Electronic Structure Theory Study of the Microsolvated Fâ(H2O) +

Article pubs.acs.org/JPCA

Electronic Structure Theory Study of the Microsolvated F−(H2O) + CH3I SN2 Reaction Jiaxu Zhang, Li Yang,* and Li Sheng* School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150001, P. R. China S Supporting Information *

ABSTRACT: The potential energy profile of microhydrated fluorine ion reaction with methyl iodine has been characterized by extensive electronic structure calculations. Both hydrogenbonded F−(H2O)---HCH2I and ion−dipole F−(H2O)---CH3I complexes are formed for the reaction entrance and the PES in vicinity of these complexes is very flat, which may have important implications for the reaction dynamics. The water molecule remains on the fluorine side until the reactive system goes to the SN2 saddle point. It can easily move to the iodine side with little barrier, but in a nonsynchronous reaction path after the dynamical bottleneck to the reaction, which supports the previous prediction for microsolvated SN2 systems. The influence of solvating water molecule on the reaction mechanism is probed by comparing with the influence of the nonsolvated analogue and other microsolvated SN2 systems. Taking the CCSD(T) singlepoint calculations based on MP2-optimized geometries as benchmark, the DFT functionals B97-1 and B3LYP are found to better characterize the potential energy profile for the title reaction and are recommended as the preferred methods for the direct dynamics simulations to uncover the dynamic behaviors.

I. INTRODUCTION Bimolecular nucleophilic substitution (SN2) reactions such as X− + CH3Y → CH3X + Y −

The transition from gas phase to liquid water kinetics has been investigated by studies of microsolvation effects on X−(H2O)n + CH3Y reaction dynamics and rate constants. The decrease in reaction efficiency with increased solvation for such SN2 reactions has been experimentally illustrated.12,19−28 From the theoretical point of view, the transition state theory (TST) rate constant and kinetic isotope effects (KIEs) for microsolvated X−(H2O) + CH3Cl (X = F and Cl) reactions were calculated by Truhlar and co-workers, and the results are in agreement with experiment.29−31 In addition to interpret experimental results, theoretical studies have also predictive capability if they are of a good enough level. The direct dynamics simulations for X− + CH3Cl (X = F and OH) reactions, with microsolvation, have predicted the reaction mechanisms and branching ratio of product channels as a function of collision energy.32−34 Binding of the halogen ions to the water molecules and the role of the water molecules in suppressing the reaction rate were both considered in simulations of hydrated Cl− reaction with CH3Br.35,36 Recently, molecular beam, ion-imaging experiments have probed the dynamics of OH−(H2O)n + CH3I reactions for n = 0−2.37−39 Important differences was found between the reaction dynamics of bare OH− and singly and doubly hydrated OH−. Chemical dynamics simulations provided an atomistic under-

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are known for their rich reaction dynamics and are of fundamental importance in chemistry.1−5 These reactions in the gas phase are characterized by a double-minimum potential energy surface (PES) with the X−---CH3Y and XCH3---Y− preand postreaction ion−dipole complexes, separated by a central barrier [X--CH3--Y]−.2,5−7 The barrier represents a transition state that corresponds to a Walden-inversion at the carbon atom and has a substantial influence on the reaction kinetics and dynamics even if it is usually submerged with respect to the reactant energy asymptote. There have been extensive studies of gas phase X− + CH3Y reactions,1−11 in particular the nonstatistical and nontraditional dynamics found for SN2 pathway.1,3−5,8,9,11 The dynamics of these reactions in aqueous solution are different and also of great interest.12−18 Reaction rates, for SN2 reaction 1 with barriers, are 10 orders of magnitude smaller in aqueous solution than in the gas phase.12,14 Both computation14−16 and experiment12,13 have probed how the solvation affects the SN2 dynamics in water. Water molecules solvate the reactants more strongly than the SN2 transition state, substantially raising the barrier for reaction in solution.13,14,18 Nonequilibrium barrier recrossing effects may be important for SN2 reactions in solution15,16 but are of less importance than the preferential solvation of the reactants. © XXXX American Chemical Society

Received: January 22, 2016 Revised: April 1, 2016

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DOI: 10.1021/acs.jpca.6b00726 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Figure 1. Geometries of stationary points for the F−(H2O) + CH3I SN2 reaction optimized at the B3LYP/ECP/d level of theory. Bond distances are in Å and angles in degrees. The available experimental values (ref 58) are in parentheses.

the F− + CH3I system under microsolvation, and what does the solvated PES look like? Bierbaum et al. investigated solvent effects on the F−(H2O) + CH3I SN2 reaction.27 The measured rate constant is ∼2 times slower than the nonsolvated one. As observed for most microsolvated X−(H2O) + CH3Y reactions,2,18−21 the formation of solvated I−(H2O) product is strongly suppressed with respect to the free I− and the detailed knowledge of water molecule transfer toward the product species during the reaction is needed to understand this observation.32,34 Interpreting and predicting the dynamics and kinetics of SN2 reactions and comparing with experiments, by either statistical calculations or chemical dynamics simulations, require accurate PESs. Most recently, a direct chemical dynamics simulation, at

standing of these experiments and predicted the role of the H2O molecule.40−42 The F− + CH3I → CH3F + I− reaction is of particular interest because its PES is substantially different from that for the double-minima, central barrier model as described above. There is a hydrogen-bonded F−---HCH2I complex in addition to the traditional F−---CH3I ion−dipole complex in the prereaction region.5,8 Though the barrier is quite low for the F−---HCH2I prereaction complex to pass the transition state and form products, F−---HCH2I is expected from the simulations to play an important part in reaction dynamics and ∼60% of the reaction proceeds via an indirect mechanism with formation of this complex.7,42 An interesting issue is, does this hydrogen-bonded complex with a similar structure exist for B


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Figure 2. Potential energy curves and stationary points for the (a) F−(H2O) + CH3I reaction at the CCSD(T)/PP/t//MP2/PP/d level and the (b) F− + CH3I reaction at the CCSD(T)/PP/t level. The potential energies in kcal/mol are classical energies without zero-point energy (ZPE). The experimental enthalpies of F−(H2O) + CH3I reaction (refs 62 and 63) in parentheses include ZPE. The results for F− + CH3I reaction (b) were adapted from ref 8.

F−(H2O) + CH3I PES are determined using the MP244,45 and DFT,46−49 with the OPBE, OLYP, BhandH, HCTH407, B97-1, B97D, and B3LYP functionals. The basis set, called ECP/d is used for both MP2 and DFT calculations. The other basis set, denoted as PP/d, is used with only MP2 to test the sensitivity of the ab initio results to the iodine basis set. For ECP/d, Dunning and Woon’s aug-cc-pVDZ basis set50,51 is used for the H, C, O, and F atoms. For iodine, the Wadt and Hay effective core potential (ECP) is used for the core electrons and a 3s, 3p basis set for the valence electrons,52 which is augmented by a dpolarization function with a 0.262 exponent, and s, p, and d diffuse functions with exponents of 0.034, 0.039, and 0.0873, respectively.53,54 The PP/d basis set are the combination of the above double-(d) ζ basis set, aug-cc-pVDZ, for the H, C, O, and F atoms, and the Peterson aug-cc-pVDZ basis set, with a pseudopotential (PP),55 for the I atom. The difference between ECP/d and PP/d is the treatment of iodine. The ECP/d basis set neglects 40 core electrons of I atom and considers the outmost s and p orbitals as valence electrons and derived from an all-electron numerical relativistic Hatree−Fock atomic wave function and fit to an analytic

the B3LYP/ECP/d level of theory, was used to study the dynamics of the F−(H2O) + CH3I SN2 reaction at a low collision energy of 0.32 eV and compare with results of the water-free system.43 To investigate the adequacy of these B3LYP direct dynamics, it is of interest to compare properties of the F−(H2O) + CH3I PES, given by the above B3LYP method and other electronic structure theoretical methods. In the work presented here, stationary point properties of microsolvated F−(H2O) + CH3I reaction are calculated by using the DFT, MP2, and CCSD(T) theories with different basis sets and DFT functionals. Comparisons are made between the results of these calculations and with experimental and previously obtained theoretical results. The difference of PES properties of the current reaction with its nonsolvated analogue and other microsolvated SN2 systems are revealed. This work may provide an insight into the SN2 mechanisms under microsolvation.

II. COMPUTATIONAL METHODS The stationary point properties for the reactants, pre- and postreaction complexes, transition states, and products on the C


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ing im1−im4, TS1 − TS3, in addition to the reactants and products. However, this model for the PES is not supported by other DFT functionals and the difference mainly lies in the postreaction region. TS3 cannot be located for the BhandH and HCTH407 and both im3 and TS3 are not found for the OPBE, OLYP, and B97D, despite numerous attempts. Failure to capture the water transfer process by these functionals might be attributed to the very flat PES in the vicinity of im3 and TS3, which are almost isoenergetic, as shown in Figure 2a. For these functionals, the system may directly pass to the postreaction complex im4, after crossing the bottleneck TS2, without first accessing an im3 complex. B. Basis Sets Effect. The MP2 calculations are used to compare stationary point properties given by the ECP/d/fc, ECP/d, and PP/d basis sets, and the calculated structures, energies, and vibrational frequencies are given in Tables S1−S3 of the Supporting Information. The ECP/d and ECP/d/fc results are quite similar. Bond lengths and angles differ by 0.03 Å and 1° or less, except for the bond F−H2 and angle F−C−I of TS3, for which the differences between ECP/d and ECP/d/ fc are 0.1 Å and 2.3°, respectively. The differences of energy and vibrational frequencies are at most 0.3 kcal/mol and 12 cm−1, respectively, illustrating the accuracy of the frozen core (fc) approximation. Overall, changing the basis set from ECP/d to PP/d has only a small effect on stationary point properties. The differences of the bond lengths and angles are generally less than 0.05 Å and 1°. The largest difference is 2.7° and lies in angle I−H1−O of I−(H2O) product. The largest frequency and energy differences are 35 cm−1 for the bound O−H str of I−(H2O) and 0.7 kcal/mol for product P1. As discussed in section II, the only difference between ECP/d and PP/d is the treatment of iodine. The number of basis functions in PP/d is larger than in ECP/d and the calculations using the former are more computationally expensive. Integrating one trajectory with the ECP/d basis is about 3 times faster than with the PP/d basis. Taking both the relative accuracy and computational efficiency of different basis sets into consideration, ECP/d with the fc model is more appropriate for the direct dynamics simulations for the title reaction. C. Properties of the Stationary Points. To test the influence of the methodology on the F−(H2O) + CH3I PES, seven different DFT functionals with ECP/d basis set are employed to investigate the stationary point properties, which are compared to the MP2 results in the following. 1. Geometries. The stationary point geometries are listed in Table S1 in the Supporting Information and depicted in Figure 1. Overall, the geometries given by the MP2 and different DFT functionals are similar. However, there are differences for the distances of weakly bonded interaction for the stationary points, i.e., H---F, H---I, F---C, and C---I distances. When compared with MP2 geometries, the largest variation in these distances obtained by the different DFT functionals are from 0.177 Å (C---I of TS3) for B97-1 to 0.817 Å (C---I of im4) for OPBE. MP2 and DFT bond lengths other than weak bonding are in good agreement and the differences are generally less than 0.05 Å. The MP2 bond angles agree well with the DFT values in most cases, except for the angles H2−F−C, F−C−I, and I−H1−O of the stationary points, which are relevant to weak bonds. Generally, DFT gives a significantly larger H2−F− C angle than does MP2, and the largest differences with MP2 ranges from 7.9° (in TS2) for BhandH to 36.5° (in im1) for B3LYP. The largest difference in the MP2 and DFT values varies from 2.9° (in im3) for BhandH to 15.7° (in TS1) for

representation for use in molecular calculations. In contrast, 28 inner core electrons (1s−3d) of the I atom are replaced by an energy-consistent pseudopotential, which is optimized in a multiconfigurational Dirac-Hartree−Fock calculation, for the PP/d basis set. Thus, a larger number of basis functions are involved in PP/d basis set and calculations with it are more computationally expensive than those with the ECP/d basis set. The frozen core (fc) orbital method was tested for the MP2 calculations. The stationary nature of the structures is confirmed by harmonic vibrational frequency calculations; that is, the potential minima possess all real frequencies, whereas the transition state possesses only one imaginary frequency. The harmonic zero-point energy (ZPE) was obtained at all the above levels of theory. To obtain more reliable energies, high-level single-point energy calculations were performed at the CCSD(T) level of theory56 with the PP/ t basis set for the MP2/ECP/d-optimized geometries. For basis set PP/t, the Peterson aug-cc-pVTZ basis, with a pseudopotential (PP),55 is used for iodine and the aug-cc-pVTZ basis50,51 for other atoms. Unless otherwise specified, the CCSD(T)/PP/ t//MP2/ECP/d single-point energies with inclusion of MP2/ ECP/d ZPE are used in the following discussions. The computer program used for the work presented here is NWChem.57

III. RESULTS AND DISCUSSION A. Stationary Points of the Potential Energy Surface. The optimized structures of stationary points as well as the available experimental values are shown in Figure 1. Figure 2a presents the potential energy curve and relative energies of stationary points for the CCSD(T)/PP/t//MP2/ECP/d PES. The initial association of F−(H2O) and CH3I can form either a hydrogen-bonded complex F−(H2O)---HCH2I (im1) or an ion−dipole complex F−(H2O)---CH3I (im2), which can readily interconvert into each other with a barrier less than 0.9 kcal/ mol (TS1). After surmounting a 5.5 kcal/mol barrier (TS2), the system undergoes the substitution reaction with a Walden inversion and falls down to the deep postreaction potential energy well leading to complex CH3F(H2O)---I− (im3), for which the water molecule is attached to both the fluorine and iodine atoms. Subsequently, the water molecule can easily move to the iodine side and the system reaches a minimum corresponding to the CH3F---I−(H2O) (im4) ion−dipole complex. This is accomplished by overcoming a barrier of only 0.2 kcal/mol (TS3). Eventually, complexes im3 and im4 take three-body dissociation to give product P1 CH3F + I− + H2O. Alternatively, the two complexes can form product P2 CH3F + I−(H2O) or P3 CH3F(H2O) + I− with iodine and methyl fluoride solvated by the water molecule, respectively. It is interesting that although P2 is more favored in energy than P1 and P3, the experiment found that the formation of free I− strongly prevails over that of I−(H2O).27 The trajectory calculations for X−(H2O) + CH3I (X = OH and F) reactions showed that the H2O molecule tends to depart the reactive system as the SN2 product CH3X is formed or before CH3X formation, which might be important for understanding this observation.40,43 As can be seen from Figures 1 and 2a, the motion of the water molecule along the reaction path is driven by the H-bonding between the water molecule and the fluorine or iodine atom. It is noted that MP2 and DFT hybrid functionals B97-1 and B3LYP43 predict the existence of all the stationary points on the CCSD(T)/PP/t//MP2/ECP/d PES mentioned above, includD


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The Journal of Physical Chemistry A Table 1. Electronic Structure Theory Energies for F¯(H2O) + CH3I Stationary Pointsa,b,c stationary points

MP2

OPBE

OLYP

BhandH

HCTH407

B97-1

B97D

B3LYP

CCSD(T)d

im1 F¯(H2O)---HCH2I

−14.9 −13.9 −14.1 −13.4 −14.2 −13.4 −7.7 −6.2 −33.8 −30.6 −33.5 −30.8 −34.8 −32.0 −14.2 −13.3 −26.0 −24.0 −18.8 −16.2

−11.1 −10.3 −9.5 −8.9 −9.6 −8.9 −7.2 −6.0

−11.3 −10.6 −10.3 −9.8 −10.4 −9.8 −8.5 −7.5

−18.5 −17.4 −17.7 −16.9 −17.8 −16.8 −13.8 −12.2 −43.7 −40.1

−13.5 −12.7 −12.8 −12.2 −12.9 −12.2 −10.6 −9.6 −34.2 −31.6

−14.9 −14.0 −14.6 −13.9 −15.4 −14.3 −15.2 −13.8

−33.2 −30.6 −20.4 −19.2 −28.8 −26.8 −21.9 −19.8

−32.5 −30.1 −19.0 −18.0 −27.7 −25.8 −21.1 −19.0

−44.2 −41.3 −21.9 −20.7 −34.7 −32.6 −29.0 −26.0

−35.6 −33.1 −18.4 −17.5 −28.8 −26.9 −21.9 −19.7

−14.3 −13.4 −13.4 −12.6 −13.5 −12.6 −11.8 −10.6 −35.8 −32.8 −35.7 −32.9 −37.2 −34.6 −19.1 −18.1 −30.0 −28.0 −22.9 −20.4

−13.6 −12.8 −12.6 −11.9 −12.8 −12.0 −11.4 −10.3 −34.4 −31.5 −34.2 −31.7 −35.7 −33.2 −19.4 −18.5 −29.6 −27.7 −22.8 −20.5

−14.7 −13.7 −13.8 −13.1 −14 −13.2 −8.5 −6.9 −35.8 −32.6 −35.6 −32.9 −36.8 −34.1 −17.6 −16.7 −28.9 −26.8 −22.0 −19.4

TS1 im2 F¯(H2O)---CH3I TS2 im3 FCH3(H2O)---I− TS3 im4 FCH3---I¯(H2O) P1 CH3F + I¯ + H2O P2 CH3F + I¯(H2O) P3 (H2O)FCH3 + I¯

−37.3 −34.8 −18.6 −17.6 −29.5 −27.6 −22.4 −19.9

expte

−18.5 −27.9

Energies are in kcal/mol with respect to the F−(H2O) + CH3I reactants and are at 0 K. bThe MP2 and DFT energies were calculated using the ECP/d basis set. The CCSD(T) single-point energies were calculated using the PP/t basis set, based on the MP2/ECP/d-optimized geometries. c For each stationary point the upper values do not include ZPE and the lower values include ZPE. dFor CCSD(T) the ZPE is calculated at the MP2/ ECP/d level of theory (see the text). eThe reaction enthalpies of reaction at 0 K with ZPE calculated from standard molar enthalpies of formation in refs 34 and 35. The harmonic MP2 frequencies are used to remove the thermal vibration enthalpies, along with the thermal rotation and translation enthalpies. a

bond length range from 0.001 Å for MP2 to 0.190 Å for OLYP, and the variations in the O−H1−I angle range from 0.5° for OPBE to 8.7° for B97D. 2. Vibrational Frequencies. Vibrational frequencies are calculated for all the stationary points by using the MP2 and DFT theories with ECP/d basis set, and the results are listed in Table S2 of the Supporting Information. In general, the MP2 and DFT frequencies are in agreement and the hybrid functionals B97-1 and B3LYP appear to give better frequencies than other functionals, when compared with MP2 frequencies. However, it is notable that MP2 gives the value for the imaginary reaction coordinate frequency of central barrier TS2 as 1.13 (for BhandH) to 1.66 (for OLYP) times larger than the DFT functional values. The relative MP2:B97D value for this imaginary frequency is even larger and 2.75:1. That the MP2 value for this frequency is substantially larger than the DFT values indicates that the MP2 and DFT theories give the different potential energy surface shapes in the vicinity of the dynamical bottleneck for the reaction. The calculated frequencies of the CH3I reactant and CH3F and H2O products are in good agreement with experiment.60−62 In terms of the relative uncertainty |νcalc − νexp|/νexp for each normal mode, the average deviation is 1−4% for the employed theories. MP2, B97-1, and B3LYP give the best agreement with the experimental frequencies with the average deviation of only 1%. Frequencies for F−(H2O) have been calculated at the MP2/ aug-cc-pVDZ level.29 The principal difference between the frequencies of the DFT/ECP/d methods and those given by MP2/aug-cc-pVDZ lies in the bound O−H stretch. The difference ranges from 25 cm−1 for B97-1 to 274 cm−1 for OPBE. Because the two theories are fundamentally the same for F−(H2O) calculations, MP2/ECP/d gives the best agreement with the MP2/aug-cc-pVDZ frequencies. The frequencies

B97D for the F−C−I angle, and from 0.9° (in im4) for OLYP to 11.2° (in I−(H2O)) for B97D for the I−H1−O angle. BhandH appears to give better bond angles than other functionals, when compared with MP2 angles. The geometries of CH3I, CH3F, and H2O obtained at the different levels of theory are compared with experimental values58 in Table S1. Bond angles deviations are within ∼1°. The relative error in the bond length, |rcal − rexp|/rexp, is determined for all the bonds and the largest relative error varies from 1% to 3% for different theories. OPBE, BhandH, HCTH407, B97-1, and B3LYP give the best agreement with experiment. The B3LYP structures, and their comparison with experiment, are summarized in Figure 1. The geometry of reactant F−(H2O) has been previously calculated at the MP2/aug-cc-pVDZ level.29 The structure obtained by our calculations is consistent with that determined from the MP2/aug-cc-pVDZ level with bond angle differences 1.2° or less. The major structural difference lies in the F−H2 bond length. The MP2/aug-cc-pVDZ value for this bond length is 1.414 Å, with which MP2/ECP/d gives the best agreement. BahndH/ECP/d theory gives the largest difference with MP2/ aug-cc-pVDZ F−H2 bond length of F−(H2O) and differs by 0.083 Å. The geometry of product I−(H2O) was obtained by the MP2/aug-cc-pVTZ/AVTZ+ECP46MWB and B3LYP/6311++G(3df,3pd)/Lanl2DZ+diff calculations.59 In general, the calculated structures with the two different theories are only slightly different. The bond distances change by 0.084 Å (O---I bond) or less, and bond angles change by 1.1° or less. The structural difference of I−(H2O) between our calculations with ECP/d basis and these two theories mainly lies in the O---I bond length and O−H1−I angle. The MP2/aug-cc-pVTZ/ AVTZ+ECP46MWB values for this bond length and angle are 3.535 Å and 163.3°, compared to which the variations in O---I E


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The Journal of Physical Chemistry A of I−(H2O) were determined previously with MP2/aug-ccpVTZ/AVTZ+ECP46MWB and B3LYP/6-311++G(3df,3pd)/ Lanl2DZ+diff theories,59 and the results are consistent with each other with the largest difference of 24 cm−1 for the free O−H stretch. Varying the basis set to ECP/d slightly affects the frequencies with the difference less than 25 cm−1 (H2O rock) for MP2 and 16 cm−1 (bound O−H stretch) for B3LYP. The difference with these two theories, for the I−(H2O) frequencies, is largest for the BhandH functional. 3. Energies. Table 1 displays the relative energies for the stationary points calculated with MP2 and DFT functionals using the ECP/d basis set. These theories give substantial differences in the energies for each stationary point. To obtain more reliable energies beyond the MP2 and DFT results, highlevel single-point CCSD(T) calculations, based on the MP2/ ECP/d-optimized geometries, are performed with the PP/t basis set and the resulting energies are listed in Table 1 and compared with experimental values. The experimental reaction exothermicities with ZPE at 0 K are −18.5 and −27.9 kcal/mol for the pathways leading to products P1 and P2, respectively,62,63 and only 1.8 and 1.1 kcal/mol more negative than the CCSD(T) values with ZPE included. This good agreement illustrates the high accuracy of the CCSD(T) calculations. The B97-1 and B3LYP functionals give stationary point structures and frequencies in good agreement with experiment and have reaction exothermicities (ZPE is included) of −18.5 and −18.1 kcal/mol for the path of P1, and −27.7 and −28.0 kcal/mol for that of P2, respectively, which are only 0.4 kcal/mol or less different than the experimental values. As shown in Table 1, MP2 and different DFT functionals, in line with CCSD(T)/PP/t/MP2/ECP/d, suggest a relatively flat PES for the reactant-side region in the vicinity of the im1 F¯(H2O)---HCH2I, im2 F¯(H2O)---CH3I, and TS1. For the energies of these structures, MP2 gives a better relative accuracy than do DFT functionals, when compared with CCSD(T). For the product-side region of the PES, MP2, B3LYP, and B97-1 give the stationary point features in agreement with those found by the CCSD(T)/PP/t/MP2/ ECP/d calculations, which predict the existence of complexes im3 CH3F(H2O)---I− and im4 CH3F---I¯(H2O), and transition state TS3. The calculations by all these theories show that the PES is also very flat in the vicinity of these postreaction stationary points. The CCSD(T) value for the central barrier of im2 → TS2 is 5.5 kcal/mol, which is closer to the MP2 value of 6.5 kcal/mol and higher than that of different DFT functionals. The DFT energies for products is generally lower in comparison with MP2 values and the former are in better agreement with CCSD(T) and experimental energies. The exception is for DFT/BhandH, whose energies for P1, P2, and P3 are 4.3, 5.8, and 7.0 kcal/mol lower, respectively, than the CCSD(T) values. The relative energies found with the MP2 and DFT levels of theory, using the ECP/D basis set, as compared with the CCSD(T)/PP/t/MP2/ECP/d single-point energies are shown in Figure 3. All stationary point energies are included in the histograms, and each is fit with the normal distribution of error curve. The position of the maximum of the normal distribution of error curve corresponds to the mean deviation of the error whereas the half-width at half-maximum reflects the scattering of the error’s standard deviation. The average values of the MP2, OPBE, OLYP, BhandH, HCTH407, B97-1, B97D, and B3LYP normal distribution curves are +1.6, +1.8, +1.9, −5.5, +0.4, −0.6, −1.5, and +0.1 kcal/mol, respectively. Their

Figure 3. Histograms of differences between stationary point energies calculated with MP2 and DFT functionals, employing the ECP/d basis set, and the CCSD(T)/PP/t values. Ten different stationary point energies are included in each of the histograms and each is fit with the normal distribution of error curve. The fitting parameters are given in the text. TS3 is not located for BhandH and HCTH407, and im3 and TS3 are not found for OPBE, OLYP, and B97D functionals (see text).

respective standard deviations are 1.4, 2.4, 1.9, 1.5, 1.1, 1.1, 2.0, and 1.5 kcal/mol. Overall, HCTH407, B97-1, and B3LYP theories give relatively smaller mean and standard deviations of the error than do the other theories, which means the energies calculated by these DFT functionals are in better agreement with the CCSD(T) values. B97-1 (−0.6 kcal/mol) has systematic errors opposite those of HCTH407 (0.4 kcal/mol) and B3LYP (0.1 kcal/mol). The standard deviations of HCTH407, B97-1, and B3LYP are not statistically different, which means these functionals are of similar accuracy. A survey of the normal distribution of error curve in Figure 3 indicates that the BhandH stationary point energies may be too low as compared with those from CCSD(T). As shown in Table 1, the principal energy differences between HCTH407, B97-1, and B3LYP functionals and CCSD(T) lie in the SN2 transition state TS2, for which the energies given by the three functionals are lower than the CCSD(T) value (−8.5 kcal/mol) by 2.1, 3.3, and 2.9 kcal/mol, respectively. As indicated in section IIIA, HCTH407 failed to capture the water migration on the exit channel and cannot locate transition state TS3. As a result, the DFT functionals B97-1 and B3LYP are expected to give the PES model with stationary point features in the best agreement with that of the benchmark CCSD(T) calculations. D. Comparison with Stationary Points of F− + CH3I and X−(H2O) + CH3Y PESs. In recent work,8 CCSD(T)/PP/t optimization calculations of the stationary points on nonsolvated F− + CH3I PES have been performed. The obtained potential energy profile is depicted in Figure 2b, where it is compared with that of the current F−(H2O) + CH3I reaction (Figure 2a), obtained by CCSD(T)/PP/t single-point calculations performed at the MP2/ECP/d-optimized geometries. Overall, the potential energy profiles for both reactions are similar. In particular, there is a hydrogen-bonded F−(H2O)n=0,1---HCH2I prereaction complex, a transition state (TS) connecting this complex with the traditional ion−dipole prereaction complex F−(H2O)n=0,1---CH3I, and then a SN2 TS connecting this complex to the postreaction complex. For the F−(H2O) + CH3I system, if the H2O molecule is removed from the potential energy minima and transition states on the entrance channel PES (i.e., im1, im2, TS1, and TS2), the F


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energy between them is very small. They cannot locate another saddle point corresponding to reaction with H2O moving in a concerted way from the F to the Cl side. This is the case for OH−(H2O) + CH3Y (Y = Cl and I)32,40 and Cl−(H2O) + CH3Br35 reactions and also found in the present calculations of F−(H2O) + CH3I reaction, for which all attempts made to stabilize the water molecule in a bridging position for the TS failed. The central barrier height from prereaction complex to SN2 TS varies for different reactions, and 11.2 kcal/mol (MP2/ 6-311++G(d,p)) for OH−(H2O) + CH3Cl, 0.1 kcal/mol (B971/ECP/d) for OH−(H2O) + CH3I, in contrast to 6.4 kcal/mol (CCSD(T)/PP/t/MP2/ECP/d) for F−(H2O) + CH3I. The dynamics simulations by Tachikawa32,33 for X−(H2O) + CH3Cl (X = F and OH) and by Cardini et al.35 for Cl−(H2O) + CH3Br suggest that the water molecule is transferred to the Cl or Br atom in a nonsynchronous pathway after the dynamical bottleneck for the reaction, in spite of no PES reported for the water migration process. Our calculations for F−(H2O) + CH3I reaction support these predictions, as shown in Figure 2a for the exit channel region of the PES. After F− displacement of I− for the SN2 reaction, the water molecule can easily shift from the fluorine to iodine side with a classical barrier of just 0.2 kcal/mol at the CCSD(T)/PP/t/MP2/ECP/d level. The inclusion of ZPE correction, calculated from the MP2 harmonic frequencies, results in the disappearance of the barrier. Thus, our conclusion is that there is little or no barrier for the water transfer, in line with that of Cl−(H2O) + CH3Br system.35 Both OH−(H2O) + CH3Cl32 and OH−(H2O) + CH3I40 have a deep postreaction potential energy minimum CH3OH(H2O)---Y− (Y = Cl and I) with the energy of −52.1 (MP2/ 6-311++G(d,p)) and −58.0 (B97-1/ECP/d) kcal/mol, respectively, with respective to the reactants. These are more negative than the CCSD(T)/PP/t/MP2/ECP/d energies of post reaction complexes im3 CH3F(H2O)---I− (−35.8 kcal/mol) and im4 CH3F---I−(H2O) (−36.8 kcal/mol) for the F−(H2O) + CH3I reaction. The structures of complex CH3OH(H2O)---Y− are similar for Y = Cl and I, where the Y and H2O are attached to the H and O atom of OH group, respectively, by the hydrogen-bonding. But they are different from the structures of im3 and im4, as shown in Figure 1. As for the present results of the F−(H2O) + CH3I reaction, three SN2 product channels P1 CH3OH + Y− + H2O, P2 CH3OH + Y−(H2O), and P3 CH3OH(H2O) + Y− were observed for the OH−(H2O) + CH3Y (Y = Cl and I) reactions with the exothermic energies decreasing in the order P2 > P3 > P1.32,40 Nevertheless, the reaction exothermicities for these channels are overall larger for the latter two reactions.

resulting structures are similar to those of corresponding stationary points for the F− + CH3I system.8 The postreaction complex FCH3---I− for the nonsolvated reaction has the C3v structure and the F−C bond and I atom are in a collinear configuration, whereas, for the solvated reaction, the reactive system first goes to a postreaction complex im3 CH3F(H2O)--I− after crossing the SN2 transition state TS2, for which the F− C---I angle is ∼114° and the water molecule is hydrogenbonded to both F and I atoms. With the increase of the F−C---I angle and F---H2 distance, im3 passes over TS3 to the other postreaction complex im4 CH3F---I−(H2O), for which the F− C---I angle is ∼173°, resulting in a nearly linear structure for the CH3F---I− heavy atoms, with H2O hydrogen-bonded to I atom. In contrast to the unique SN2 products CH3F + I− for the F− + CH3I reaction, the involvement of water molecule opens up new SN2 pathways giving products P1 CH3F + I− + H2O, P2 CH 3 F + I − (H 2 O), and P 3 CH 3 F(H 2 O) + I − with P 2 energetically the most favored. The F− + CH3I → CH3F + I− reaction is the most exothermic (∼−42.4 kcal/mol at the CCSD(T)/PP/t level) of the set of nonidentity halide-exchange SN2 reactions. Solvating the reactant species reduces the reaction exothermicity of the solvated system, with the values not more than −28.9 kcal/mol for the three product channels, as shown in Figure 2. The CCSD(T)/PP/t/MP2/ECP/d energies of the prereaction complexes relative to reactants F−(H2O) + CH3I were found to be −14.7 and −14.0 kcal/mol for the hydrogen-bonded F−(H2O)---HCH2I (im1) and ion−dipole F−(H2O)---CH3I (im2), respectively. These values are smaller than the corresponding energies of −19.5 and −17.1 kcal/mol for the unsolvated prereaction complexes. The destabilization of the hydrated complexes can be related to the increase of the F---H3 distance for im1 and the F---C distance for im2, compared to the case for the nonhydrated system. These bond lengths are 1.835 Å for the im1 and 2.701 Å for im2 at the MP2/ECP/d level, in contrast to respective 1.574 and 2.433 Å at the same level for their nonhydrated analogs. The solvated energy barrier from the prereaction complex to the corresponding transition state is 0.9 kcal/mol for the im1 → TS1 and 5.5 kcal/mol for the im2 → TS2, which are 2.0 kcal/mol lower and 5.0 kcal/mol higher than the corresponding unsolvated values, respectively. The increased overall SN2 central barrier from im1 to TS2 for the solvated system (Figure 2) contributes to the decreased solvated reaction rate as compared to the case of the nonsolvated one, as observed in experiment.27 The PES information for the microsolvated SN2 reactions is limited. Hase and co-workers have studied the energy diagrams for the OH−(H2O) + CH3I reaction at the B97-1/ECP/d level of theory. 40 Two structures, i.e., hydrogen-bonded HO−(H2O)---HCH2I and ion−dipole HO−(H2O)---CH3I, were found for the prereaction complex, to which the energy release from reactants is ∼−12.5 kcal/mol for both structures. These features and energetics are in agreement with the present results for the entrance channel of the F−(H2O) + CH3I PES. The structures of the transition state have been investigated for several X−(H2O) + CH3Y SN2 reactions. For the identity Cl−(H2O) reaction with CH3Cl,30,31 Truhlar et al. found a C2v TS structure with the water molecule located symmetrically between the two chlorine atoms, whereas for the nonidentity F−(H2O) + CH3Cl reaction,29 the calculated saddle point geometry shows that the water molecule remains on the fluorine side by hydrogen-bonding. Given the large separation between the water molecule and chlorine atom, the interaction

IV. CONCLUSIONS In this work, extensive electronic structure calculations including MP2 and CCSD(T) theories and the DFT functionals OPBE, OLYP, BhandH, HCTH407, B97-1, B97D, and B3LYP were performed to investigate the properties of stationary points on the microslovated F−(H2O) + CH3I PES and to compare different electronic structure theories. The behavior of solvating water molecule and its influence on the reaction mechanism are probed by comparison to the nonsolvated analogue and other microsolvated SN2 systems. The main results can be summarized as follows: (1) The initial association of reactants can form either a hydrogen-bonded complex F−(H2O)---HCH2I (im1) or an ion−dipole complex F−(H2O)---CH3I (im2), which G



(2)

(3)

(4)

(5)

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can easily interconvert into each other via TS1. Then im2 undergoes Walden inversion via SN2 transition state TS2 to form postreaction complex CH3F(H2O)---I− (im3), followed by the water shift to CH3F---I−(H2O) (im4). Subsequently, complexes im3 or im4 can dissociate to give exothermic products P1 CH3F + I− + H2O, P2 CH3F + I−(H2O), or P3 CH3F(H2O) + I−, with the formation of P2 being the most energetically favored. Overall, the potential energy profile of microslovated F−(H2O) + CH3I reaction is similar to that of the nonsolvated system (Figure 2). The motion of the H2O molecule along the reaction path is driven by the Hbonding between the H2O and the fluorine or iodine atom. If the H2O molecule is removed from the potential energy minima (im1, im2, and im4) and transition states (TS1 and TS2), the resulting structures are similar to those of corresponding stationary points for the F− + CH3I system.8 In comparison with the F− + CH3I reaction, the involvement of water molecule generally increases the energies of the stationary points on the solvated F−(H2O) + CH3I PES (Figure 2). The central barrier from complex im1 to TS2 for F−(H2O) + CH3I reaction is 6.4 kcal/mol at the CCSD(T)/PP/t/MP2/ECP/d level and higher than that of 2.8 kcal/mol (CCSD(T)/ PP/t) for the nonsolvated F− + CH3I reaction. This might be one of the multiple factors responsible for the ∼2 times lower reaction rate of solvated F−(H2O) + CH3I reaction as compared to that of nonsolvated one, besides the steric effects by the water molecule that prevent reactive collision for the solvated dynamics.33 The calculated saddle point structure of TS2 shows that the water molecule remains on the side of the fluorine atom, and the interaction between the water and iodine atom is neglected. After the system crosses this dynamical bottleneck (TS2), the water molecule can easily shift on the iodine side with little or no barrier. These features for the present studies strongly support the previous prediction for microsolvated X−(H2O) + CH3Y reactions that the water molecule is transfer to Y atom in a nonsynchronous reaction path after the X− displacement of Y− for the SN2 reaction.29,32,33,35 When compared with CCSD(T)/PP/t/MP2/ECP/d calculations, DFT B97-1 and B3LYP functionals are generally expected to provide a better description of the stationary point properties on the F−(H2O) + CH3I PES and recommended as the preferred methods to perform direct dynamics simulations of this system.

Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b00726. Stationary point geometries, frequencies, and relative energies calculated by MP2 and DFT with different basis sets. Cartesian coordinates and absolute energies of the stationary points. (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*L. Yang. E-mail: [email protected]. *L. Sheng. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science 631Foundation of China (nos. 21573052, 21403047, 51536002), 632the Fundamental Research Funds for the Central Universities, 633China (AUGA5710012114, 5710012014), the SRF for ROCS, 634SEM, China, and the Open Project of Beijing National 635Laboratory for Molecular Sciences (no. 20140103). The authors wish to thank the permission from Elsevier for re-using Figure 2b.

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REFERENCES

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