atom moves in location previously occupied by atom .

Schematic representation of the exchange and dissociation processes in the Zundel cation. Red atoms are oxygens, gray atoms are hydrogens, and blue∕green atoms are deuteriums. In the kinetic Monte Carlo scheme, and . The “ball and stick” models represent the minimum energy structure (min) and the transition state (TS) for the exchange process.

Schematic representation of the exchange and dissociation processes in the Zundel cation. Red atoms are oxygens, gray atoms are hydrogens, and blue∕green atoms are deuteriums. In the kinetic Monte Carlo scheme, and . The “ball and stick” models represent the minimum energy structure (min) and the transition state (TS) for the exchange process.

Distribution of the number of trajectories with a specific total angular momentum (in a.u.) sampled during the Monte Carlo EMS simulations at three different energies.

Distribution of the number of trajectories with a specific total angular momentum (in a.u.) sampled during the Monte Carlo EMS simulations at three different energies.

Logarithm of the rate constants vs (kcal∕mol) for the exchange (exch) and dissociation (diss) processes computed with MD simulations and statistical theories (stat) on the OSS2 surface.

Logarithm of the rate constants vs (kcal∕mol) for the exchange (exch) and dissociation (diss) processes computed with MD simulations and statistical theories (stat) on the OSS2 surface.

Angular momentum-resolved rate constants for the exchange (a) and dissociation (b) processes as a function of the angular momentum for different energies (OSS2 PES). The values of have been coarse grained using bin width of 1 and of for exchange and dissociation, respectively.

Angular momentum-resolved rate constants for the exchange (a) and dissociation (b) processes as a function of the angular momentum for different energies (OSS2 PES). The values of have been coarse grained using bin width of 1 and of for exchange and dissociation, respectively.

Lifetime distribution for the exchange (a) and dissociation (b) processes for trajectories with and . The dashed curves represent the lifetime distribution obtained using the MD computed rate constant for the two processes.

Lifetime distribution for the exchange (a) and dissociation (b) processes for trajectories with and . The dashed curves represent the lifetime distribution obtained using the MD computed rate constant for the two processes.

Branching ratio as a function of the internal energy of the Zundel cation. “MD_{D} mass” and “MD” indicate results obtained using trajectories employ for H and D either the correct isotopic mass or, disregarding the difference, the proton mass for both. “KMC” indicates results obtained using kinetic Monte Carlo, whereas “statistical ratio” gives the statistical probability of dissociating in isotopically different species starting from a randomized .

Branching ratio as a function of the internal energy of the Zundel cation. “MD_{D} mass” and “MD” indicate results obtained using trajectories employ for H and D either the correct isotopic mass or, disregarding the difference, the proton mass for both. “KMC” indicates results obtained using kinetic Monte Carlo, whereas “statistical ratio” gives the statistical probability of dissociating in isotopically different species starting from a randomized .

Time evolution of the O–O distance and internal coordinates for two representative trajectories with different values of : (a) 82 and (b) . To improve the clarity of the pictures, the oxygen-oxygen distance (lowest line, red) has been scaled by a factor of 0.95. For the same reason, some of the curves representing for the protons are shown only in the vicinity of exchange events. The latter are defined as the time when , i.e., as the crossing time of two different curves (different colors). Notice that exchanges happen primarily close to the outer or inner turning points of the oxygen-oxygen vibration, and that, upon increasing the energy, the frequency of two exchanges happening after a short time gap increases substantially, leading to more exchanges clustered together.

Time evolution of the O–O distance and internal coordinates for two representative trajectories with different values of : (a) 82 and (b) . To improve the clarity of the pictures, the oxygen-oxygen distance (lowest line, red) has been scaled by a factor of 0.95. For the same reason, some of the curves representing for the protons are shown only in the vicinity of exchange events. The latter are defined as the time when , i.e., as the crossing time of two different curves (different colors). Notice that exchanges happen primarily close to the outer or inner turning points of the oxygen-oxygen vibration, and that, upon increasing the energy, the frequency of two exchanges happening after a short time gap increases substantially, leading to more exchanges clustered together.

Energy dependence of the delay time (ps) probability for two consecutive exchanges obtained using the OSS2 potential. The numbers in brackets represent the fraction of exchange events with .

Energy dependence of the delay time (ps) probability for two consecutive exchanges obtained using the OSS2 potential. The numbers in brackets represent the fraction of exchange events with .

Fraction of consecutive exchanges happening within (red) or after (blue) . The solid lines represent a reverse rotation , the long dashed lines indicate a rotation in the same direction of the original exchange , and the short dashed lines are exchanges with protons or [Fig. 1(b)].

Fraction of consecutive exchanges happening within (red) or after (blue) . The solid lines represent a reverse rotation , the long dashed lines indicate a rotation in the same direction of the original exchange , and the short dashed lines are exchanges with protons or [Fig. 1(b)].

Energy barrier for the pseudorotation of the moiety in the Zundel cation as a function of the O–O distance computed using the OSS2 potential.

Energy barrier for the pseudorotation of the moiety in the Zundel cation as a function of the O–O distance computed using the OSS2 potential.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content