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F- þ CH3I f FCH3 þ I- Reaction Dynamics. Nontraditional Atomistic Mechanisms and Formation of a Hydrogen-Bonded Complex €ller,§ Jiaxu Zhang,† Jochen Mikosch,‡,^ Sebastian Trippel,‡ Rico Otto,‡ Matthias Weidemu ,‡ ,† Roland Wester,* and William L. Hase* †
Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, ‡Physikalisches Institut, at Universit€at Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany, and §Physikalisches Institut, Universit€ Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany
ABSTRACT Ion imaging experiments and direct chemical dynamics simulations were performed to study the atomic-level dynamics for the F- þ CH3I f FCH3 þ ISN2 nucleophilic substitution reaction at 0.32 eV collision energy. The simulations reproduce the product energy partitionings and the velocity scattering angle distribution measured in the experiments. The simulations reveal that the substitution reaction occurs by two direct atomic-level mechanisms, that is, rebound and stripping, and an indirect mechanism. Approximately 90% of the indirect events occur via a prereaction F- 3 3 3 HCH2I hydrogen-bonded complex. This mechanism may play an important role for other F- SN2 reactions due to the strong electronegativity of fluorine. The average product energy partitioning for the F- þ CH3I indirect mechanism agrees with the prediction of PST, even though a FCH3 3 3 3 I- postreaction complex is not formed. SECTION Dynamics, Clusters, Excited States
“roundabout” mechanism in which the reactants' initial collision results in complete transfer of the Cl- translation energy to C-I stretch vibration and rotation of CH3 about the massive I atom, leading to the SN2 reaction after one CH3 rotation.5 Though the postreaction ClCH3 3 3 3 I- ion-dipole complex is not formed, this mechanism leads to a ClCH3 þ I- translational energy distribution which is in line with the statistical prediction. The PES for an SN2 reaction may be different than that for the double-minima, central barrier model. For the OH- þ CH3F reaction, there is a hydrogen-bonded CH3OH 3 3 3 Fcomplex in the product channel instead of the traditional HOCH3 3 3 3 Y- complex.12 The F- þ CH3Y f FCH3 þ Y- (Y = Cl, Br, I) family of reactions is of particular interest because of their large reaction exothermicity, especially for F- þ CH3I, and its possible effect on the features of the PES and the chemical reaction dynamics.13-15,17 Similar to our work on Cl- þ CH3I,5,6 we experimentally studied reactive scattering of the F- þ CH3I f CH3F þ Ireaction with crossed-beam velocity map ion imaging. These single-collision experiments, with a well-defined initial relative kinetic and internal energy, measure directly the velocity vector of the I- product, revealing the energy- and angledifferential reaction cross section. The translational energy
T
here have been extensive experimental, theoretical, and computational investigations1-17 of the chemical dynamics for X- þ CH3Y f XCH3 þ Y- SN2 nucleophilic substitution reactions. The traditional potential energy surface (PES) for these reactions, as for Cl- þ CH3Cl and Cl- þ CH3Br, has potential minima for the X- 3 3 3 CH3Y and XCH3 3 3 3 Y- pre- and postreaction ion-dipole complexes and a potential maximum for the [X 3 3 3 CH3 3 3 3 Y]- central barrier. The statistical model of the atomic-level dynamics for such a PES1-3 is (1) formation of the X- 3 3 3 CH3Y complex by ion-molecule capture; (2) rapid intramolecular vibrational energy redistribution (IVR) within this complex so that it dissociates back to reactants and crosses the central barrier to form the XCH3 3 3 3 Y- complex with RRKM lifetimes; and (3) rapid IVR for the XCH3 3 3 3 Y- complex so that it dissociates to XCH3 þ Y- products with a statistical energy distribution.18 Both experimental and computational studies have shown that the above model is incomplete for describing the X- þ CH3Y f XCH3 þ Y- reaction dynamics.4-12,14,15 The unimolecular dynamics of the X- 3 3 3 CH3Y complex is not consistent with rapid IVR,4,7,10,19-22 and the energies of the XCH3 þ Y- products do not agree with the statistical prediction.10,23 As the translational energy is increased, a “direct” reaction pathway, without trapping in either of the ion-dipole complexes, becomes important.8,11,24,25 Calculations show that C-Yvibrational excitation of the CH3Y reactant promotes a direct reaction,26 but this has not been confirmed experimentally. For the Cl- þ CH3I f ClCH3 þ I- reaction, there is a
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Received Date: August 1, 2010 Accepted Date: August 30, 2010 Published on Web Date: September 03, 2010
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Table 1. Average fractions of Product Energy Partitioninga,b frot0 direct rebound
PSTc
fint0
0.50 ( 0.04 0.45 ( 0.04 0.55 ( 0.04
0.08 ( 0.01 0.71 ( 0.02 0.21 ( 0.02 0.79 ( 0.02 0.07 ( 0.01
total expt.
frel0
0.07 ( 0.01 0.47 ( 0.03 0.46 ( 0.03 0.54 ( 0.03
direct stripping 0.05 ( 0.01 indirect
fvib0
0.62 ( 0.02 0.31 ( 0.02 0.69 ( 0.02 70 ( 10% 88%
-
The F þ CH3I collision energy is 0.32 eV. The vibrational and rotational temperatures of CH3I are 360 and 75 K, respectively.6 The f 's are fractions of energy partitioning for rotational, vibrational, translational, and internal energy. b Trajectories were averaged over all impact parameters (b) and properly weighted by b and the reaction probability versus b. c The loose transition-state model of PST; ref 30. a
Figure 1. Center-of-mass image of the I- reaction product velocity from reactive scattering of F- and CH3I at a collision energy of 0.32 eV. The dashed ring with the largest radius represents the kinematical cutoff for the SN2 reaction with no product excitation. The smaller rings represent spheres of increasing product excitation, spaced at 1 eV intervals.
distribution of I- is determined at each scattering angle, and by conservation of energy and center-of-mass motion, the CH3F þ I- relative translational energy and CH3F internal energy distributions are found. Figure 1 gives the measured velocity map image of the I- product from F- and CH3I reactive scattering at a mean collision energy of 0.32 eV and a rms collision energy spread of 0.07 eV. The velocity vectors of the reactants F- and CH3I line up horizontally and point in opposite directions, as indicated by the arrows in the centerof-mass frame at the top of Figure 1. A rather isotropic distribution of product velocity scattering angles is observed in the experiment. The average percentage of the available product energy partitioned to CH3F internal energy (i.e., vibration and rotation) is found to be 70 ( 10%. More information on the experiment will be given in a forthcoming publication. Statistical models for the product energy partitioning assume that a long-lived FCH3 3 3 3 I- postreaction complex is formed with complete randomization of its vibrational energy.18 Though the trajectories, described below, show that this complex is not formed, a statistical prediction of the energy partitioning is still of interest. Different statistical models have been proposed, depending on the assumed dynamics as the products separate.27-29 The loose transition-state (TS) model of PST was used here, for which the TS is placed in the product asymptotic limit.18,30 As summarized in Table 1, PST predicts a much higher 88% partitioning to the CH3F internal energy than experiment. To assist in understanding these experimental results, detailed electronic structure calculations were performed to investigate the F- þ CH3I f CH3F þ I- PES.17 The highest level of theory employed, CCSD(T)/CBS, does not identify a F- 3 3 3 CH3I ion-dipole minimum nor a traditional [F 3 3 3 CH3 3 3 3 I]- central barrier as stationary points on the PES. This is also the result of DFT calculations with different functionals. The CCSD(T) and DFT calculations identify a
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Figure 2. Energies of stationary points for the F- þ CH3I f FCH3 þ I- PES as given by DFT/B97-1/ECP/d theory.17 The energy in kJ/mol is at 0 K and does not include ZPEs.
Cs hydrogen-bonded F- 3 3 3 HCH2I potential minimum and a [F 3 3 3 HCH2 3 3 3 I]- TS connecting this minimum to the FCH3 3 3 3 I- ion-dipole minimum as stationary points on the PES. Thus, the proposed IRC reaction path31 for product formation is F- þ CH3I f F- 3 3 3 HCH2I f [F 3 3 3 HCH2 3 3 3 I]- f FCH3 3 3 3 I- f FCH3 þ I-. The DFT/B97-1/ECP/d level of theory was found to give the best agreement with the benchmark CCSD(T)/CBS energies for the stationary points on the PES with the largest difference of 7.5 kJ/mol for the postreaction minimum FCH3 3 3 3 I-. The IRC reaction path and energies of the stationary points for the DFT theory are depicted in Figure 2. Stationary points on a PES often provide limited insight into chemical reaction dynamics since the actual atomic-level dynamics may deviate substantially from that predicted by the stationary points and the IRC.5,12 The direct and roundabout mechanisms for the Cl- þ CH3I SN2 reaction are
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Figure 3. Atomistic dynamics of typical trajectories for the direct rebound and stripping reaction mechanisms.
Cl- þ CH3Cl.8 For the indirect reactions, ∼90% occurred by forming the hydrogen-bonded F- 3 3 3 HCH2I complex, illustrating the importance of this complex in the indirect mechanism. The atomistic dynamics for this mechanism are depicted in Figure 4, where F- interacts attractively with a H atom and the system becomes temporarily trapped in the prereaction potential energy well of the hydrogen-bonded complex F- 3 3 3 HCH2I (see Figure 2). Then, F- attacks the C atom backside and directly displaces I-. The complex F- 3 3 3 HCH2I is formed by F- interacting with either one (∼42%) or different H atoms (∼58%), with a complex lifetime ranging from ∼150 fs to 3 ps. Animations of trajectories for the three different mechanisms are presented on the Web site monte.chem.ttu.edu. Instead of sampling the impact parameter b randomly, the trajectories were calculated at fixed impact parameters of 1, 2, 3, 4, 5, 7, 8, and 8.5 Å, for which the respective reaction probabilities Pr(b) are 0.64 ( 0.04, 0.60 ( 0.04, 0.70 ( 0.04, 0.62 ( 0.05, 0.55 ( 0.04, 0.45 ( 0.04, 0.22 ( 0.04, and 0.03 ( 0.01. For b = 8.75 Å, there were no reactions out of 200 trajectories. The reaction cross section σr was obtained Rby averaging Pr(b) over the impact parameter, that is, σr = Pr(b)2πb db, and the resulting value was 106 ( 9 Å2. The direct stripping mechanism occurs for large impact parameters in the range of ∼3.0-8.5 Å, and its cross section is estimated as ∼29 ( 5 Å2. The direct rebound mechanism is a small impact parameter process, ∼0-5.0 Å, and its cross section is approximated as ∼16 ( 2 Å2. The indirect
illustrative examples of this latter behavior.5 Thus, chemical dynamics simulations are necessary to study the actual F- þ CH3I SN2 reaction dynamics. These simulations were performed by ab initio direct dynamics with the B97-1/ECP/d level of theory using the VENUS general chemical dynamics computer program32,33 interfaced to the NWChem electronic structure computer program.34,35 To compare with the experiments, the simulations were performed at a collision energy of 0.32 eV and CH3I vibrational and rotational temperatures of Tv =360 and Tr =75 K, respectively.6 Each trajectory was integrated for a maximum of ∼5 ps. Integrating one trajectory for 5 ps required ∼2 days on a 3.0 GHz dual-slot quad-core node with 16 GB RAM. The simulations revealed that the substitution reaction occurs by two direct atomic-level mechanisms, that is, rebound and stripping, and a dominant indirect mechanism. These mechanisms were identified by the atomistic motions of the trajectories and are depicted in Figures 3 and 4. For the rebound mechanism, F- attacks the backside of CH3I and directly displaces I-. Stripping occurs when F- approaches CH3I on its side and directly strips away the CH3 group. As discussed in more detail below, the rebound mechanism occurs at small impact parameters and gives backward scattering. In contrast, stripping occurs for large impact parameters and results in forward scattering. The direct rebound mechanism has been observed in previous simulations of the Cl- þ CH3Y (Y = Cl, Br, I) SN2 reactions,5,8,11 and for high collision energies, the stripping mechanism was seen for
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Figure 4. Atomistic dynamics of a typical trajectory for the indirect reaction mechanism that proceeds via forming the hydrogen-bonded F- 3 3 3 HCH2I complex.
mechanism occurs over a broad range of impact parameters, the largest being ∼8.5 Å, and its cross section is ∼61 ( 6 Å2. The experimental F- þ CH3I f CH3F þ I- rate constant is weakly dependent on the vibrational and rotational temperature Tvr and, for the Et = 0.32 eV studied here, is approximately 1.7 10-9 cm3 mol-1 s-1 at Tvr = 297 K.36 The calculated total cross section gives a rate constant of k(Et,Tv,Tr) = v(Et)σ(Et,Tv,Tr) = (2.0 ( 0.2) 10-9 cm3 mol-1 s-1, where Tv and Tr equal 360 and 75 K, respectively. There is very good agreement between the calculated and experimental rate constants. To assist in verifying the above atomic-level reaction mechanisms, the partitioning of available product energy to CH3F vibration and rotation energy and the product velocity scattering angle distribution, found from the simulations, may be compared with those determined from the ion imaging experiments. The comparison between the simulation and experimental results for the product energy partitioning are summarized in Table 1. When the trajectories are properly averaged over all impact parameters, the overall fraction partitioned to internal excitation of CH3F is in the range of 0.67-0.71 and agrees well with the experiments. This partitioning is primarily to vibration with a fraction of 0.62 ( 0.02, with rotation's fraction 0.07 ( 0.01. The direct rebound, direct stripping, and indirect atomiclevel mechanisms give different product energy partitionings, as shown in Table 1. Though they occur at different impact parameters, the direct rebound and direct stripping reaction trajectories have similar product energy partitionings. For the indirect trajectories, the partitioning to CH3F vibration is 0.71
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and is larger than the 0.47-0.50 for the direct rebound and stripping trajectories. The average partitioning to CH3F internal energy is 0.79 ( 0.02 for the indirect trajectories and is in approximate agreement with the PST prediction. This agreement occurs even though the FCH3 3 3 3 I- postreaction complex is not formed as assumed by PST. The distribution of the velocity scattering angle θ obtained from the simulations is shown in Figure 5a. For the direct rebound reaction, the scattering is primarily backward within a cos(θ) range of -1.0 to -0.1. The average value of cos(θ) is -0.55 and 80% of the scattering that occurs between a cos(θ) of -1.0 and -0.2. The direct stripping reaction mainly displays forward scattering within a cos(θ) range of -0.1-1.0. The average value of cos(θ) is 0.6 and 80% of the scattering that occurs between a cos(θ) of 0.25 and 1.0. All of the stripping trajectories scatter forward, except the one with cos(θ) = -0.1. For this trajectory, as F- approaches the side of CH3I, there is a strong attractive interaction, changing the direction of the F- velocity vector and resulting in a scattering angle of 98. This result suggests that a small fraction of the stripping will have scattering angles that are slightly in the backward direction. The scattering angles for the indirect reaction cover a quite broad cos(θ) range of -1.0-1.0, with the scattering most probable at these limiting values of cos(θ). The scattering for these three mechanisms combines to give an isotropic scattering distribution which is in overall quite good agreement with the experimental distribution in Figure 5b. In summary, the work reported here (1) identifies a new atomic-level mechanism for gas-phase X- þ CH3Y f XCH3 þ Y- SN2 nucleophilic substitution reactions and (2) emphasizes
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AUTHOR INFORMATION Corresponding Author: *To whom correspondence should be addressed. E-mail: bill.hase@ ttu.edu (W.L.H.);
[email protected] (R.W.).
Present Addresses:
^ National Research Council of Canada, Steacie Institute for Molecular Sciences, 100 Sussex Drive, Ottawa, Ontario K1A OR6, Canada.
ACKNOWLEDGMENT The calculations reported here are based upon work supported by the National Science Foundation under Grants CHE-0615321 and CHE-0957521 and the Robert A. Welch Foundation under Grant D-0005. Support was also provided by the High-Performance Computing Center (HPCC) at Texas Tech University, under the direction of Philip W. Smith. Support was also provided by the Texas Advanced Computing Center (TACC) at the University of Texas at Austin and the Environmental Molecular Sciences Laboratory (EMSL) at the Pacific Northwest National Laboratory (PNNL). The presented experimental work is supported by the Deutsche Forschungsgemeinschaft. Dr. Li Yang is acknowledged for important discussions concerning the direct dynamics simulations.
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Figure 5. (a) Velocity scattering angle distributions for the individual reaction mechanisms and for the total reaction. The red dashed, green dashed-dot, blue dot, and olive solid lines represent the direct rebound, direct stripping, indirect reactions, and total reaction, respectively. The trajectory results are properly weighted by b and the reaction probability versus b. (b) The experimental scattering angle distribution.
the interplay of experiments and simulations in establishing atomic-level mechanisms for chemical reactions. The product translational and velocity scattering angle distributions measured by ion imaging for the F- þ CH3I f FCH3 þ I- reaction provide detailed information concerning the atomic-level dynamics, but alone, they do not identify the atomic-level reaction mechanism(s). The simulations find three atomiclevel mechanisms for the F- þ CH3I f FCH3 þ I- SN2 reaction at a 0.32 eV collision energy, which are consistent with the overall energy partitioning and angular distribution found in the experiment. The experiments are critical for confirming the accuracy of the simulations. Two of the mechanisms are direct, that is, rebound and stripping, and the third is indirect, proceeding via a F- 3 3 3 HCH2I hydrogen-bonded complex. The direct mechanisms have been observed before in both experiments and simulations; however, the hydrogen-bonded indirect mechanism is new. It will be of interest to determine its importance for the F- þ CH3I SN2 reaction at higher collision energies as well as for other F- þ CH3X SN2 reactions.
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