SN2 Reactions with an Ambident Nucleophile: A Benchmark Ab Initio Study of the CN– + CH3Y [Y = F, Cl, Br, and I] Systems

We characterize the Walden-inversion, front-side attack, and double-inversion SN2 pathways leading to Y– + CH3CN/CH3NC and the product channels of proton abstraction (HCN/HNC + CH2Y–), hydride-ion substitution (H– + YH2CCN/YH2CNC), halogen abstraction (YCN–/YNC– + CH3 and YCN/YNC + CH3–), and YHCN–/YHNC– complex formation (YHCN–/YHNC– + 1CH2) of the CN– + CH3Y [Y = F, Cl, Br, and I] reactions. Benchmark structures and frequencies are computed at the CCSD(T)-F12b/aug-cc-pVTZ level of theory, and a composite approach is employed to obtain relative energies with sub-chemical accuracy considering (a) basis-set effects up to aug-cc-pVQZ, (b) post-CCSD(T) correlation up to CCSDT(Q), (c) core correlation, (d) relativistic effects, and (e) zero-point energy corrections. C–C bond formation is both thermodynamically and kinetically more preferred than N–C bond formation, though the kinetic preference is less significant. Walden inversion proceeds via low or submerged barriers (12.1/17.9(F), 0.0/4.3(Cl), −3.9/0.1(Br), and −5.8/–1.8(I) kcal/mol for C–C/N–C bond formation), front-side attack and double inversion have high barriers (30–64 kcal/mol), the latter is the lower-energy retention pathway, and the non-SN2 electronic ground-state product channels are endothermic (ΔH0 = 31–92 kcal/mol).


INTRODUCTION
Bimolecular nucleophilic substitution (S N 2) reactions have been widely studied both experimentally and theoretically, and their Walden-inversion and front-side attack mechanisms have been known at the atomic level since the 1930s. 1−6 The traditional S N 2 reaction pathway at the carbon center goes through pre-and post-reaction ion-dipole wells separated by a penta-covalent, usually submerged/high-energy transition state, where the angle of the nucleophile−central atom−leaving group is around 180°/ 90°for Walden inversion/front-side attack. 3,5 However, recent works in the past two decades uncovered that the S N 2 reactions are not so simple. 7−15 Besides ion-dipole complexes, hydrogenand halogen-bonded complexes can be formed in the entrance and/or exit channels, which may strongly affect the dynamics of the S N 2 reactions. 10−15 Moreover, post-reaction hydrogenbonded complex formation may open new product channels for ion−molecule reactions, as recent dynamics studies showed in the case of the XH − + CH 3 F [X = O and S] systems, which can lead to HF + CH 3 X − products besides F − + CH 3 XH. 15,16 Furthermore, our dynamics simulations revealed a doubleinversion mechanism for S N 2 reactions, where a protonabstraction induced inversion (first inversion) is followed by a substitution via the Walden-inversion transition state (second inversion), resulting in retention of the initial configuration. 9 In the simplest S N 2 reactions, the nucleophile is a halide or hydroxyl ion and most of the nontraditional S N 2 pathways were uncovered by studying their reactions with methyl-halides. 4−6 In the present study, we investigate the reactions of the simplest ambident nucleophile, the cyanide ion (CN − ), with the CH 3 Y [Y = F, Cl, Br, and I] molecules. Ambident nucleophiles have two reactive centers like CN − , where the negative charge is delocalized, allowing the formation of C−C and C−N bonds in the S N 2 reactions with CH 3 Y. Following the early experimental and theoretical investigations on the CN − + CH 3 Y S N 2 reactions, 17−21 in 2003, Gonzalez et al. 22 characterized the pre-and post-reaction ion-dipole complexes and the Waldeninversion transition state of the CN − + CH 3 F system using the focal-point analysis approach based on MP2/aug-cc-pV5Z and CCSD(T)/aug-cc-pVTZ energies as well as considering core correlation and relativistic effects at the CCSD(T)/TZ2P + dif geometries. In 2014 and 2015, Wang and co-workers 23,24 performed QM/MM computations in aqueous solution for the CN − + CH 3 Br and CN − + CH 3 Cl reactions, respectively. However, none of the abovementioned theoretical studies considered the ambident character of the CN − nucleophile and only the thermodynamically favored C−C bond formation was investigated. In the early 2010s, Bierbaum and co-workers 25,26 measured the rate coefficients and kinetic isotope effects for the CN − + CH 3 I/CD 3 I systems using flowing afterglow-selected ion flow tube mass spectrometry, however, it was without distinguishing between the C−C and C−N bond formations. The first combined experimental−theoretical study on the CN − + CH 3 I two-channel reaction was reported in 2015 by Wester and co-workers, 27 where both the I − + CH 3 CN/CH 3 NC S N 2 Walden-inversion pathways were characterized using the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVDZ level of theory and velocity map imaging. Experimentally, the I − anion was detected, and thus direct separation of the two different product channels was not possible. Nevertheless, the measured translational energy of I − could be used to predict the neutral counterpart, allowing the experimental determination of the isomer branching ratios. In 2019, in our group, the reaction pathways of the CN − + CH 3 Y [Y = F, Cl, Br, and I] systems were characterized using the explicitly correlated CCSD(T)-F12b/ aug-cc-pVnZ [n = D, T, and Q] levels of theory. 14 In the above study, for the first time, we considered front-side attack and double inversion for the CN − nucleophile; however, we only investigated the C−C bond formations. In the present work, we report stationary points characterizing the C−N bond formations as well and we consider electron correlation beyond CCSD(T), core correlation, and scalar relativistic effects, thereby determining the benchmark energetics of the title reactions superseding the accuracy of previous work. Furthermore, besides the S N 2 pathways, we compute the enthalpies of several additional product channels obtained by, for example, proton abstraction, halogen abstraction, and hydrogen substitution, considering the ambident character of the CN − reactant, thereby anchoring the different asymptotes of the global potential energy surfaces (PESs) of the title reactions, by which information may be utilized in future analytical PES developments and reaction dynamics studies. In Section 2, we describe the computational details, the results are presented and discussed in Section 3, and the paper ends with summary and conclusions in Section 4.

COMPUTATIONAL DETAILS
The mapping of the stationary points for the title reactions is performed based on previous studies 14,21,22,27 of the C−C bondforming NC − + CH 3 Y [Y = F, Cl, Br, and I] processes and chemical intuition. Initially, the structures are determined using the second-order Møller−Plesset perturbation theory (MP2) 28 with the aug-cc-pVDZ basis set. 29 To get the most accurate geometries, we use the explicitly correlated coupled-cluster singles, doubles, and perturbative triples method (CCSD(T)-F12b) 30 with the correlation-consistent aug-cc-pVDZ and augcc-pVTZ basis sets. Harmonic vibrational frequencies are also calculated using the previously mentioned levels of theory. For the open-shell products, we use restricted second-order Møller− Plesset perturbation theory (RMP2) 31 and the restricted openshell Hartree−Fock-based unrestricted explicitly correlated coupled-cluster singles, doubles, and perturbative triples method (UCCSD(T)-F12b). 32 For bromine and iodine, we employ a relativistic effective core potential (ECP), which replaces the inner-core 1s 2 2s 2 2p 6 and 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 electrons, respectively, and use the corresponding aug-cc-pVnZ-PP [n = D, T, and Q] basis sets. 33 For the F12b computations, the default auxiliary basis sets are used as implemented in MOLPRO. 34 To achieve sub-chemical accuracy, the following single-point energy computations are also performed at geometries obtained at the CCSD(T)-F12b/aug-cc-pVTZ level of theory: (1) CCSD(T)-F12b/aug-cc-pVQZ to account for basis set effects. (2) Coupled-cluster, singles, doubles, and triples [CCSDT] 35 and coupled-cluster, singles, doubles, triples, and perturbative quadruples [CCSDT(Q)] 36 methods with aug-cc-pVDZ basis to calculate post-CCSD(T) correlation. The corrections are defined as follows: (3) The CCSD(T) method with the aug-cc-pwCVTZ basis 37 is used to calculate frozen-core (FC) and all-electron (AE) energies. The core correction is as follows: As default, the frozen-core approach correlates only the valence electrons, while the all-electron method correlates both valence electrons and the outer-core electrons on the main shell below the valence shell. For example, in the case of Y = F, Cl, Br, and I, all-electron means 1s 2 2s 2 2p 5 , 2s 2 2p 6 3s 2 3p 5 , 3s 2 3p 6 3d 10 4s 2 4p 5 , and 4s 2 4p 6 4d 10 5s 2 5p 5 , respectively.
(4) Douglas−Kroll (DK) 38  We are not able to determine the scalar relativistic effect for Y = Br and I via eq 4 because non-DK computations have to use ECPs with the PP basis sets for Br and I, which already incorporate scalar relativistic effects for these atoms. In order to estimate the uncertainty of the ECP computations, we compare the DK-AE-CCSD(T)/aug-cc-pwCVTZ-DK (without ECP) and AE-CCSD(T)/aug-cc-pwCVTZ-PP (with ECP) energies in the case of Y = Br and I. However, these energy differences are not included in the final benchmark data.
The following expression is used to calculate the benchmark classical relative energies for the CN − + CH 3 Y [Y = F and Cl] systems:  (6) where classical refers to static nuclei without zero-point energy (ZPE). We can compute the adiabatic benchmark energies with the following equations:  showing the benchmark stationary-point relative energies along the back-side attack (Walden-inversion), front-side attack, and double-inversion pathways are given in Figures 1 and 2, respectively. The geometries of the S N 2 stationary points highlighting the most important benchmark structural parameters are shown in Figures 3 and 4 for the C−C and N−C bond formations, respectively. Qualitatively the C−C and N−C bond-forming S N 2 reactions proceed via similar pathways, though subtle differences exist. Back-side attack Walden inversion goes through a C 3v central transition state (WaldenTS) and forms the products via a deep minimum (WaldenPostMIN, C 3v ) along collinear N/C−C−Y arrangement, except for Y = F, where only a hydrogen-bonded minimum (PostHMIN2, C s ) is found in the exit channel. In the case of the C−C-bond-forming S N 2 channel, PostHMIN2s exist for Y = Cl, Br, and I as well, and their energies are similar to those of the corresponding WaldenPostMINs. However, PostHMIN2 with the N−C bond has only been found for Y = F. In the entrance channel, more differences are observed depending on the reactive center of the ambident nucleophile. Ion-dipole complexes (PreMIN) with C 3v point-group symmetry are formed for all Y if NC − reacts with its C-side, whereas PreMIN is only obtained for Y = F and Cl in the case of N−C bond formation. Hydrogen-bonded complexes (HMIN1) with nearly collinear H···CN are obtained only for H···C bonding and Y = Br and I; however, HMIN1 complexes are slightly less stable than PreMINs. For Y = I, a transition state (HTS2) connecting HMIN1 and PreMIN is also found. In all the NC − /CN − + CH 3 Y [Y = F, Cl, Br, and I] cases, a non-traditional complex (HMIN2) also exists in the entrance channel, which corresponds to the deepest minimum in the pre-reaction well. For Y = Cl, Br, and I, halogen-bonded minima (FSMIN, C 3v ) are found for both Y···CN and Y···NC bonding, which are unbound for Y = Cl and the most stable for Y = I. The front-side attack retention pathways go over a high-energy transition state (FSTS) with Y− C−C/N angles around 80°. Double inversion opens a slightly lower-energy retention pathway, where the first inversion occurs via a so-called double-inversion transition state (DITS), having a nearly collinear C···HCN or C···HNC arrangement. This first, proton-abstraction-induced inversion is followed by a substitution via WaldenTS, resulting in retention of the initial configuration. Quantitatively, the main difference between the NC − /CN − + CH 3 Y reactions is that thermodynamically, the Y − + CH 3 CN formation is clearly favored over the Y − + CH 3 NC channel, as the latter is above the former by 24.6 kcal/mol. The      Tables 1 and 2. The non-S N 2 channels are always endothermic, the endothermicity decreases with the increasing atomic number of Y, and the C-bond formations are always favored thermodynamically. Usually, proton abstraction is the lowest-energy non-S N 2 channel, with reaction enthalpies between 58.91−36.70 kcal/mol (HCN + CH 2 Y − ) and 74.39− 52.15 kcal/mol (HNC + CH 2 Y − ), showing that the ZPEcorrected energy of HCN is below that of HNC by 15.5 kcal/ mol. Halogen-abstraction forming two doublet products (YCN − /YNC − + CH 3 ) is found to be often competitive with the proton-abstraction channels, except for Y = F. For Y = Cl, Br, and I, the reaction enthalpies of the YCN − /YNC − + CH 3 channels differ by only a few kcal/mol from the enthalpies of the corresponding HCN/HNC + CH 2 Y − products and for Y = Br and I, halogen abstraction is clearly less endothermic. Note that two doublet products like YCN − /YNC − + CH 3 can be formed on a singlet potential energy surface, and the singlet products (YCN/YNC + CH 3 − ) have significantly higher energies as Tables 1 and 2 show, and thus, the latter products correspond to an excited electronic state. Considering the structures shown in Figure 5, one can see that YCN molecules are linear, whereas the YCN − anions are bent for Y = F and Cl and linear for Y = Br and I. CH 3 and CH 3 − have planar and pyramidal structures with D 3h and C 3v point-group symmetry, respectively ( Figure 6). The 0 K reaction enthalpies of hydride anion substitution are in the ranges of 57.08−58.10 and 75.96−80.67 kcal/mol for C−C and N−C bond formation, respectively, showing similar endothermicity as proton abstraction for Y = F, whereas hydride substitution is significantly more endotherm than proton abstraction for Y = Cl, Br, and I. The finding that the reaction enthalpies of hydride substitution do not show substantial Y dependence can be explained by the fact that the C−Y bond is a spectator in these processes and in every case, a C−H bond breaks heterolytically and a C−C/N−C bond forms, and thus the reaction enthalpies only depend significantly on the reactive site of the nucleophile. The reaction enthalpies of the YHCN − + 1 CH 2 channels decrease from 66.40 to 51.65 kcal/mol with the increasing atomic number of Y, whereas for YHNC − + 1 CH 2 , the enthalpies are in a narrower range of 62−67 kcal/mol. These data are similar to those of hydride substitution in the case of YHCN − formation, whereas they are significantly below the hydride substitution values for the YHNC − channel. Here, two notes should be mentioned. First, the above results correspond to the singlet methylene ( 1 CH 2 ), whereas the ground electronic state of CH 2 is triplet. We consider here 1 CH 2 because on a singlet potential energy surface, YHCN − /YHNC − + 1 CH 2 can be formed, whereas triplet CH 2 formation would proceed via non-adiabatic dynamics. Second, YHCN − /YHNC − complexes are linear consisting of an YH and a CN − /NC − fragment for Y = F and an Y − and a HCN/HNC unit for Y = Cl, Br, and I, as the bond lengths show in Figure 5. This finding can be explained by considering the proton-affinity order of the Finally, we discuss the accuracy and uncertainty of the new benchmark energies considering the basis-set convergence and the magnitude of the different auxiliary corrections. The relative energies obtained by different ab initio levels of theory as well as the post-CCSD(T), core, relativistic, and ZPE corrections are given in Tables 1 and 2 Tables 1 and 2 show, the MP2 method performs reasonably well for the pre-reaction complexes since the MP2 and CCSD(T)-F12b relative energies usually agree within 0.5− 1.0 kcal/mol. However, for the transition states and product channels, chemical accuracy is usually not achieved with the MP2 method, the absolute differences between the MP2 and CCSD(T)-F12b results are usually in the 1−5 kcal/mol range, but even larger deviations are also obtained. Thus, it is clear that the coupled-cluster method is needed to accurately account for the dynamical electron correlation in these systems.   kcal/mol and often have the same sign, thus resulting in post-CCSD(T) correlation effects around ±(0.2−0.6) kcal/mol usually, but not always, with negative signs (Figures 9 and 10). The most substantial post-CCSD(T) corrections are obtained for the FSTSs (often around −1 kcal/mol, especially for Y = Cl, Br, and I) and for the FNC − + CH 3 channel (−1.06 kcal/mol). Core correlation corrections are usually negligible for the entrance-channel complexes but can be significant, ±(0.2−0.5) kcal/mol, for the transition states and product channels. The largest core correction values around 0.8 kcal/mol are obtained for the enthalpies of the CN − + CH 3 I reaction, as somewhat expected. However, it is important to note that the magnitudes of the core correction values do not show significant Y dependence as Figures 9 and 10 show. Relativistic corrections are usually small (<0.1 kcal/mol) and have opposite signs than the corresponding, usually much larger, core corrections. The most substantial relativistic correction is −0.21 kcal/mol (ClNC − + CH 3 ). For the Y = Br and I systems, the Δ rel values shown in Tables 1 and 2 correspond to the difference between DK and ECP results, where the latter already incorporates scalar relativity for the heavy halogen atoms. Therefore, these Δ rel values are not included in our benchmark energies in the case of Y = Br and I; we rather use these data to estimate the uncertainty of the ECP computations. As seen in Tables 1 and 2, these DK − ECP values are usually less than 0.1 kcal/mol. Considering all the auxiliary corrections shown in Figures 9 and 10, we can conclude that the different contributions often partially cancel each other; however, in some cases, significant cumulative effects (>0.5 kcal/mol) still occur. Based on the above analysis of basis-set convergence and the magnitudes of the auxiliary corrections, we estimate that the uncertainty of our final benchmark classical relative energies is around 0.1−0.2 kcal/ mol. To obtain the adiabatic results, the ZPE corrections have to be considered, which are given in Tables 1 and 2. As seen, Δ ZPE is small, usually around 0.3−0.5 kcal/mol, for the pre-reaction complexes, WaldenTSs, and FSTSs, whereas it is significantly larger, 2−7 kcal/mol, for the DITSs and product channels. The ZPE corrections are positive for the pre-reaction complexes, WaldenTSs, and S N 2 products, whereas they are negative for the other product channels, FSTSs, and DITSs. In some cases, especially for some of the product channels, the neglected anharmonicity (about 5% of Δ ZPE ) may increase the uncertainty of the adiabatic relative energies. Thus, our prediction is that the present benchmark adiabatic relative energies are accurate within 0.1−0.4 kcal/mol.

SUMMARY AND CONCLUSIONS
Following our previous work 14 on the C−C bond-forming NC − + CH 3 Y [Y = F, Cl, Br, and I] S N 2 reactions, in the present study, we have considered the ambident character of the nucleophile and characterized the stationary points for the N−C bondforming pathways. Moreover, besides the S N 2 channels, we have computed reaction enthalpies for various endothermic product channels such as proton abstraction, hydride-ion substitution, halogen abstraction, and YHCN − /YHNC − complex formation. To obtain the best technically feasible ab initio properties of the stationary points, we have used the explicitly correlated CCSD(T)-F12b method with the aug-cc-pVTZ basis set to determine accurate structures and frequencies, and for energy computations, the basis set has been increased to aug-cc-pVQZ and auxiliary corrections have been computed such as post-CCSD(T), core, and relativistic corrections. The computations reveal that (a) Thermodynamically, C−C bond formation is much more favored than N−C bond formation, whereas the kinetic preference of the former is less significant.      The present comprehensive ab initio stationary-point characterization of the title reactions is expected to guide future global potential energy surface developments and reaction dynamics studies, thereby revealing the competition between the above-proposed reaction pathways of an ambident nucleophile. Furthermore, future experiments may look for the Table 2. continued cc-pVTZ. k Benchmark adiabatic relative energies obtained as classical + Δ ZPE . l CCSD(T)-F12b/aug-cc-pVDZ geometry and frequencies. m MP2/ aug-cc-pVDZ geometry and frequencies.    Table 1).
The Journal of Physical Chemistry A pubs.acs.org/JPCA Article different product ions formed by the various endothermic product channels investigated in the present work.  Table 2).
The Journal of Physical Chemistry A pubs.acs.org/JPCA Article