Unexpected steric hindrance failure in the gas phase F− + (CH3)3CI SN2 reaction

Base-induced elimination (E2) and bimolecular nucleophilic substitution (SN2) reactions are of significant importance in physical organic chemistry. The textbook example of the retardation of SN2 reactivity by bulky alkyl substitution is widely accepted based on the static analysis of molecular structure and steric environment. However, the direct dynamical evidence of the steric hindrance of SN2 from experiment or theory remains rare. Here, we report an unprecedented full-dimensional (39-dimensional) machine learning-based potential energy surface for the 15-atom F− + (CH3)3CI reaction, facilitating the reliable and efficient reaction dynamics simulations that can reproduce well the experimental outcomes and examine associated atomic-molecular level mechanisms. Moreover, we found surprisingly high “intrinsic” reactivity of SN2 when the E2 pathway is completely blocked, indicating the reaction that intends to proceed via E2 transits to SN2 instead, due to a shared pre-reaction minimum. This finding indicates that the competing factor of E2 but not the steric hindrance determines the small reactivity of SN2 for the F− + (CH3)3CI reaction. Our study provides new insight into the dynamical origin that determines the intrinsic reactivity in gas-phase organic chemistry.

For the title organic reactive system consisting of fifteen atoms with multiple heavy atoms, considerable computation effort has to be involved in the electronic structure calculation. In general, the explicitly correlated coupled-cluster (CCSD(T)-F12) method is chosen to gain the benchmark ab initio energies. Due to the huge computational cost of the gold standard coupled-cluster calculations, we employed a newly proposed hybrid function CAM-XYG3 [2,3] by Xu and coworkers, which is the combination of the hybrid qualities of XYG3 [3] and the long-range correction with the Coulomb-attenuating method (CAM) [2]. This method archives the similar level of accuracy as compared to CCSD(T)/AVTZ(-PP) but significantly reduces the computational effort. It takes about half an hour of real CPU time for a single point using seven-threads in one computer node, indicating this method is ideal for the F − + (CH 3 ) 3 CI reaction. Besides, the CAM-XYG3   representation of long-range interaction between fragments shows good behavior, which plays an important role in the ion-molecular reaction. On the whole, energies of all collected geometries were computed with the hybrid function CAM-XYG3 using Gaussian 09 [6], together with Dun- ning's augmented correlation-consistent triple-zeta (aug-cc-pVTZ) basis set and the corresponding aug-cc-pVTZ-PP basis set for iodine atom.
Due to the configuration space of the investigated system is extremely large, we employed the space partitioning and energy splitting methods to overcome the huge difficulties of fitting all the data points. For example, the geometries of the asymptotic region of the reactants F − + (CH 3 ) 3 CI were collected by the way of energy splitting.
We first constructed an accurate FI-NN tert-butyl iodine ((CH 3 ) 3 CI) local PES based on the CAM-XYG3 method. Random configurations of the (CH 3 ) 3 CI reactant were picked from the local PES and combined with the F − atom. The geometries of the asymptotic region were selected by randomly changing the distance and orientation of the reactants.
We splitted the total energy of a single point into the energy of each reactant and their interaction energy, and then fitted the energies of monomer and interaction energies between the reactants, respectively. The accuracy of the PES with the asymptotic region represented by the combination of the (CH 3 ) 3 CI PES and the interaction energy PES is highly improved. The above strategy is called "energy splitting" method.
Furthermore, we divided the configuration space into three partitions to improve the fitting accuracy and efficiency: 1) the asymptotic region of the reactants (the distance between the center of mass of F − and (CH 3 ) 3 CI is larger than 7 Å) 2) the interaction region 3) the asymptotic region of the E2 product channel (the minimum distance between the center of mass of three products (CH 3 ) 2 C=CH 2 + HF + I − ) is larger than 5.5 Å). Adjacent regions was connected smoothly by the switch function. The energies of Part 3 were splitted into the energy of the three fragments and their interaction energies in the same way as the Part 1. The sub-PESs of (CH 3 ) 2 C=CH 2 and HF were also accurately constructed. With respect to Part 2, we used the direct dynamics simulations based on the unrestricted B3LYP/6-31+G* level of theory to obtained the initial data set starting from the initially guessed transition states of S N 2 and E2. More configurations were iteratively added into the data set by further QCT calculations based the preliminary PES and the updated PESs. In addition, the configurations along the minimum energy path and all optimized stationary points were added into the corresponding data set.
Finally, the data points of each part were selected using the following criterion, respectively.
Here, n represents the number of bond lengths and r i is the i-th bond length of a specific geometry.
The D is an adjustable parameter, here it was set to 0.005. We used the sieve D to discard those data points which are too close in the energy domain and/or geometry domain, in order to improve the efficiency of the FI-NN fitting process. Overall, a total of roughly 50,000, 135,000 and 35,000 data points in the three configuration space parts were calculated using hybrid function CAM-XYG3, respectively.
We used the newly proposed fundamental invariant (FI)-neural network fitting approach [4,5,[7][8][9][10][11][12] to guarantee the permutational symmetry of identical atoms. Although FIs can minimize the number of invariants compared to permutationally invariant polynomials (PIP) [13,14], there are still 1282 FIs with a maximum degree of three without considering the permutation symmetry of H atoms on different methyl groups for the F − +(CH 3 ) 3 CI reaction. The FIs were truncated at the number of 500, which has proven large enough to get an accurate fit. Finally, the 500-50-100-1 NN structure was chosen to fit the energy points of the interaction region (Part 2) and the interaction energies between the reactant (Part 1) and product fragments (Part 3). Furthermore, the 746 FIs up to 3 degree were employed to fit the (CH 3 ) 3 CI local PES, together with 50 and 100 neurons on the first and the second hidden layer. Besides, we used the 606-10-100-1 NN structure to train the (CH 3 ) 2 C=CH 2 PES with all FIs up to degree 3. Note that each bond length x i in FIs was further replaced by its inverse 1/x i , which displays better performance in the fitting accuracy.
In the NN training processes, the Levenberg-Marquardt algorithm [15] was employed to update the weights and biases, which aim to obtain an optimal fit. The root mean square error (RMSE) defined in Equation (2) was applied to measure the fitting error.
Overall, a total of ∼ 135,000 energy points in Part 2 was fitted using the optimal 500-50- Overall, the total RMSE of all data points of the three parts is only 8.3 meV. Figure S1 shows the fitting errors of all data points with respect to their corresponding CAM-XYG3/AVTZ (-PP) energies. Although the energy range of the current PES is fairly large (∼ 8 eV), the ab initio Standard QCT calculations [17,18] for the F − + (CH 3 ) 3 CI reaction were carried out at collision energies ranging from 0.2 eV to 1.9 eV on the FI-NN PES, for the (CH 3 ) 3 CI reactant initially in the ground rovibrational state. We randomly sampled the normal coordinates and momenta to get the initial coordinates and momenta of (CH 3 ) 3 CI. Adjustments were then made to the momenta to force the angular momentum of (CH 3 ) 3 CI to zero. The initial distance between the center of mass of two reactants was √ x 2 + b 2 , where b is the impact parameter and x was set to 38.0 Bohr due to the large long-range interactions in the entrance channel for such a ion-molecular reaction.
Here, the orientation of (CH 3 ) 3 CI was randomly sampled with respect to the F anion. The impact parameter b was scanned from 0 to the maximum impact parameter (b max ) with a step size of 0.5 Bohr. The value of b max was determined ranging from 21.0 Bohr to 10.0 Bobr after preliminary tests as the collision energy increases.
Our PES can cover the region where the distance between the centers of the mass of two reactants is 25 Å in the entrance channel. In this work, all trajectories were run using the Velocity-Verlet integration algorithm with a time step of 0.024 fs for a maximum time of 25 ps. We ter- Cl − + (CH 3 ) 3 CI and those for the S N 2 reaction on the modified PES. A repulsive potential between Cl − and β-H in the vicinity of the E2 transition state was added in the modified PES, which blocks the E2 pathway but nothing is changed for S N 2 as presented for F − + (CH 3 ) 3 CI.