Quantum Dynamics Study of the Potential Energy Minima Effect on

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Quantum Dynamics Study of Potential Energy Minima Effect on Energy Efficiency for the F + CHCl # FCH + Cl Reaction –

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Yida Li, Yuping Wang, and Dunyou Wang J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b01547 • Publication Date (Web): 27 Mar 2017 Downloaded from http://pubs.acs.org on March 30, 2017

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The Journal of Physical Chemistry

Quantum Dynamics Study of Potential Energy –

Minima Effect on Energy Efficiency for the F + –

CH3Cl → FCH3 + Cl Reaction Yida Li, Yuping Wang, and Dunyou Wang* College of Physics and Electronics, Shandong Normal University, Jinan 250014, Shandong, China

* Author to whom correspondence should be addressed. Email: [email protected]

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ABSTRACT The Polanyi rules on the energy efficiency on reactivity are summarized solely from the locations of barriers on the potential energy surfaces. Here our quantum dynamics –

–

study for the F + CH3Cl → FCH3 + Cl reaction shows that the two potential energy minima in the entrance channel on the potential energy surface play an essential role in energy efficiency on reactivity. The reactivity of this reaction is dominated by the low collision energies where two distinctive reaction mechanisms involve the two minima in the entrance channel. Overall, the Cl-CH3 stretching motion and C-H3 umbrella motion both are more efficient than the translational motion in promoting this reaction. Although this reaction has a negative energy barrier, our study shows that it is the minima in the entrance channel, together with the energy barrier relative to these minima, that determine the energy efficacy on reactivity.

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I. INTRODUCTION The Polanyi rules,1 derived from the atom-diatom reactions, state that for late barrier on potential energy surface(PES), the vibrational energy is more effective than translational energy in surmounting the energy barrier into products, and the reverse is true for an early barrier reaction. Thus the Polanyi rules are entirely based on the location of the transition state on the PESs for the tri-atomic reaction systems. In recent years, both experimental and theoretical studies2-28 have been shown that there does not exist a unified rule on the energy efficacy regarding the locations of transition states on more than three-atom reaction systems. The PESs of the poly-atomic reaction systems are more complex usually with potential energy minima in both the reactant and product channels. For example, for the F + H2O reaction23, its PES has an early barrier with two main van der Waals(vdW) wells(one in the reactant channel, the other product channel). There is also an additional vdW complex in the product channel not directly connected to the transition state. For this reaction, the reactant H2O vibrational energy is more effective than translational energy in promoting the reaction,7 which contradicts to the Polanyi rules. For the O + CH4/CD4/CHD3 reaction with a slightly late barrier, where the PES has two vdW wells in the entrance channel and one in the product channel,24 studies13-16 on the reactions show that the translational energy is more effective than all the vibrational motions in surmounting the slightly late barrier. The Polanyi rules cannot be applied to this system either. Then for the Cl + CHD3 reaction system with a later barrier,25 it also has two vdW wells in the entrance channel and one in the 3



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product channel, both experimental5 and theoretical study4 confirmed that overall the C-H vibrational motion is more effective than the translational motion for promoting reactivity. Hence, for this reaction, the Polanyi rules are still upheld. Therefore, if one only considers the locations of transition states on the PESs, the Polanyi rules cannot be simply extended to the poly-atomic reaction systems. Since the poly-atomic reactions usually have energy minima on their PESs, which makes one wonder whether the energy minima, especially the entrance channel wells before the transition state, might also play a role that cannot be neglected on energy efficacy on reactivity. There have been extensive studies on Nucleophilic Substitution (SN2) reactions due to their great importance in organic chemistry.29-41 For a typical SN2 reaction, it is a backside attack of the substrate from the nucleophile with a Walden-inversion –

mechanism. On the PES of the title SN2 reaction F + CH3Cl constructed by Szabó –

and Czakó,42 there are two potential minima corresponding to the F ---CH3Cl and –

FCH3---Cl ion-dipole complexes in the entrance and exit channels respectively. In –

addition, for this PES, there is also a H-bonded minimum F ---HCH2Cl in the –

entrance channel which has a lower energy than the usual F ---CH3Cl pre-reactive complex. The relative energy barrier height with respect to the hydrogen-bonded complex is 4.8 kcal/mol, and the relative energy difference of the pre-active complex with respect to the hydrogen-bonded complex is 1.5 kcal/mol. The reaction energy barrier is below the asymptotic reactants by -12.8 kcal/mol with exoergic energy at -31.8 kcal/mol,42 which means this reaction has an early, negative energy barrier. Su et al. used a model potential to study the rate constants of the title reaction43 4


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assuming that the negative-barrier is not important to the reactivity. However, statistical theory study on rate constants by Hase’s group44 showed that negative-barrier did affect the rate constants. They also found in another classical trajectories study45 that the excitation of C-Cl stretch mode of CH3Cl had little effect on the reaction rates, but at high relative translational energies, the C-Cl excitation leads to a significant increase in the rate constants. Szabó and Czakó performed a quasi-classical trajectory(QCT) calculation on their full-dimensional potential energy surface46. They found that at low collision energies, the pre-reactive minimum –

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F ---CH3Cl and H-bonded F ---HCH2Cl minimum in the entrance channel play a major role in the dynamics. At high collision energy, the direct rebound mechanism plays a dominate role for the dynamics47,48. They also found that the integral cross section decreases rapidly with increasing of the translational energy. Later, they updated their PES42 by including more reaction channels other than the backside attack and redid the quasi-classical calculation using the new PES. They found that the C-H symmetric stretching vibrational mode has only slight effect on the SN2 reactivity. Recently, a six degree-of-freedom (DOF) quantum dynamics and QCT calculation by Wang et al49 was carried to study the mode-specific reactivity on this reaction. The reaction probability ratios between the vibrational excited states and the ground state, as well as the integral cross section(ICS) of the ground state were calculated with both the quantum dynamics and QCT methods; however, the integral cross sections of the vibrational excited states were not calculated. In the present paper, we want to obtain not only the ICS of the ground state but also the ICSs of the 5



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vibrational excited states; therefore we can investigate, under the equal amount of total energy, the energy efficacy on the reactivity; we want to find out whether the energy efficiency on reactivity also depends on the potential energy minima, besides the saddle point, on the PES for this reaction. If so, what roles do they play?

II. THEORY In this work, we performed a quantum dynamics calculation to study the reaction –

–

on the new updated F + CH3Cl PES by Szabó and Czakó.42 The F + CH3Cl → –

FCH3 + Cl SN2 reaction is a synchronized one bond broken and one bond formed mechanism, and the reaction also involves a Walden-inversion motion where the three H atoms move in sync and invert their configuration at the transition state. So in our quantum dynamics study, we included the three signature motions of this SN2 reaction: the bond-broken coordinate of the leaving group Cl to CH3, the bond-forming –

coordinate of the nucleophile F to the substrate CH3Cl, the three Hs move-in-phase coordinate, the umbrella motion, C-H3. Furthermore, we included the attacking angle –

between F and the CH3Cl to allow the nucleophile to attack the substrate from all directions. Since the QCT study by Szabó and Czakó42 shows that C-H symmetric stretching motion only severs as a spectator and has slight effect on the SN2 reactivity, thus it is not included in this model. Thus in this study, as seen in Figure 1, we use the reactant Jacobi coordinates to describe the system.

R is the distance from the nucleophile F– to the center of mass

CH3Cl to represent the attacking motion; r is the distance from the center of mass 6


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of CH3 to Cl to represent the leaving motion;

ρ is the distance from C atom to the

center of mass of the three hydrogen atoms to represent the Walden-inversion motion, thus here, the three hydrogen atoms are treated as one pseudo-atom X and move in phase;

γ is the attacking angle formed by the leaving coordinate r and the

attacking coordinate

R . So there are four degrees of freedom (4DOF) to describe the

title reaction's SN2 mechanism. The 4DOF Hamiltonian in the reactant Jacobi coordinates is written as，

(J − j h2 ∂ 2 H = − + 2 2µ ∂R 2µ R2 ∧

)

2

+ hr ( r

) + hρ ( ρ ) +

j

2

(1)

2µ r r r2

+ V4 D ( R, r , ρ , γ )

Here, the first term is the translational energy of the reaction system. Where

µ is the

reduced mass of the whole system and µ r is the reduced mass of CH3 and Cl; J

is

the total angular momentum operator of the system, and j is the rotational angular momentum operator of Cl-CH3. Jacobi angle θ and the torsion angle ϕ are fixed at their transition-state geometry. The vibrational reference Hamiltonians hr(r ) and hρ( ρ ) are given as,

hr ( r

)

= −

hρ ( ρ ) = −

h2 ∂ 2 + V1D ( r 2µr ∂r 2

)

h2 ∂ 2 + V1D ( ρ ) 2µρ ∂ρ 2

(2)

(3)

Where V1D(r ) and V1D( ρ ) are the one-dimensional effective potentials for r and

ρ coordinates by putting the reaction system in the reactant asymptotic region with other coordinates fixed at the equilibrium geometry. The split-operator method50 was employed here to propagate the wave packet for 7



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the quantum scattering process. The time-dependent wavefunction was expanded in terms of the body-fixed rovibrational eigenfunctions in the reactant Jacobi coordinates. After the time-dependent wave function was propagated passing the transition state, the initial-state-selected reaction probability was extracted using the time-dependent reactive flux method.51,52 The initial-state-selected reaction probabilities of different

E） were added up to obtain initial-state-selected integral cross partial waves Pv0j 0（ k0 J

section (ICS) σv 0j0(E ),

συ

0 j0

(E ) =

In the above Eq. (4),

1 π 2j0 + 1 k 2

∑ (2J

+ 1) PυJ j K

J

0 0

0

(E )

(4)

E is the collision energy, K 0 is the projection of J onto the

body-fixed z axis of the system, j 0 denotes the initial rotational quantum number,

ν 0 denotes the initial vibrational quantum number and k is the wavenumber,

k = ( 2uE)1/ 2 . The standard centrifugal sudden (CS) approximation53,54 was employed in calculation for J > 0 , since the computational cost of the title reaction is extremely expensive, the exact close-coupling(CC) calculation was not feasible. Nonetheless, our calculated ICS of the ground state has an excellent agreement with the ones of the 6DOF and QCT results(see Figure 2), which means that the CS calculation is a good approximation for the current system. For the translational coordinate R in the range from 3.3 to 25.0 bohr, we use 310 sine basis functions to expand the wave function, among these 110 are chosen to expand the wave function in the interaction region; we use 97 potential-optimized vibrational DVR points55 for the r coordinate in the range of 2.3 to 8.0 bohr, 12 potential-optimized vibrational DVR points for

ρ coordinate covering the range of 8


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0.0 to 1.5 bohr, and 110 spherical harmonic rotational functions for

γ . The

time-dependent wave packet is propagated with a time step of 15 atomic unit time (~ 0.36 fs) for a total propagation time of about 600,000 a.u. time ( ~ 14.5 ps). Note due –

to the long-range ion and dipole interaction between the nucleophile F and the substrate CH3Cl, a very long attacking coordinate up to 25.0 bohr was needed to describe the correct attacking motion. Furthermore, due to the two energy minima in the entrance channel, a very large 600,000 a.u. propagation time was needed to propagate the wave packet to obtain each converged reaction probability. On top of the above, reaction resonances were found in reaction probabilities with partial waves calculations, the J-shifting method56 cannot be used to obtain reliable ICSs. Therefore, with each integral cross section calculation, the reaction probability of every different partial wave up to J = 300 was needed to be calculated one by one. The computational cost was huge for this calculation.

III. RESULTS AND DISCUSSION The vibrational levels (ν r , ν ρ ) of ClCH3 assigned to their corresponding vibrational excitation states are listed in Table 1. Our calculated vibrational frequencies of Cl-CH3(1, 0) and C-H3(0, 1) are 740 cm-1 and 1486 cm-1. Their corresponding normal mode frequencies57 are 754 cm-1 and 1394 cm-1 on the new PES by Szabó and Czakó. In Figure 2, we compared our quantum integral cross section (ICS) of the ground state with the QCT result and the 6DOF result. This figure shows this reaction does 9



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not have a reaction threshold due to a negative reaction barrier. The ICS decreases dramatically as the translational energy increases at relatively low translational energies. For example, the ICS of the ground state decreases about 89% from 1067.7 bohr2 to 110.9 bohr2 as the translational energy increases from 0.46 to 4.8 kcal/mol, then slowly decreases to 1.8 bohr2 at 15 kcal/mol. This means that the reactivity of the title reaction is dominated by the translational energies lower than 4.8 kcal/mol. Our quantum ICS of the ground state has an excellent agreement with the 6DOF quantum result and agrees very well with the QCT one. This comparison shows that our 4DOF quantum approach produces almost the same ICS as the 6DOF result does. Figure 3 shows the comparison of the ICSs among the ground state (0, 0), the first excited Cl-CH3 vibrational state (1, 0) and the first excited C-H3 vibrational state (0, 1). We calculated every reaction probability for different partial waves up to J = 300 to converge the three ICSs for translational energy up to 15 kcal/mol. All three ICSs decrease significantly as the translational energy increases until 4.8 kcal/mol. This indicates that the reactivity of the title reaction is indeed dominated by the translational energy lower than 4.8 kcal/mol. This translational energy 4.8 kcal/mol is the dividing point for the reactivity. In order to investigate the energy efficiency on reactivity, the ICS ratios between the vibrational excitation state (1, 0) and the ground vibrational state (0, 0), σ(1, 0)/σ(0, 0), and between (0, 1) and (0, 0), σ(0, 1)/σ(0, 0), are shown in Figure 4A and 4B on the basis of an equal amount of total energy. Figure 4 demonstrates that both ratios decrease to reach a minimum at 4.8 kcal/mol and increase at relative high 10


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energies after 4.8 kcal/mol. This translational energy 4.8 kcal/mol serves as another dividing point again, here as the dividing point on two different energy efficiency roles on reactivity. Namely, the energy efficiency on reactivity has been distinguished on two sides of this dividing point at 4.8 kcal/mol. This dividing energy point has to be associated with some special characters on the PES. We found that the dividing energy point, 4.8 kcal/mol, is exactly the relative energy barrier height of the negative –

barrier (-12.8 kcal/mol) with respect to the lower energy minimum, the F ---HCH2Cl hydrogen-complex(-17.6 kcal/mol), in the entrance channel.42 This means the energy efficacy at the left side of 4.8 kcal/mol is associted with translational energies smaller –

than the relative barrier height with respect to the F ---HCH2Cl hydrogen-bond complex, and the right side of 4.8 kcal/mol is associted with translational energies –

larger than the relative barrier height with respect to the F --- HCH2Cl hydrogen-bond complex. Thus the energy efficacy on reactivity for tranlational energies lower than 4.8 kcal/mol (in Figure 4), or the dominant reactivity for tranlational energies lower than 4.8 kcal/mol (in Figure 2), depends on the relative barrier height between the transition state and the hydrogen-bond minimum, which means the dominant reactivity here is related to this minimum and the transition state. That is, the biggest reactivity takes palces when the reactants go through the wells in the entrance channel first then scale the transtition state. The dominance of low collision energies by forming the pre-reaction complex has also been found in the direct dynamics classical –

trajectory simulation study on the similar Cl + CH3I reaction by Zhang et al.58 In Szabó and Czakó's QCT study,46 they also found the trajectories indeed can trap in the 11



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two minima in the entrance channel to form long-lived complexes. The indirect reaction mechanism that reactants trapped in the pre-reaction complexes has also been observed in the studies of F− + CH3I40 and OH− + CH3I41 since the PESs for F− + CH3I and OH− + CH3I are quite similar to that for F− + CH3Cl. The above studies show that although these reactions have negative barriers, the reactants need to go through the potential energy minima to for the pre-reaction complexes to let reactions occur, and low-collision-energy reactivities dominate these reactions. Note at the translational energy 1.5 kcal/mol, the values of the two ICS ratios are equilvalent at 3.0. For translational energies lower than 1.5 kcal/mol, all the σ(0, 1)/σ(0, 0) values in Figure 4B are bigger than the σ(1, 0)/σ(0, 0) values in Figure 4A. For translational energies larger than 1.5 kcal/mol, the situation is reversed as all the σ(1, 0)/σ(0, 0) values in Figure 4A are bigger than the σ(0, 1)/σ(0, 0) values in Figure 4B. This energy value 1.5 kcal/mol at this equilvalent ratio point happenes to be the –

energy difference of the pre-reactive complex F ---CH3Cl (-16.1 kcal/mol) with –

respect to the hyrogen-bond complex F ---HCH2Cl(-17.6kcal/mol) in the entrance channel.42 Based on the above observed features, there are two dividing points 4.8 kcal/mol and 1.5 kcal/mol at the relative low translational energies: one is the relative barrier height, 4.8 kcal/mol, of the transition state with respect to the hyrogen-bond –

complex F ---HCH2Cl, the other is the relative energy height, 1.5 kcal/mol, of the –

pre-reactive complex F ---CH3Cl with respect to the hyrogen-bond complex –

F ---HCH2Cl. Therefore the energy effacicy on reactivity, for the translational energies lower than 4.8 kcal/mol (as seen in Figure 2), is relative to the PES features 12


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of the transition state and the pre-reacitve complex with respect to the lowest hydrogen-bonded complex mininum respectively. In other words, the donimant reactivity(in Figure 2), for the translational energies lower than 4.8 kcal/mol, is controlled by the two energy minina and the transition state together. As mention above, the dominance of the indirect reaction mechanisms at low collision energies by –

forming the pre-reaction complex has also been found in the similar reaction Cl + CH3I by Zhang et al.58 Furthermore, for the translational energies lower than 1.5 kcal/mol, the C-H3 vibration is more efficient than the CH3-Cl vibration in promoting this reaction. This –

indicates the C-H3 vibration motion favors the formation of the F --HCH2Cl –

hydrogen-bond complex which is 1.5 kcal/mol lower than the F ---CH3Cl complex. For the translational energies larger than 1.5 kcal/mol, the CH3-Cl vibration is more effecitent than the C-H3 vibration. It is understandable because the CH3-Cl vibration –

favors the reactants to form F ---CH3Cl complex whose energy is 1.5 kcal/mol higher –

than the hydrogen complex F ---HCH2Cl. When the collision energy is lower than 1.5 –

kcal/mol to form the F ---HCH2Cl hydrogen complex, this is the indirect mechanism –

as F has to hydrogen-bond with one H first then rotate itself to face and attack the backside of the C atom. For energies larger than 1.5 kcal/mol up to 4.8 kcal/mol, the CH3-Cl vibration is more efficient than the C-H3 vibration since it mainly forms the –

F ---CH3Cl pre-reactive complex. This is the indirect rebound reaction mechanism –

since the nucleophile F needs to form the pre-reactive complex with the substrate CH3Cl, then attack C center atom directly, or it is called the backside attack 13



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mechanism described in textbooks for the SN2 reactions. Overall, on both sides of the minimum, the vibrational motions of Cl-CH3 and C-H3 are more efficient than the transiational motion in enhancing the reactivity. As for the translational energies below the relative barrier height, Figure 4 shows that both vibrational stretching of CH3-Cl and C-H3 are more important than the translational energy in enhancing the reactivity; however, as the translational energy increases, the importance of these two vibrations in enhancing reactivity decreases; Furthermore, Figure 2 shows that the ICSs decrease dramatically before 4.8 kcal/mol; these two features are due to the fact that, as translational energy increases, the reactants will not have enough time to orientate themselves to form the two minima complexes in the entrance channel. The energy efficacy comparison provides direct evidence here that the two minima in the entrance channel play an essential role on reactivity at the lower translational energies: they determine the energy efficacy on reactivity at the relative low translational energies. For the translational energies larger than the relative reaction barrier, 4.8 –

kcal/mol, the reactants can skip the reactant channel minima and the nucelophile F

can attack the C atom from the backside directly to let the reaction occure, thus it's a direct rebound mechanism. In addition, since the translational energy at this part is larger than the relative barrier height, so the reaction can occur without forming the –

transition-state complex, and the nucelophile F can approch the side of the substrate to directly strip CH3 away. Hence there are two reaction mechanisms occuring simultaneously at this energy range: the direct rebound and strip away mechanisms. 14


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For energy higher than 4.8 kcal/mol, both the CH3-Cl and C-H3 stretching motions become more efficient than at relative lower translational energy because these two –

vibrations make the substrate a larger target to be approached, and thus make the F

directly attack C atom or strip away CH3 easier. This is also the reason, in the QCT calculations by Szabó and Czakó,42,46 they found the stripping mechasiman happens for large impact parameters. Xie et al. have also discussed both the direct and indirect – – – – – mechanisms in the similar reactions of X (X = F , Cl , OH ) + CH3I.47

Note both the Cl-CH3 vibration and the C-H3 vibration are more efficient than the translational motion in enhancing the reactivity at relative high translational energies; however, the Cl-CH3 ratio is larger than the one of C-H3, which means the Cl-CH3 vibration plays a more effective role than the C-H3 vibration on promoting this reaction. The Cl-C stretch excitation promoting reaction for a high translational energy has also been found in the trajectory study45. That the Cl-CH3 vibration is more effective than the C-H3 vibration on promoting this reaction has been also observed in the 6DOF quantum dynamics calculation;49 however, the 6DOF ICSs of these two vibrtional excited states were not calculated in that study, the conclusion was drawn from the reaction probability comparison. There are also qunatum dynamics studies that have been done on the similiar, –

–

non-symmetric SN2 reactions Cl + CH3Br59,60 and Cl + CH3I61. Both the 4DOF –

time-independent quantum studies of Cl + CH3Br and the 3DOF time-dependent –

quantum dynamics study of the Cl + CH3I indicate that, in general, the C-H3 umbrella mode and the C-X(Cl, Br, I) stretching mode in the substrate, similar as in 15



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the title reaction, can both enhance the reactivities of these non-symmetric SN2 reactions.

IV. CONCLUSIONS –

–

Overall, for the F + CH3Cl → FCH3 + Cl SN2 reaction, it is not the absolute negative barrier, but the relative barrier and the minima in the entrance channel that determine the energy efficiency on the reactivity. The Cl-CH3 vibrational motion is more efficient than the C-H3 vibrational motion in promoting this reaction. For the Cl-CH3 vibrational motion, the ratio of the ICS is larger than one for the whole energy range we studied here, which means the Cl-CH3 vibrational motion is more efficient than the translational motion in enhancing the reactivity, although this reaction has an early barrier. Around the relative barrier height ~ 4.8 kcal/mol, the translational energy almost has the same efficiency as vibrational motions. Nevertheless, the ICSs are dominated by the translational energies lower than 4.8 kcal/mol, which means that the reactivity is most effective when involving the two potential minima in the entrance channel. Or in other words, the two minima on the PES have an dominate effect on the reactivity. Therefore, the energy efficacy is determined by not only the relative transition state, but also more importantly the two minima in the entrance channel for this reaction. Recent studies show that the Polanyi rules cannot be simply extended to poly-atomic reactions for more than three-atom systems. In these studies, the energy efficacy was considered solely based on the locations of the transition states. However, our results on the energy efficacy based on the equal amount of total 16


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energy show that potential energy minima in the entrance channel also play a significant role on the reactivity. Thus, for the poly-atomic reactions with minima on –

–

their PESs, at least for the SN2 reactions as X + CH3Y → XCH3 + Y , one needs to consider the potential energy minimum (minima) to get a general energy efficacy rule on reactivity. Nonetheless, we think more theoretical studies, as well as experimental studies, are needed to reveal the potential minima effects on the energy efficacy in promoting reactivity for poly-atomic reaction systems.

ACKNOWLEDGEMENTS We thank Prof. Czakó for sending us the PES of the title reaction. This work is supported by the National Natural Science Foundation of China (Grant No. 11374194) and Taishan Scholarship Fund from Shandong province. The computation was carried out at the Shenzhen Supercomputer Center in China.

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Communication:

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of

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molecular collisions. jz‐conserving coupled states approximation. J. Chem. Phys., 1974, 60, 2488-2499. (54) Pack, R. T. Space‐fixed vs body‐fixed axes in atom‐diatomic molecule scattering. Sudden approximations. J. Chem. Phys. 1974, 60, 633-639. (55) Echave, J.; Clary, D. C. Potential optimized discrete variable representation. Chem. Phys. Lett. 1992, 190, 225-230. (56) Bowman, J. M. Reduced dimensionality theory of quantum reactive scattering. J. Phys. Chem., 1991, 95, 4960-4968. (57) Szabó, I.; Czakó, G. Revealing a double-inversion mechanism for the F− + CH3Cl SN2 reaction. Nat. Commun. 2015, 6, 5972. (Data in Supporting Information) (58) Zhang, J.; Lourderaj, U.; Sun, R.; Mikosch, J.; Wester, R.; Hase, W. L. Simulation studies of the Cl− + CH3I SN2 nucleophilic substitution reaction: Comparison with ion imaging experiments. J. Chem. Phys. 2013, 138, 114309. (59) Schmatz, S. Four-mode quantum calculations of resonance states in complex-forming bimolecular reactions: Cl− + CH3Br. J. Chem. Phys. 2005, 122, 234306. (60) Hennig, C.; Schmatz, S. Four-dimensional quantum study on exothermic complex-forming reactions: Cl− + CH3Br → ClCH3 + Br−. J. Chem. Phys. 2005, 122, 234307. (61) Kowalewski, M.; Mikosch, J.; Wester, R.; de Vivie-Riedle, R. Nucleophilic substitution dynamics: Comparing wave packet calculations with experiment. J. Phys. Chem. A 2014, 118, 4661-4669.

23



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Table 1. Initial vibrational states （ν r ，ν ρ） of ClCH3. The energy levels Ea and E – are relative to the energy of the F + CH3Cl asymptote and the ground vibrational

state of CH3Cl, respectively.

State No.

(ν r , ν ρ )

1

(0, 0)

1119

0

2

(1, 0)

1859

740

3

(2, 0)

2586

1467

4

(0, 1)

2605

1486

5

(3, 0)

3305

2186

6

(1, 1)

3339

2220

7

(4, 0)

4015

2896

8

(2, 1)

4060

2941

9

(0, 2)

4091

2972

Ea(cm-1)

E(cm-1)

24


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Figure 1. Reactant Jacobi coordinates for the

–

–

F + CH3Cl → FCH3 + Cl SN2

reaction.

25



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Figure 2. The comparison of the integral cross sections of the ground state among our 4DOF quantum result, the QCT result[Ref. 49], and 6DOF quantum result[Ref. 49].

26


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Figure 3. The integral cross sections of the (0, 0), (1, 0), and (0, 1) states as a function of (A) translational energy and (B) total energy. In order to show the ICSs' difference at relative high translational energies, a logarithmic plot of the ICSs is also inserted in Figure A. 27



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Figure 4. The ICS ratios for σ(1, 0)/σ(0,0) and σ(0, 1)/σ(0, 0) against the translational energy. The vibrational energy difference ∆E1 between the first Cl-CH3 excited state(1, 0) and the ground state(0, 0) is 2.1 kcal/mol. The vibrational energy difference

∆E 2 between the first C-H3 exited state (0, 1) and the ground state (0, 0) is 4.2 kcal/mol. 28


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TOC graphic

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Quantum Dynamics Study of the Potential Energy Minima Effect on

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