J. Phys. Chem. 1994, 98, 13532-13540
13532
The sN2 Identity Exchange Reaction FPredictions
+ CH3F - FCH3 + F-:
Definitive ab Znitio
Brian D. Wladkowski*$? Center for Advanced Research in Biotechnology, National Institute of Standards and Technology, 9600 Gudelsky Drive, Rockville, Maryland 20850 Wesley D. Allen and John I. Brauman Department of Chemistry, Stanford University, Stanford, Califomia 94305-5080 Received: May 30, 1994; In Final Form: September 12, 1994@
-
Critical features of the potential energy surface for the sN2 identity exchange reaction F- 4-CH3F FCH3 F- have been examined using high-quality a b initio quantum chemical techniques. Geometric structures, vibrational frequencies, and relative energies for the separated reactants, ion-molecule complex, and sN2 transition state have been determined at various levels of theory by employing Gaussian basis sets ranging in and accounting for electron correlation by means of both quality from TZ(+)(d,p) to [ 13~8p6d4f,8~6p4d](+) coupled-cluster techniques [CCSD and CCSD(T)] and Mgller-Plesset perturbation methods [MP2-MP4(SDTQ)]. The final predictions for the vibrationally adiabatic complexation energy and intrinsic activation barrier are hE" (F- CH3F [F-. CHsF]) = -13.6 f 0.5 kcal mol-' and AE* ([F-. CH3F] [FCH3F]-t) = 12.8 f 1.5 kcal mol-', respectively, placing the net sN2 barrier 0.8 kcal mol-' below separated reactants. Remarkably, this intrinsic activation barrier for fluoride exchange thus appears to lie within 1 kcal mol-' of that for the chloride analog reaction, at variance with the view that F- is intrinsically less reactive than C1in sN2 displacement reactions. To facilitate comparisons among halide identity exchange rates, the bimolecular rate coefficient (kobs) for the title reaction has been estimated by employing statistical microcanonical variational RRKM theory with the predicted spectroscopic and thermodynamic data. Within this model kobs is 1.5 x lo-" cm3 s-' at 300 K and displays a negligible temperature dependence over a wide range.
+
+
-
-
Introduction Bimolecular nucleophilic substitution (SN2) reactions at tetrahedral carbon centers represent one of the most basic of chemical transformations. Over the past 20 years research efforts have focused on simple sN2 reactions in the gas phase in order to explore intrinsic chemical behavior and more clearly expose solvent effects in the corresponding condensed-phase systems. Of current interest are energy exchange mechanisms, statistical versus nonstatistical reaction dynamics, orientational effects during association, and fundamental aspects of rateequilibrium and structure-reactivity relationships. Traditional kinetic and equilibrium experiments complemented by highlevel ab initio quantum mechanical results have been successful in elucidating key features of the potential energy surfaces and intricate reaction dynamics for a few model systems.lT4 The structure-reactivity relationships underlying intrinsic nucleophilicity, however, remain a particularly compelling problem. For the general thermoneutral sN2 system given by eq 1, X-
+ CH,X - XCH, + X-
(1)
the gas-phase activation barrier is a measure of the intrinsic reactivity of a nucleophile X- toward a methyl center, in the absence of both solvation effects and a thermodynamic driving force. As such, this quantity is a fundamental property of the nucleophile and can be used to characterize the reactivity of anions in a more general sense. Remarkably, intrinsic activation barriers have been detennined quantitatively for very few
@
National Research Council Postdoctoral Fellow. Abstract published in Advance ACS Abstracts, November 1, 1994.
nucleophiles, either by e ~ p e r i m e n t a l ~or - ~ theoretical techniques .4,7-10 The halide series, where X- E (F-, C1-, Br-, I-) in eq 1, represents a paradigm of comparative reactivity. It has been demonstrated that the reactivity of alkyl halides in solution follows the order RI > RBr > RC1 >> RF."J2 Specifically, alkyl fluorides are known to be highly inert toward nucleophilic displacement for all but the strongest of nucleophiles. Many attribute this nonreactivity to unfavorable thermodynamics; the large C-F bond energy [Do(CH3-F) = 108, as compared to D"(CH3-Cl) = 83.5, D"(CH3-Br) = 70, and D"(CH3-I) = 56 kcal mol-'] l2 renders the displacement reactions involving alkyl fluorides either endothermic or only slightly exothennic for most anionic nucleophiles.11~12 Others have argued that the slow rates of reaction involving alkyl fluorides are, at least in part, a consequence of differential solvation effects. Most evidence to date, however, suggests that solvation effects do not dominate and the observed reactivity ordering also holds in the gas phase, being a reflection of the relative intrinsic reactivity of the ions, as manifested in the activation barrier of eq 1. A central implication of these observations is that for X = F the intrinsic activation barrier of the sN2 reaction is much higher than for other halides, i.e., F- acting as a nucleophile is fundamentally distinct. In order to determine if in fact F- is intrinsically less reactive than other halides, the activation barrier of the corresponding gas-phase identity exchange reaction, eq 2, must be determined quantitatively. Unlike chlorine and
F-
+ CH,F
-
FCH,
+ F-
(2)
bromine, fluorine exists in only one stable and naturally abundant isotopic form. Consequently, the reactant and product
0022-3654l942098- 13532$04.50/0 0 1994 American Chemical Society
The sN2 Identity Exchange Reaction ions for eq 2 cannot be readily distinguished from one another, and neither the rate of reaction nor the activation energy can be measured directly using available experimental techniques. Recent work by Matsson et ~ 1 . 'suggests ~ that this difficulty may eventually be overcome using a short-lived radioactive isotope of fluorine (18F), as demonstrated by their measurement of the fluorine kinetic isotope effect for the sN2 reaction of 2,4dinitrofluorobenzene with piperidine, the first determination of its kind. Although at present the activation energy for eq 2 cannot be obtained directly from experiment, it can be inferred through the use of rate-equilibrium relationships such as Marcus theory, or it can be determined via direct computation using either semiempirical models or rigorous ab initio quantum mechanics. The first estimates of intrinsic activation barriers for gas-phase sN2 reactions based on Marcus theory formalisms were presented by Pellerite and Brauman14 in 1983 and led to a general scale of intrinsic nucleophilicity toward methyl centers. With the use of Marcus theory and the associated additivity postulate, activation barriers for identity exchange reactions with immeasurable rates were ascertained indirectly from kinetic and thermodynamic data for related cross reactions. In this original work the activation barrier for eq 2 was estimated to be 26.2 kcal mol-', and the corresponding reaction rate was predicted to be immeasurably slow at room temperature. Most importantly, the fluoride exchange barrier was predicted to be much higher than that for other halides (Cl- % 12 kcal mol-'; Br- % 10 kcal mol-'), consistent with the view that alkyl fluorides are intrinsically inert to nucleophilic attack. Using newly acquired kinetic and thennodynamic data, Bierbaum and co-workers6 later questioned the validity of the initial prediction for the activation barrier of eq 2. Kinetic results for related sN2 cross reactions were found to be internally inconsistent with those used in the earlier analysis. Although a quantitative estimate was never made, Bierbaum and coworkers argued that the activation barrier must be much lower than 26 kcal mol-' and more in line with the other halide identity exchange barriers. More recently, Wladkowski and Braumanl5 provided experimental c o n f i a t i o n of the general applicability of Marcus theory to alkyl group transfer reactions like eq 1 but raised the possibility that certain chemical systems may be inappropriate for such an analysis due to constraints inherent in the model and in the accuracy of experimental measurements. Reactions involving alkyl fluorides were demonstrated to be particularly problematic. Over the years various aspects of the potential energy surface for eq 2 have been the subject of semiempirical and ab initio computational s t ~ d i e s . ~ - ~ Nevertheless, J~-~~ eq 2 has not received nearly as much attention from the theoretical community as its chloride analog, in part due to the lack of direct experimental data for the fluoride exchange rate. Listed in Table 1 is a summary of previous ab initio energetic results obtained at varying levels of theory. The qualitative potential energy surface and relevant energetic parameters are depicted in Figure 1. Dedieu and Veillard17J8were the first to report predictions for the energy differences hE" and AI?, viz., -13.2 and +5.9 kcal mol-', respectively, at the restricted Hartree-Fock (RHF) level using basis sets of double-C plus polarization (DZP) quality. These authors also mentioned that limited configuration interaction (CI) appears to have little influence on the thermochemistry. Keil and Ahlrichszl were the first to report explicit energetic predictions on eq 2 incorporating the effects of electron correlation, obtaining results for of +4.21 and +8.85 kcal mol-', in order, at the RHF and CEPA levels of theory using an extended basis set of DZP valence quality. Of particular
J. Phys. Chem., Vol. 98, No. 51, 1994 13533
TABLE 1: Previous ab initio estimates for the Energetics (kcal mol-') of the sN2 Identity Exchange Reaction F- f CHlF FCHq f Fleveloftheory hE" AI? AE* reference
-
Dedieu and Veillard ref 17 ref 18 ref 19 Duke and Bader DZP RHF//DZ RHF6 +7.2 ref 20 Keil and Ahlrichs DZP(+) RHF +4.21 ref 21 DZP(+) CEPA +8.85 ref 21 Schlegel and co-workers 4-31G RHF -9.1 -2.6c 11.7 refs9a,b Urban, Cernusik and Kello [4s2pld/2s] RHFd +5.7 refs 22-24 [4s2p1d2s] MP4(SDTQ) f3.3 Vetter and Ziilicke ref 8 [3s2pld,2slp](+) RHF' -12.6 +7.4 20.0 [3~2pld,2slp](+)CISDC -13.3 f 3 . 8 17.1 Shi and Boyd 6-31++G** RHF -12.8 +5.7 18.5 ref7 6-31++G** MP2 -13.9 -1.0 12.9 Wolfe and Kim 6-31+G* MP2f -13.9 -1.4 12.5 ref25 6-31+G* MP4 -14.2 -4.1 10.1 [5s3pld,3slp] RJ3F' [5s3pld,3slp] RHF TZP CISD
+7.9 -13.2 +5.9 +5.9
Reference geometry obtained with an even smaller basis set, ref 16. * D Z P is only broadly descriptive of the basis sets used, since incomplete sets of polarization functions were employed, and the reference geometries were obtained with a simple sp basis. Includes correction for basis set superposition error (BSSE). Reference 9b also focused on other reaction pathways besides backside inversion. Basis set also includes a partial set of diffuse functions. Reference geometry and zero-point vibrational energy (ZPVE) correction taken from refs 21 and 22, respectively. e Based on partial geometry optimization at the RHF level. !Based on 6-31+G* RHF reference geometries. Reoptimization of the structures at the 6-31 +G* MP2 level alters these results by a few tenths of a kilocalorie/mole.
-
['F - 0 CHzF]
I'FCH~ F - 1
kl
-
k -1
k -2
k2
Figure 1. The fluoride thermoneutral S Nidentity ~ exchange reaction, including relevant thermodynamic parameters and reaction steps.
note were the peculiar indications that electron correlation increases the activation barrier. Notwithstanding the several ensuing theoretical investigation^^-^^^^-*^ aimed at resolving sundry energetic and dynamical questions, the recent work of Vetter and Ziilicke,8 Shi and Boyd,' and Wolfe and Kimz5 highlights the fact that a definitive determination of the most salient energetic features of the surface is by no means at hand, as the best A@ predictions from these studies span a range of 8 kcal mol-'. In summary, while computational techniques do not suffer from the same limitations inherent in the experimental measurements, previous theoretical results for eq 2 offer only limited assistance in resolving the issue of relative fluoride intrinsic reactivity. The ordering of intrinsic nucleophilicity for the halide series is brought into question further by the semiempirical valence bond configuration mixing (VBCM) studies of Shaik and
13534 J. Phys. Chem., Vol. 98, No. 51, 1994 Extensively developed over the past decade, the VBCM model has been applied with success to a number of different reactions in solution and in the gas phase, including identity exchange sN2 reactions. In the case of the halide series, the intrinsic barriers, AE*, predicted by the VBCM model are F-, 19.5; C1-, 14.3; Br-, 10.8; and I-, 6.3 kcal mol-'. These findings show a smooth monotonic trend in the halide series and support initial estimates of a high intrinsic activation barrier for fluoride exchange. However, Sini et al.33have recently completed an extensive and general appraisal of the VBCM model by means of quantitative multistructure valence-bond computations on eq 2 with a basis set involving pseudopotentials for the core electrons, a double-(; plus polarization valence space, and diffuse orbitals on fluorine. This method gives an intrinsic barrier (AE*) of only 11.3 kcal mo1-I and a net barrier of AEd = -5.3 kcal mol-', which places the sN2 transition state significantly below the reactants and in the very least vitiates the qualitative VBCM barrier trends. The root causes of the low central barrier for eq 2 in the quantitative valence bond computations are the unusually low energy of the F-CH3+F- triple-ion structure and a resonance energy between the intersecting Heitler-London covalent configurations which is almost twice that normally assumed. Nevertheless, the rigorous valence bond results do confirm many of the basic features of the more qualitative VCBM model. In the current investigation, a concerted effort is made to finally resolve the issue of intrinsic F- reactivity through a quantitative determination of both the complexation energy and activation barrier for eq 2 to the level of 1 kcal mol-'. An estimate of the corresponding bimolecular reaction rate using the microcanonical variational statistical reaction rate theory of Rice-Ramsperger-Kassel-Marcus (RRKM) is also given. Theoretical Methods The atomic-orbital basis sets employed in this study are denoted as TZ(+)( d,p), QZ(+)( 2d,2p), QZ( +)(2dl f,2p 1d), PZ(+)(3d2f,3p2d), and [ 13~8p6d4f,8~6p4d](+) and are comprised of 90, 123, 156, 210, and 438 contracted Gaussian functions, respectively, for the CH3F2- system. In the first four designations of the form A(x,y),A is broadly descriptive of the sp basis [TZ, QZ, PZ = triple-, quadruple-, penta-C], and x and y specify the number and types of polarization manifolds appended to the (C, F) and H atoms, respectively. In the notation for the last basis set, the number of shells of each orbital type is explicitly listed for the (C, F) and H atoms, in order. The suffix (+) in all cases signifies the addition of single sets of diffuse s and p functions to the heavy-atom centers and a diffuse s orbital to the hydrogen atoms. In the TZ and QZ cases, the heavy-atom sp sets are Huzinaga-D~nning~~,~~ (lOs6p/5s3p) and (lOs6p/5s4p) contractions, respectively, whereas for hydrogen an analogous (5s/3s) basis is utilized in each instance.35 In the PZ basis, the primitives of Partridge36 were used to generate an sp set consisting of (13s8p/6s5p) and (6s/4s) contractions for the (C, F) and hydrogen atoms, respectively. The sp space of the [ 1 3 ~ 8 ~ 6 d 4 f , 8 ~ 6 ~ 4 dbasis ] ( + ) is comprised of the uncontracted primitives of van D ~ i j n e v e l d t . ~For ~ the diffuse orbitals constituting the (+) augmentations, the following exponents were employed, as derived by even-tempered extension of the respective valence sp sets: TZ and QZ, a,(C) = 0.045 61, a,(C) = 0.033 44, a,(F) = 0.1087, ap(F) = 0.069 04, and a,(H) = 0.070 94; PZ, as(C) = 0.041 979, ap(C) = 0.030 523, as(F) = 0.095 994, ap(F) = 0.059 153, and a,(H) = 0.082 217; [13~8p6d4f&6p4d], a,(C) = 0.039 90, ap(C)= 0.027 665, a,(F) = 0.093 077, ap(F)= 0.059 326, and a,(H) = 0.029 254.
Wladkowski et al. To provide more accurate energetic predictions, the correlation-optimized exponents given by Dunning38are utilized in the polarization manifolds of the TZ, QZ, and PZ basis sets. In the [ 13~8p6d4f,8~6p4d](+) set, the polarization exponents are selected as members of geometric series with ratios of 0.4 which fully span the regions critical to the recovery of valence-shell correlation energy. The first exponents in these series are &(C) = 7.12, ar(C) = 3.42, Q(F) = 16.01, ar(F) = 7.68, ap(H) = 9.88, and %(H) = 4.0. In actuality, the [13s8p6d4f,8s6p4d](+) basis consists of the uncontracted primitives within the atomic-natural-orbital(ANO) basis sets of Almlof and Taylor39 less the g and f manifolds for the (C, F) and H atoms, respectively. In all basis sets the d and f manifolds involve only real combinations of the I = 2 and 3 spherical harmonics. Reference electronic wave functions were determined in this investigation by the single-configuration, self-consistent-field, restricted Hartree-Fock method (RHF).40-42 Various formalisms were invoked to account for dynamical electron correlation, including Moller-Plesset perturbation theorf3-& through fourth order [MP2, MP3, and MP4(SDTQ)] and coupled-cluster theo$7-54 incorporating various degrees of excitation [CCSD and CCSD(T)]. The %diagnosti& computed as the Euclidean norms of the tl amplitudes of the QZ(+)(2dlf,2pld) CCSD wave functions were found to be 0.0105, 0.0156, and 0.0198, respectively, for CH3F, [F-.CH3F], and the sN2 transition state. Because these values do not exceed 0.02,55the multireference character of the electronic wave functions is not substantial enough to be of particular concern in the higher-order correlation procedures here. The 1s core orbitals of the C and F atoms were excluded from the active space in the correlation treatments as well as the high-lying, core-localized virtual orbitals appearing above selected energy thresholds. The total number of such frozen virtual orbitals in the TZ(+)(d,p), QZ(+)(2d,2p), QZ(+)(2d lf,2p Id), PZ(+)(3p2f,2p1d), and [ 13s8~6d4f,8s6p4d] (+) correlation treatments were 3, 3, 3, 3, and 104, respectively. The electronic structure computations were performed using the program packages PSI56 and GAUSSIAN92.57 for the RHF, MP2, and Analytic gradient CCSD methods were used to perform complete geometry optimizations in the internal coordinate space. Quadratic force fields were evaluated via analytic second-derivative techniques for RHF58.61 and MP262,63wave functions. In the harmonic vibrational analyses reported here, normal modes were quantitatively assigned in internal coordinates by the total energy distribution (TED) method.@ Improved force fields at salient points on the CH3F2- surface were obtained according to the scaled quantum mechanical (SQM) force field p r o ~ e d u r e , 6 ~ - ~ ~ as calibrated on empirical data for the fundamental frequencies of CH3F. A recent paper by Allen et aL71 succinctly presents the formalism of the SQM procedure and reviews previous applications of this technique. Total electronic energies for all computations along with the final SQM quadratic force fields for the three relevant structures can be found in.the supplementary material.
Features of the Potential Energy Surface The geometric structures at various levels of theory for the separated reactants, ion-molecule complex, and sN2 transition state along the reaction coordinate of eq 2 are presented in Table 2. The spectroscopically determined re structure72for methyl fluoride is also given for comparison, along with final geometric predictions for the complex and transition state based on the CCSD data and corresponding error estimates. The C3"- and D3h-symmetry structures of the complex and transition state are depicted in Figures 2 and 3.
J. Phys. Chem., Vol. 98, No. 51, 1994 13535
The sN2 Identity Exchange Reaction
TABLE 2: Geometric Structures of Stationary Points along the sN2 Reaction Path for Flevel of theorv
a(H-C-F)
1.3710 1.0829 108.67
1.3644 1.0802 108.79
C-F) r(C-F-) r(C-H) a(H-C-F)
1.4129 2.6964 1.0761 108.53
1.4049 2.6880 1.0735 108.70
r(C-F) r(C-H)
Separated Reactant 1.3614 1.3601 1.0804 1.0805 108.90 108.93 Association Complex (C3J 1.4013 1.4000 2.6958 2.6906 1.0736 1.0737 108.83 108.85 sN2 Transition State (D3h) 1.8417 1.8407 1.0584 1.0583
+CHP
1.3912 1.0853 108.65
1.3864 1.0876 108.74
1.382 1.090 108.4
1.4369 2.6034 1.0788 108.48
1.4301 2.5982 1.0806 108.62
(1.426) (2.58) (1.083) (108.3)
1.8217 1.8264 (1.82) 1.8459 1.8441 4C-W 1.0681 1.0689 (1.071) 1.0585 r(C-H) 1.0619 Distances in 8, and angles in deg. Reference 72 for CH3F. Entries in parentheses are estimated final values based on the CCSD predictions. shown in Table 2, the final estimates for the [F-*C H A complex are re(C-F-) = 2.58 A, re(C-F) = 1.426 A, re(C-H) = 1.083 A, and &(H-C-F) = 108.3", the last three parameters being derived by appending to the QZ(+)(2d,2p) CCSD results the analogous shifts vis-b-vis experiment found for free CH3F. As part of a recent computational spectroscopy study on anionic Figure 2. Structure of the intermediate ion-molecule complex complexes, Botschwina and Seeger30 recently determined for [F-CHsFI. [F-. CH3F] the optimum values re(C-F-) = 2.55 A, re(C-F) = 1.428 A, re(C-H) = 1.083 A, and &(H-C-F) = 109" at the CEPA-1 level with a modest basis set, in good agreement with the structure proposed here. I F__...______.__...__.__ ...................... F In the sN2 transition state, the C-F bonds are extended by almost 0.4 compared to the equilibrium distance in CH3F. It is notable that electron correlation contracts the C-F distances by %0.02 A, as found for r(C-F-) in the antecedent complex, Figure 3. Structure of the sN2 transition state [FCH3q-1 but to a diminished extent. The C-H distances are substantially shortened in traversing the transition state, a phenomenon also The variations among the predicted geometric parameters of observed for [CNCHzCl$ and other [XCH3X]- system^.^%^*^^ CH3F are in complete accord with expectation?l For example, The same considerations used in the [F-• C H P ] case lead to with the QZ(+)(2d,2p) basis set, the C-F bond length is re(C-F) = 1.82 8, and r,(C-H) = 1.071 8, as final estimates underestimated by m0.02 8, with the RHF method but overesfor the structure of the [FCH3F]-+ saddle point, giving a small timated by mO.01 8, at the MP2 level. The QZ(+)(2d,2p) CCSD looseness parameter Lt = 55.3% indicative of a rather tight structure displays the most favorable balance of the principal transition ~ t a t e . * By ~ , ~comparison, ~ in two of the most recent factors governing the bond distances, i.e., contraction upon basis theoretical studies on the [FCH3FI-+ saddle point, Vetter and set enlargement and elongation due to electron ~ o r r e l a t i o n . ~ ~ Zulicke8 found values of 1.851 and 1.065 8, at the DZP RHF Specifically, the errors in the QZ(+)(2d,2p) CCSD values for level for the C-F and C-H optimum distances, respectively, r(C-F) and r(C-H) are only f0.0044 and -0.0024 A, while Shi and Boyd7 obtained 1.836 and 1.074 8, at the respectively, supporting the use of optimum structures at this 6-31++G** MP2 level for these same structural parameters. level of theory as reference geometries for subsequent energetic The vibrational analysis of the three stationary points along predictions. The H-C-F angle in methyl fluoride is reproduced the sN2 reaction path is summarized in Table 3. Included in to 0.5" or better by all levels of theory employed here. the table are the theoretical harmonic frequencies obtained at Upon formation of the sN2 backside ion-molecule complex, the QZ(+)(2d,2p) MP2 level, scaled (SQM) fundamental the C-F distance in the CH3F framework increases by about frequencies derived from the QZ(+)(2d,2p) MP2 force fields, 0.04 A, and concomitantly the C-H bond lengths and the and assignments for each normal mode based on the TEDs. The H-C-F angles contract slightly, by ca. 0.007 A and 0.1", experimental fundamental frequencies of methyl fluoride77 respectively. Because the CH3F group essentially remains intact employed in the SQM analysis are also given. The vibrational in the [F-CH3fl adduct, the trends among the various theoretical spectrum of CH3F has been the subject of other recent and more intrafragment parameters closely mimic those observed for the extensive theoretical s t ~ d i e s . ~Of ~ -particular ~ ~ ~ ~ note, ~ ~ ~ ~ reactant species. As documented for numerous other ionSchneider and ThielZ8obtained harmonic and scaled force fields molecule complexes, including [Cl-. CH3ClIP [ C P CNCHzClIP of CH3F at the DZP RHF level as part of a larger study on [FHC1]-,74 [F-.HzO]?~,~~ and CH30HF-,76 the interfragment H3MX molecules, whereas Dunn et ~ 1 computed . ~ variational ~ separation in E-*C H a is highly sensitive to the level of theory. vibrational energy levels of CH3F up to 6000 cm-' using an ab The QZ(+)(2d,2p) correlation treatments decrease r(C-F-) by initio partial quartic force field. The goal of the present SQM almost 0.1 A, an occurrence primarily attributable to dispersion analysis is not to augment these investigations but to obtain effects. This interfragment contraction is comparable to that accurate fundamental frequencies for the ion-molecule complex observed for similar species, and continued theoretical improveand sN2 transition state of the F- CH3F system using methyl ments to address remaining basis set incompleteness and higherorder correlation errors should reduce r(C-F-) further.4~~~ fluoride as a calibration. As
"\
i
1-
+
13536 J. Phys. Chem., Vol. 98, No. 51, 1994
Wladkowski et al.
+
TABLE 3: Vibrational Analysis for the Stationary Points along the S NReaction ~ Path for F- C H P normal mode description assignment w(MP2) WQWb total energy distribution (TED) CH3F CH3 sym stretch 3095.2 2909.2 (2919.57) CH3 umbrella 1518.3 1450.7 (1459.39) C-F stretch 1067.7 1048.4(1048.61) 3195.9 CH3 asym stretch 3004.1 (2998.97) CH3 deformation 1539.0 1472.5(1467.81) CH3 tilt 1222.9 1182.4(1182.68) 25.16 23.91 ZPVE [F-.CH3F] CH3 sym stretch 3159.2 2969.4 1414.2 1350.5 CH3 umbrella C-F stretch 915.7 898.8 161.4 C-F- stretch 161.4 CH3 asym stretch 3277.6 3081.1 CH3 deformation 1513.3 1446.9 CH3 tilt 1143.2 1103.6 94.7 F--C-F bend 94.4 ZPVE 25.32 24.06 [FCH3F]-' CH3 sym stretch 3205.8 3013.7 CH3 umbrella 1265.6 1212.3 C-F sym stretch 378.1 374.5 C-F asym stretch 584.8i 578.3i 3405.5 CH3 asym stretch 3201.8 1443.1 CH3deformation 1380.3 CH3 tilt 1130.2 1112.2 F-C-F bend 345.3 339.4 ZPVE 25.01 23.83 All vibrational frequencies in cm-', zero-point vibrational energy (ZPVE) in kcal mol-'. The reference quadratic force field was determined at the QZ(+)(2d,2p) MP2 level of theory. Experimental fundamental frequencies in parentheses from ref 77.
The internal displacement coordinates used in the SQM analysis and in the TED decompositions are as follows:
S, = 3-1'2(r,
+ r2 + r3)
(3a)
s2 = 3-'/2(Y,
+ Y2 -k Y 3 )
(3b)
S3 = R
(3c)
S4 = 6-'12(2r, - r2 - r,)
(3d)
S, = 6-'12(2a, - a, - a,)
(3e)
= 6-1~2 6
(2Pl - P 2 - I331
(30
s, = 2-l12(r2 - r3)
(3g)
S, = 2-'"(a,
- a3)
(3h)
s9= 2-'12@,
- p3)
(3i)
S,, = R'
(3J)
S,, = 6-'I2(2p,' - p2/
s,, = 2-"2@;
- p3/)
- p3')
(3k)
(31) where R refers to the C-F stretch, R' the C-F- stretch, ri the C-Hi stretch, ai the H,CHk bend, @i the HICF bend, yi the HiCHjHk out-of-plane angle, and the HIC-F- bend. Distinct scale factors, z1, z2, z3, and r4, were ascribed to the C-F stretch (S3), C-H stretches (Si,S4, and S7), H-C-H bends (Sz, S5, and &), and H-C-F bends (& and S9), respectively. The leastsquares fit to the experimental fundamental frequencies of CH3F
provided the values (TI,t 2 , z3, and z4) = (0.8836, 0.9625, 0.9143, and 0.9366). Whereas the QZ(2d,2p) MP2 harmonic frequencies of CH3F are uniformly larger than the corresponding empirical fundamentals by 5-7% (Table 3), the scaling procedure yields effective anharmonic frequencies with an average absolute error of only 4.4 cm-', within 0.6% of experiment in each case. For the ion-molecule complex and sN2 transition state, the scale factors obtained for CH3F were applied as fixed parameters for Sl-S9, and the newly formed vibrational modes (Slo-Sl2) were assigned a scale factor of unity. The C-F stretch in free methyl fluoride, v3 = 1048 cm-', is downshifted to 899 cm-I in the ion-molecule complex, correlating ultimately to the symmetric stretch vg = 375 cm-' in the transition state. The FCH3F [F-*CH3F] and [F-• CH3F] [FCH3F]-+ steps concomitantly engender the following successive changes in the frequencies of the CH3F modes which are preserved along the reaction path: dvI(C-H stretch) = [+60,+451, dv4(C-H stretch) = [+77,+121], dv2(CH3 umbrella) = [-100,-1381, dvs(CH3 deformation) = [-26,-671, and dvg(CH3 tilt) = [-79,+9] cm-'. Clearly, the fluxional weakening of the C-F bond upon fluoride attack is attended by a significant tightening of the C-H bonds and a loosening of the methyl bending modes. The presence of unusually large CH stretching frequencies in sN2 transition states indeed appears to be quite common.2*4,7,8,25 It is remarkable that the effects of fluoride complexation on the vibrational spectrum of free CH3F are generally as substantial as the ensuing shifts accompanying the ascent of [F-• CH3F] to the transition state. Nevertheless, the interfragment modes in the [F-* CH3F] adduct exhibit frequencies (v4 = 161 and v8 = 95 cm-') which are characteristic of relatively weak ion-dipole complexes with predominantly electrostatic binding." By comparison, the fluoride in-plane stretching and bending frequencies (v9 = 420 and v10 = 177 cm-') of the CH30HF- complex?6 which has considerable covalent character, are larger by factors of 2.6 and
-
+
-
The sN2 Identity Exchange Reaction
+
-
J. Phys. Chem., Vol. 98, No. 51, 1994 13537
TABLE 4: Complexation Energy (AP,kcal mol-') for CH3F F[F-CHJFI" TZ(+)(d,p) QZ(+)(2d,2p) QZ(+)(2d 1f,2p 1d) PZ(+)(3d2f,2p 1d) [ 13s8p6d4f,8s6p4dI(+) -11.78 -11.64 -11.61 -11.84 " 3 F I -12.04 -0.03 -1.03 -1.34 -1.47 6[MP2] -1.01 -0.28 -0.3 1 [-0.311 [-0.311 d[MP3] -0.32 (6[MP4], S[CCSD]) (+0.27, +0.08) (+0.09, +O. 10) (+0.06, +0.11) [+0.06, +0.11] [+0.06, +O. 111 S[CCSD(T)] (-0.34, -0.15) (-0.27, -0.28) (-0.25, -0.30) [-0.25, -0.301 [-0.25, -0.301 AEe(corr) -12.46 -13.31 -13.17 [- 13.451 [- 13.731 A P = AEe[fp]+ A[ZPVE] = -13.73 0.15 = -13.58 kcal mol-' All entries in kcal mol-' and based on the QZ(+)(2d,2p) CCSD reference geometries. RHF and MP2 results obtained at their respective optimum geometries for each basis set differ by less than 0.01 kcal mol-' from the values given. The symbol 6 denotes the increment in the relative to the preceding level of theory. In evaluating these contributions, the MP3 (MP4, CCSD) CCSD(T) higherreaction energy (Me) order correlation sequences are constructed as complementary indicators. For the [13~8~6d4f,8~6p4d](+) basis set, the increments in brackets are net reaction energy, AEe(corr),is equivalent assumed values based on the QZ(2dlf,2pld)CCSD(T) predictions. The estimated [ 13~8p6d4f,8~6p4d](+) to the energy change, AEJfp], predicted at the focal-point (fp) level of theory described in the text.
+
-
-
-
TABLE 5: S N Barrier ~ (AE*, kcal mol-') for [F-oCH~F] [FCHJFI-t TZ(+)(d,p) QZ(+)(2d,2p) QZ(+)(2dlf,2pld) PZ(+)(3d2f,2pld) [13~8~6d4f,8~6p4d](+) 20.12 20.09 20.25 19.55 &[mI 19.22 -6.01 -6.58 -6.41 6[MP2] -5.15 -6.10 [+3.37] +3.37 [+3.37] 6[MP3] +3.29 +3.43 (-5.58, -1.90) (-5.59, -1.85) [-5.59, -1.851 [-5.59, -1.851 (6[MP4], S[CCSD]) (-5.40, -2.12) [+1.55, -2.191 (+1.55, -2.19) [+1.55, -2.191 6[CCSD(T)] (+1.33, -1.95) (+1.53, -2.15) AEdCOrr) 13.29 12.83 13.41 [13.00] [13.04] AE* = AEe[fp] + A[ZPVE] = 13.04 - 0.23 = 12.81kcal mol-' AEd = A F + AE* = -0.77 kcal mol-' All entries in kcal mol-'. See footnote a of Table 4. The assumed geometries are the QZ(+)(2d,2p)CCSD optimum structures given in Table 1.9, respectively. The tightness of the sN2 transition state vis&-visthe backside complex is evidenced by the lack of vi values below 300 cm-' in magnitude, including the single imaginary frequency (v4 = 5781' cm-') which identifies the D3h structure as a genuine transition state. Electronic structure predictions for the complexation energy (AEW) and activation barrier (AE*) of eq 2 are given in Tables 4 and 5, respectively. From previous computational studies of the title system and other sN2 reactions, it has become evident that extended correlation treatments with large one-particle basis sets are required to predict energetic features for these reactions to chemical accuracy. The principal technique employed here toward this end entailed the direct computation of QZ(+)(2dlf,2pld) CCSD(T) results for AEW and AE* to which QZ(+)(2dlf,2pld) MP2 [ 13~8p6d4f$s6p4d](+) MP2 shifts were appended as correlated basis set incompleteness corrections. Ample evidence has been compiled suggesting that this procedure, termed the focal point (fp) level of theory, provides an excellent approximation to the [ 13~8p6d4f,8~6p4d](+) CCSD(T) r e ~ ~ 1 t .The ~ philosophy ~ ~ ~ ~ ,behind ~ ~ the , ~ fp~ technique is that higher-order correlation increments to energetic quantities converge rapidly with respect to basis set augmentation, even though the underlying MP2 predictions may exhibit a much slower approach to their limiting values. In order to demonstrate the fp phenomenon, the AE'" and AE* data for each basis set are presented as increments in the correlation sequence RHF MP2 MP3 [MP4(SDTQ), CCSD] CCSD(T), an order consistent with the theoretical foundations of each method. In particular, the CCSD(T) approach is fully correct to fourth order and partially correct to fifth order in perturbation theory, while also including certain correlation terms to infinite 0rder.53~81~82 In Table 4 the initial RHF results for the complexation energy (AE'")cluster in a narrow range of [-11.61,-12.041 kcal mol-'. The only significant source of variations in the net AE,(corr) values is the d[MP2] term, which steadily increases across the table from -0.03 to -1.47 kcal mol-'. However, the fp
-
- - -
-
convergence of the remaining increments is far better, apparently within 0.1 kcal mol-', and the net higher-order correlation contribution to AE'" lies between -0.4 and -0.5 kcal mol-' for all basis sets. Thus, correlation effects account for about 2 kcal mol-', or 15%, of the binding energy. By comparison, the appreciably electrostatic [FHClI- adduct74and the partially covalent CH30HF- species76have large vibrationless fluoride affinities of 23.3 and 30.0 kcal mol-', respectively, but dispersion components which are not much different on a percentage basis than that present for the relatively weak [F-. CH3F] complex. The final extrapolated binding energy is AEe(fp) = -13.73 kcal mol-'. To gauge the accuracy of this result, the effects of basis set superposition error (BSSE) were quantified by computing counterpoise corrections ( E B S S E ) to the QZ(+)(2d,2p) and PZ(+)(3d2f,2pld) MP2 binding energies given by correlation treatments in which no core or virtual orbitals were frozen. The E B S S E adjustments in the QZ(+)(2d,2p) and PZ(+)(3d2f,2pld) MP2 cases were +0.74 and +OS4 kcal mol-', respectively, the corresponding RHF quantities being less than 0.03 kcal mol-', as expected. Because the immense [13sSp6d4f,8~6p4d](+) set is over twice as large as the PZ(+)(3d2f,2pld) basis, the BSSE effect on the final fp prediction is probably only 0.2-0.3 kcal mol-'. This BSSE deficiency is too small to adversely affect the final AEW value, especially since the general trend observed for 6[MP2] in Table 4 is a compensating aggrandizement of the second-order term as the one-particle basis is saturated. After including the small ZPVE correction to the binding energy, the final AEW prediction becomes Do(CH3F+F-) = 13.6 f 0.5 kcal mol-'. The data in Table 5 for the sN2 inversion barrier @E*) display the same high degree of basis set convergence found for the ion-molecule binding energy, despite the extensive electronic structure rearrangements manifested by the transition state. Both the positive AEe[RHF] and negative d[MP2] entries generally increase in magnitude by modest amounts upon basis set augmentation, leading to net second-order barriers which lie in every case within 0.4 kcal mol-' of the [13s8p6d4f,-
Wladkowski et al.
13538 J. Phys. Chem., Vol. 98, No. 51, 1994 8s6p4d](+) MP2 result (13.71 kcal mol-'). Remarkable fp convergence to the level of 0.1 kcal mol-' is observed once again in the higher-order terms, which gives rise to net CCSD(T) predictions consistently appearing 0.7 k 0.1 kcal mol-' below the MP2 results. The overall invariance of the AEe(COrr) quantities to the massive expansions of the one-particle space are indeed striking. The d[CCSD(T)] pairs indicate that the MP4 and CCSD values lie below and above the CCSD(T) predictions by ca. 1.5 and 2.0 kcal mol-', respectively. Insofar as these increments are gauges of convergence toward the full configuration interaction limit, it is clear that the inexactness of the correlation treatments is the predominant source of the remaining uncertainty in the sN2 barrier. The fp prediction for the classical barrier is AEe[fp] = 13.0 kcal mol-', to which error bars of k1.5 kcal mol-' may be cautiously assigned. With the ZPVE correction AE* becomes 12.8 kcal mol-', which places the vibrationally adiabatic SN2 barrier 0.8 kcal mol-' below the separated reactants, i.e., A@ = -0.8 kcal mol-' in Figure 1. The inescapable question prompted by these final predictions is why they should be considered in any sense definitive, especially in light of the widely scattered results from earlier investigations (see Table 1). The most direct response to this query is that the current theoretical analysis is the only one which simultaneously meets both the basis set and correlation requirements known from myriad ab initio thermochemical studies to be necessary for chemical accuracy. To wit, the largest basis set employed here contains approximately 5 times as many contracted Gaussian functions as any of those used previously for the CH3F2- system. Moreover, the CCSD(T) electron correlation method applied in this study is fully correct to fourth order and partially correct to fifth order in perturbation theory, while including certain terms to infinite order. By comparison, only the MP4 predictions in Table 1 are even correct to fourth order, and these suffer from a considerable incompleteness of the selected one-particle basis sets. Most importantly, the systematic partitioning appearing in Table 4 and 5 of the approach to the exact solution of the nonrelativistic Schrodinger equation provides direct and compelling evidence of convergence to the level of 1 kcal mol-'. It is instructive to compare the current final predictions [AE"(F-), AE*(F-), and A@(F-)] = -(13.6, 12.8, and -0.8) kcal mol-' to the analogous energetic quantities for the chloride CH3Cl. Experimental equiidentity exchange reaction, C1librium measurements by Larson and McMahonS3have led to the complexation energy AE" (Cl-) = -12.2 f 2 kcal mol-', and interpretation of the available kinetic data5 has produced estimates for the effective activation energy A@(Cl-) ranging from +1.0 to f 3 . 5 kcal mol-'. The best theoretical predictions4 for these same energetic parameters, as derived from high quality ab initio results, are D ( C l - ) = -10.6 and I1Ed(C1-) = +1.8 kcal mol-', which correspond to an intrinsic activation barrier of AE*(Cl-) = 12.4 kcal mol-'. These data indicate that even though the complexation energy, AE", and effective activation barrier, A@, for the fluoride and chloride sN2 systems differ by 2-3 kcal mol-', the intrinsic activation barriers are nearly the same. This direct comparison clearly demonstrates the remarkable energetic similarity between the fluoride and chloride sN2 identity exchange potential surfaces. Based on the available theoretical results,s and on experimental datal5 from related sN2 systems, the corresponding bromide identity exchange barrier is also likely to be of comparable height. Together, these results suggest that in the absence of solvation effects and a thermo-
+
dynamic driving force, the intrinsic nucleophilicity toward displacement at alkyl centers is remarkably constant for F-,C1-, and Br-.84
Statistical Reaction Rate Utilizing the quantitative structural, spectroscopic, and energetic results for the prototype sN2 system presented above, an estimate of the low-pressure bimolecular reaction rate for eq 2 can be made for the first time. In this investigation a microcanonical variational transition state analog of the wellknown RRKM85-88 statistical reaction rate theory (pVTSRRKM) is used. Over the past several years statistical versus nonstatistical behavior in sN2 reaction dynamics has been a topic of much Evidence from recent e ~ p e r i m e n t a l ~ ~ - ~ ~ and theoreticalg6studies suggests that the dynamics of certain sN2 reactions do exhibit nonstatistical components. As a consequence, many have argued against the use of statistical theories in estimating rates for simple sN2 reactions. Here the goal is neither to refute nor confirm the nonstatistical proposal but merely to present an accurate prediction of the overall rate for eq 2 within the constraints of the statistical model. This quantity can then be used as a basis for comparison with other systems in which similar statistical models have been used. In this way, dynamical dissimilarities between the sN2 reaction in eq 2 and its other halide counterparts which may contribute to the observed kinetic behavior can be quantified for the comparison. Details of the statistical theory as applied to gasphase sN2 reactions are presented elsewhere: and only a brief description of the relevant issues will be given here, along with pertinent data used in the statistical analysis. Figure 1 shows a one-dimensional representation of the potential energy surface, along with the component steps, for the thermoneutral gas-phase sN2 reaction of eq 2. The overall rate expression for such a system can be easily derived by using the steady-state approximation and assuming the intermediate lifetimes are long on the time scale of reaction:
In eq 4, @(T)is the reaction efficiency, which is a function of only unimolecular rate coefficients. The unimolecular rates, and hence the reaction efficiency, can be calculated using the well-known pVTS-RRKM expression,86-8s~91~g7~g8
in which (5 is the reaction path degeneracy, R denotes the reaction coordinate, c(J;R) = E - V(R) - E,(J;R), WLVTST [E,JI is the number of accessible states at the transition state (located at R = R*) for each (E,J) channel, and e[€(J;Re)]is the corresponding density of states for the intermediate ionmolecule complex (for which R = Re). The functions V(R) and E,(J;R) represent the approximate potential energy (including ZPVE) and orbital rotational energy, respectively, along the reaction coordinate. The sum and density of states for each structure along the reaction pathway are determined directly from the appropriate SQM vibrational frequencies within the harmonic approximation. For the dissociation channels of the complex, V(R) can be modeled via simple classical electrostatics based on the molecular parameters of CH3F, namely, the polarizability, dipole moment, and complexation energy (AE"), as determined theoreti~ally.~~ In the isomerization step V(R)
J. Phys. Chem., Vol. 98,No. 51, 1994 13539
The s N 2 Identity Exchange Reaction
Figure 4 also provides useful information regarding the expected temperature dependence of the reaction rate for the title reaction. The data clearly show that within the constraints of the statistical model, the overall reaction rate shows little or no temperature dependence over a range 200-600 K. The invariance of the reaction rate to temperature is characteristic of chemical systems with double-well potential surfaces and activation barriers near threshold. This effect might prove to be a useful probe for the study of energy exchange phenomena in such systems.
5x1 0'"
4x10'''
Acknowledgment. We are grateful to the National Science Foundation for support. B.D.W. would like to thank Dr. A. L. L. East for stimulating discussions and assistance with technical aspects of the various electronic structure codes.
1X
l
o+
I 200
I
250
I 300
I 350
I 400
I 450
Temperature
I
I
500
550
I 600
(K)
-
Figure 4. Plot of the bimolecular rate coefficient for the thennoneutral sN2 identity exchange reaction FCH3F FCH3 -I-F- versus temperature, as given by a statistical RRKM model.
+
becomes the vibrationally adiabatic intrinsic activation barrier, AE*. The rotational energy term E,(J;R) is obtained directly from the computed molecular structure along the reaction coordinate. Once averaged over the appropriate chemically activated energy and angular momentum distribution, the macroscopic efficiency is obtained for a given temperature. Details regarding the choice of the reaction pathway and the assumed form of the potential, as well as the conservation of angular momentum and the specifics of the state-counting algorithm are given in the aforementioned study." Shown in Figure 4 is the pVTS-RRKM statistical reaction rate for eq 2 as a function of temperature (200-600 K) resulting from the final ab initio predictions for the intrinsic activation barrier, AE* = 12.8 kcal mol-', and complexation energy, A,??" = -13.6 kcal mol-'. Within this statistical model the overall rate coefficient is predicted to be kobs = 1.5 x lo-'' cm3 s-' at 300 K. This value can be compared to the bimolecular reaction rate of the corresponding chloride exchange reaction determined using similar statistical models. In all cases the calculated rate for chloride exchange is found to be within an order of magnitude of that determined experimentally by Bierbaum and co-workers, k&s = 3.5 x cm3 s - ' . ~ Thus, if both reactions behave statistically, fluoride exchange is predicted to be more facile by nearly 3 orders of magnitude. It must be emphasized however, that the enhanced rate of fluoride identity exchange relative to chloride found statistically is primarily the result of an effective activation barrier, A@, which is approximately 2.6 kcal mol-' lower in energy. Once the difference in the ionmolecule complexation energies for the two systems is taken into account, the kinetic results are consistent with the nearly equivalent intrinsic activation barriers reported above for the two systems, and it is the intrinsic activation energies which are most relevant for comparison with solution-phase results. These data further suggest that the kinetic ordering of identity displacement at alkyl centers for the halides in aqueous solution, namley I- > Br- > C1- >> F-, obtained by Albery and Kreevoy" using Marcus theory arguments, is likely a result of differential solvation effects.
Supplementary Material Available: Table VI listing total energies at various levels of theory and Tables VII-IX listing SQM quadratic force constants for C H P , [F-.CH3Fl, and [F.CH3Fl-t, respectively (3 pages). Ordering information is given on any current masthead page. References and Notes (1) Merkel, A.; Havlas, Z.; Zahradnfk, R. J. Am. Chem. SOC.1988, 110, 8355.
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