Modified Gaussian-2 level investigation of the identity ion-pair SN2 reactions of lithium halide and methyl halide with inversion and retention mechanisms

Modified Gaussian-2 Level Investigation of the IdentityIon-Pair SN2 Reactions of Lithium Halide and Methyl

Halide with Inversion and Retention Mechanisms

YI REN,1 SAN-YAN CHU2

1Faculty of Chemistry, Sichuan University, P.O. Box 73, Chengdu,610064, People’s Republic of China

2Department of Chemistry, National Tsing Hua University, Hsinchu 30013, Taiwan, China

Received 27 June 2003; Accepted 5 September 2003

Abstract: Identity ion-pair SN2 reactions LiX � CH3X3 XCH3 � LiX (X � F, Cl, Br, and I) have been investigatedin the gas phase and in solution at the level of the modified Gaussian-2 theory. Two possible reaction mechanisms,inversion and retention, are discussed. The reaction barriers relative to the complexes for the inversion mechanism[�Hcent

� (inv)] are found to be much higher than the corresponding values for the gas phase anionic SN2 reactions,decreasing in the following order: F (263.6 kJ mol�1) � Cl (203.3 kJ mol�1) � Br (174.7 kJ mol�1) � I (150.7 kJmol�1). The barrier gaps between the two mechanisms [�Hcent

� (ret) � �Hcent� (inv)] increase in the order F (�62.7 kJ

mol�1) � Cl ( 4.4 kJ mol�1) � Br (24.9 kJ mol�1) � I (45.1 kJ mol�1). Thus, the retention mechanism is energeticallyfavorable for fluorine and the inversion mechanism is favored for other halogens, in contrast to the anionic SN2 reactionsat carbon where the inversion reaction channel is much more favorable for all of the halogens. The stabilization energiesfor the dipole–dipole complexes CH3X . . . LiX (�Hcomp) are found to be similar for the entire set of systems with X �F, Cl, Br, and I, ranging from 53.4 kJ mol�1 for I up to 58.9 kJ mol�1 for F. The polarizable continuum model (PCM)has been used to evaluate the direct solvent effects on the energetics of the anionic and ion-pair SN2 reactions. Theenergetic profiles are found to be still double-well shaped for most of the ion-pair SN2 reactions in the solution, but thepotential profile for reaction LiI � CH3I is predicted to be unimodal in the protic solvent. Good correlations betweencentral barriers [�Hcent

� (inv)] with the geometric looseness of the inversion transition state %C—X�, the dissociationenergies of the C—X bond (DC—X) and Li—X bond (DLi—X) are observed, respectively.

© 2004 Wiley Periodicals, Inc. J Comput Chem 25: 461–467, 2004

Key words: ion pair; SN2 reaction; modified Gaussian-2 theory; reaction mechanism; inversion and retention; solventeffects

Introduction

The bimolecular nucleophilic substitution reaction (SN2) is one ofthe most important reactions in chemistry.1,2 Many theoretical andexperimental efforts have been devoted to the gas phase anionicreaction in aliphatic systems,3 in which the incoming nucleophilicanion reacts with substrate through an anionic transition state togive a neutral substitution product and an anionic nucleofuge.However, most of SN2 reactions in the solution phase may actuallyinvolve neutral ion pairs as nucleophiles, which are the source ofthe anionic species. The ion pairs are expected to have ratherdifferent reactivity from anion species. It appears that the ion-pairreactions have received less attention. Harder and coworkers4

studied gas phase ion-pair SN2 reactions MX � CH3X (M �Li,Na; X � F, Cl) at the level of MP4/6-31�G(d)//HF/6-31�G(d)�ZPE(HF/6-31�G(d)). They proposed two different

mechanisms, inversion and retention. The calculated identity re-actions of the methyl halides with lithium and sodium halidesinvolve a preliminary encounter dipole–dipole complex instead ofa negatively charged ion–dipole complex in anionic SN2 reactions,then proceeds via a cyclic inversion or retention transition struc-ture with highly bent X—C—X bonds behaving as assemblies ofions. Streitwieser et al.5 extended the work to the higher alkyls

Correspondence to: Y. Ren; e-mail: [email protected]; S.-Y. Chu;e-mail: [email protected]

Contract/grant sponsor: the National Science Council and the Ministryof Education of Taiwan; contract/grant numer: 89-FA-04-AA

This article includes Supplementary Material available from the authorsupon request or via the Internet at http://www.interscience.wiley.com/jpages/0192-8651/suppmat.

© 2004 Wiley Periodicals, Inc.

employing different levels of theory (RHF, MP2, and B3LYP)with a 6-31�G(d) basis set and discussed some steric effects forthe ion-pair displacement reactions. More recently, Leung andStreitwieser6 reported a theoretical study on ion-pair SN2 reactionsof metal cynates and methyl halides.

To investigate the fundamental identity ion-pair SN2 reactionsat carbon systematically, we examine the following set of reac-tions:

LiX � CH3X 3 CH3X � LiX �X � F, Cl, Br and I (1)

It is well known experimentally and theoretically that theanionic SN2 reaction is very sensitive to solvent effects. In fact, thebehavior it exhibits when it is carry out in the gas phase is differentfrom that in solution. The solvent is found to change both theanionic SN2 reaction rate and the mechanism. In solution, the rateconstants decrease in some cases by 20 orders of magnitudes, andthe double-well potential is replaced by a single unimodal reactionbarrier. However, to the best of our knowledge, no theoretical dataare available for the solvent effects on the ion-pair SN2 reactionseven though there were some experimental reports. It will beinteresting to compare the differences between anionic and ion-pair SN2 reactions in different solvents.

Glukhovtsev et al.7 pointed out that SN2 reaction of CH3X withX� can, at least in principle, take place by either front- or backsideattack, leading to displacement products with inversion or reten-tion of configuration, though the barrier for the front attack issignificantly higher. Interestingly, the two reaction mechanism,inversion and retention, involved in the ion-pair SN2 reactions arecompetitive with each other. One aim of this article is to discussthe possible reaction pathway followed by different halogen andthe factors that might influence the reaction mechanism. In addi-tion, some important differences between the ion-pair and anionicSN2 reactions in the gas phase and solution will be underlined.

Computational Method

It is clear from the very large number of computations alreadycarried out on the gas phase anionic SN2 reactions that the energyprofiles are very sensitive to the level of theory employed. For thisreason, here we use a higher level of theory, specifically a modi-fication of the Gaussian-2 (G2M) theory introduced by Mebel andcoworkers,8 which is more accurate than G2 for atomization en-ergies, and has been extensively used in the study of reactionmechanisms,9–12 and hope to obtain more reliable estimation ofthe energy profile for the ion-pair SN2 reactions.

Previous study13 indicates that the diffusion function is neces-sary in structure optimization for the SN2 reaction. Therefore, allreference geometries, including reactants, complexes, and transi-tion states of the title reactions, were obtained by the hybriddensity functional B3LYP method (Becke’s three-parameter non-local exchange functional14–16 with the correlation functional ofLee, Yang, and Parr17) with the 6-311�G(d,p) basis sets instead of6-311g(d,p) in the original G2M. Vibrational frequencies wereemployed to characterize stationary points, and the unscaled zero-point energies were included in comparison of relative energies.

The electron correlation effect was taken into account by means ofcoupled cluster calculation including triple excitations nonitera-tively [CCSD(T)]. This level of theory is termed as G2M(�), inwhich the “(�)” stands for the addition of diffuse function to thebasis sets used in obtaining the reference geometries. Full detailsof the procedures can be found in refs. 7 and 9.

All calculation were performed with the Gaussian-98 pack-age.18 All electron (AE) calculations were run for the first andsecond row elements, while Hay and Wadt effective core poten-tials19 were used for the bromine- and iodine-containing species,referred as G2M(�)-ECP. Charge were calculated by the naturalpopulation analysis (NPA)20–23 at the MP2/6-311�G(3df,2p)level on B3LYP/6-311�G(d,p) geometries. The NPA charge of allspecies involved in this article are given in Supplementary mate-rial.

Cartesian coordinates of significant structures are availablefrom the authors by request.

The anionic SN2 reactions at carbon X� � CH3X have been thesubject of many theoretical treatments at a variety of theorylevels.3 To put the anion and ion-pair results on the same level oftheory, the energetics for the reactions [eq. (2)] were also calcu-lated using the G2M(�) theory.

X� � CH3X 3 CH3X � X� �X � F, Cl, Br and I (2)

The direct solvent effects on the energetics of the f SN2 reactionwill be addressed by the polarized continuum model (PCM)24 atthe level of B3LYP/6-311�G(d,p) on the reference geometries. Inthe PCM procedure, the molecule is inserted in a cavity of realisticshape formed by interlocking spheres centered on solute atoms oran atomic group, and solute–solvent interactions are reproduced bymeans of point charges disseminated on the cavity surface, whichcan obtain very accurate solvation-free energies for a large varietyof compound. For all species involved in eqs.(1) and (2), the PCMcalculations were performed with two dielectric constants of � �24.55 for C2H5OH and � � 20.70 for CH3COCH3. In the twodifferent solvents, CH3COCH3 is the dipolar aprotic solvent,which is characterized by a large dielectric constant, a sizeabledipole moment, and the inability to act as hydrogen bond donor,and C2H5OH belongs to the dipolar protic solvent and is hydrogenbond donor.

Throughout this article, all internuclear distances are in ang-stroms, and all angles are in degrees. Relative energies correspondto enthalpy changes (�H) at 0 K or 298 K in kJ mol�1.

The present work represents the first computational study ofthis fundamental ion-pair SN2 reactions [eq. (1)] at such a highlevel, and will hopefully provide reliable energy parameters, whichmay be useful for future experimental studies.

Results and Discussions

The potential energy profile for the gas phase identity reactionsbetween methyl halide and lithium halide is described by a sym-metrical double-well potential curve, which is the characteristiccurve for all of the classic SN2 reactions.2 The reaction involvesthe initial formation of a reactant dipole–dipole complex 1. This

462 Ren and Chu • Vol. 25, No. 4 • Journal of Computational Chemistry

complex must then overcome the central activation barrier to reacha symmetrical inversion transition structure 2 or retention transi-tion structure 2�. The latter then breaks down to give the productdipole–dipole complex, which subsequently dissociates into theseparate products. The key energetic quantities involved in reac-tions [eq. (1)], as depicted in Figure 1, are labeled as follows:�Hcomp are the complexation energies for the dipole–dipole com-plexes. �Hcent

� are the central activation barriers with respect tocomplexes, and �Hovr

� is the overall activation barriers relative tothe free reactants.

The key geometrical properties for both of the anionic andion-pair SN2 reactions were summarized in Figure 2.

Reactants

The predicted properties of LiX (X � F, Cl, Br, and I) arecompared with the MP2 and the experimental results25 in Table 1.It is worth noting that the bond lengths at the level of B3LYP/6-311�G(d, p) are in good agreement with the experimental data,the mean signed error (MSE) is only 0.012 Å, better than MP2results. The calculated bond lengths for Li—X (X � F, Cl, Br, andI) by MP2(fc)/6-31�G(d) are significantly longer than the exper-imental results and the MSE is 0.053 Å. The experimental har-monic vibrational frequencies and the dipole moment values arealso reproduced well by the B3LYP method.

The geometrical parameters for CH3X (X � F, Cl, Br, and I)are listed in Table 2. The theoretical C—X bond lengths heregenerally agree well with the previous results of the G2(�)theory26 and experiments.27–30 Comparing with the experimen-tal data, the MSE for the C—X bond lengths in CH3X are 0.026Å, while the largest deviation for the C—H bond lengths is0.006 Å (for CH3F). The calculated XCH angles differ fromexperimental values by up to 1.0° (X � I).

The natural population analysis (NPA) shows that the F atom inCH3F bears a considerable negative charge (�0.43e), in contrast tothe situation for the other CH3X molecules where chlorine has a�0.1e charge and bromine has almost a zero charge while iodineactually has a positive charge.

Ion–Dipole and Dipole–Dipole Complexes

G2M(�) complexation energies for X� . . . CH3X (X � F, Cl, Br,and I) are compared with the G2(�) theory and available experi-mental data in Table 3. The calculated results are in excellentagreement with the experiments31–32 and the other high-levelcalculations—W113 and G2(�).26 Interactions of CH3X with X�

release 56.2 kJ mol�1 (X � F), 43.9 kJ mol�1 (X � Cl), 40.7 kJmol�1 (X � Br), and 36.0 kJ mol�1 (X � I) at 0 K , respectively.

For the ion-pair SN2 reactions of LiX � CH3X (X � F, Cl, Br,and I), there are two possible conformers of the dipole–dipolecomplexes. The first conformer places the lithium cation in com-plexing with the halogen to form a so-called “X-philic” prereactioncomplex CH3X . . . LiX.4 In the alternative one, the halogen atomcan coordinate with carbon and three hydrogen atoms to form thecomplex LiX . . . CH3X, similar to the ion–dipole complex in theanionic SN2 reaction, which is found to be less stable than theX-philic complex. For example, at 0 K at the B3LYP/6-311G(d,p) � �ZPE level, the LiF . . . CH3F complex is 56.6 kJmol�1 higher in energy than the complex CH3F . . . LiF, while theenergy of LiCl . . . CH3Cl is found to be higher than CH3Cl . . .

LiCl by 40.3 kJ mol�1. Therefore, only X-philic complexes areconsidered here.

G2M(�) complexation energies for complexes CH3X . . . LiX(1a–1d) are very similar in magnitude, spanning a range of just 5kJ mol�1, which is smaller than the corresponding range (�20 kJmol) for ion–dipole complexes X� . . . H3CX (X � F–I).Thecomplexation energies �Hcomp(0K) decrease in the following or-der: F (58.9 kJ mol�1) � Cl (56.4 kJ mol�1) � Br (55.8 kJmol�1) � I (53.4 kJ mol�1) and show a reasonable linear rela-tionship with the halogen electronegativities using the Mullikenscale33 (R2 � 0.927, Fig. 3). The correlation is analogous to theone found in the anionic SN2 reactions.26

The effects of CH3X . . . LiX complexation are twofold: (1) itincreases the C—X bond distance in the free reactants from 1.389to 1.446 Å in 1a, 1.807 to 1.839 Å in 1b, 1.968 to 1.995 Å 1c, and2.158 to 2.177 Å in 1d; (2) it increases the effective positivecharge on the CH3 group in the complex H3CX . . . LiX from�0.43 to �0.51e (1a), �0.11 to �0.20e (1b), �0.02 to 0.12e (1c),and �0.08 to �0.01e (1d), respectively, which are favorable forthe proceeding of the subsequent nucleophile attack.

The data in Table 3 also indicate that G2M(�) complexationenergies for ion-pair SN2 reactions are generally lower than theresults of MP2 method. At the MP4/6-31�G(d)// HF/6-31�G(d)�ZPE level, the complexation energies are 67.8 kJ mol�1 for 1a,61.5 kJ mol�1 for 1b, which are higher than the present results ofG2M(�) by 9.3 and 5.1 kJ mol�1, respectively.

Transition State Structures and Central Barrier Heights

The inversion LiX/CH3X(X � F, Cl, Br, and I) transition struc-tures (2a–2d) have C2V symmetry at the G2M(�) level of theory,which is different from the anionic SN2 TS [X � CH3 � X]�� withD3h symmetry. The CS symmetry for the retention LiX/CH3X TSs(2�a–2�d) is the same as the one in the anionic SN2 reactions.

The most important geometrical feature in 2a–2d is a remark-able deformation from the linear geometry found in the anionicSN2 reaction at carbon. The bridging of the Li cation causes a large

Figure 1. Schematic potential energy surface for the gas phase iden-tity ion-pair SN2 reactions LiX � CH3X 3 CH3X � LiX(a: X � F;b: X � Cl; c: X � Br; d: X � I).

Identity Ion-Pair Reactions of Lithium Halide with Methyl Halide 463

decease of X–C–X angle from 180° to 88.8° (2a), 100.8° (2b),107.2° (2c), and 111.5° (2d), which may be responsible for themuch higher central barriers for the ion-pair reactions than thecorresponding anionic SN2 reactions. The decrease of the angle

X–C–X will increase the electrostatic repulsion between X� . . .

X� and thus destabilize the ion-pair TS relative to the anionic TS.In contrast, smaller geometry changes relative to anionic SN2 TSwith retention of the configuration are observed for the retention

Figure 2. Main geometries of the reactants (left), complexes (middle), and transition structures (right) inthe gas phase reactions X� � CH3X and LiX � CH3X (X � F, Cl, Br, and I) at the level ofB3LYP/6-311�G(d, p). The data listed from up to down correspond to the results of X � F, Cl, Br, andI, respectively. The data in parentheses are the geometrical looseness for the corresponding bonds.


LiX/CH3X TS, in which the already existing acute X–C–X anglesdecrease from 81.2° to 75.9° in 2�a, 86.4° to 82.9° in 2�b, 88.2° to85.8° in 2�c, 90.7° to 88.9° in 2�d. The geometrical similarity ofretention transition structures will lead to a smaller differencebetween the retention central barrier heights for the anionic andion-pair reactions.

Other geometrical features in both of the inversion andretention LiX/CH3X TSs are the elongation of bonds C—X and

Li—X relative to dipole– dipole complexes. In the inversionLiX/CH3X TS, the C—X bond distances increase from 1.446 to2.182 Å (2a), 1.838 to 2.590 Å (2b), 1.996 to 2.703 Å (2c)f, and2.177 to 2.867 Å (2d). As for the retention LiX/CH3X transitionstructures, the C—X bond lengths increase to 2.067 Å in 2�a,2.692 Å in 2�b, 2.890 Å in 2�c and 3.137 Å in 2�d. Meanwhile,the Li—X bonds increase from 1.617 Å to 1.768 Å (2a) or 1.690Å (2�a), 2.062 Å to 2.253 Å (2b) or 2.145 Å (2�b), 2.232 Å to

Table 1. Properties of LiX (X � F, Cl, Br and I).

Species Level r(Li—X) �/(cm�1) � (Dye) DLi—X (kJ/mol�1)

Lif G2M(�)a 1.582 900 6.354 574.4 (578.0)d

MP2(full)/6-31�G(d)b 1.588MP2(fc)/6-31�G(d) 1.609exptlc 1.564 910 6.284 577.0 (�21)e

LiCl G2M(�) 2.024 640 7.080 470.4 (473.8)MP2(full)/6-31�G(d)a 2.056MP2(fc)/6-31�G(d) 2.062exptlc 2.021 643 7.085 469.0 (�13)e

LiBr B3LYP/6-311�G(d,p)-ECP 2.191 555 7.210 408.6 (411.8)MP2(fc)/6-31�G(d)-ECP 2.238exptlc 2.170 563 7.226 418.8 (�4.2)e

LiI B3LYP/6-311�G(d,p)-ECP 2.397 496 7.338 344.4 (347.5)MP2(fc)/6-31�G(d)-ECP 2.450exptlc 2.392 498 7.428 345.2 (�4.2)e

aThe optimized bond lengths, frequencies, and dipole are calculated at the B3LYP/6-311�G(d,p) level, the bonddissociation energies are from the G2M(�) theory.bRef. 5.cRef. 25.d298 K values are given in parentheses.eAt 298 K, from ref. 42, 9-105–9-107.

Table 2. Gemoetries for CH3X and the Dissociation Energies for Bond C—X in CH3X(X � F, Cl, Br and I).

Level R(C—X) r(C—H) �X—C—H � (Dye) Dc—x (kJ mol�1)

CH3F G2M(�)a 1.396 1.092 108.6 2.085 463.1G2(�)b 1.407 1.090 108.0 463.0exptl 1.383c 1.086c 108.8c 1.858g 465.4h

CH3Cl G2M(�) 1.806 1.087 108.3 2.106 349.5G2(�) 1.780 1.089 108.9 347.3exptl 1.785d 1.090d 108.1d 1.892g 342.0h

CH3Br G2M(�)-ECP 1.969 1.086 107.7 2.026 288.6G2(�)-ECP 1.954 1.088 108.0 285.9exptl 1.934e 1.082e 107.7e 1.822g 289.9h

CH3I G2M(�)-ECP 2.159 1.085 107.6 1.793 236.4G2(�)-ECP 2.140 1.088 108.0 237.0exptl 2.132f 1.085f 108.6f 1.620g 231.2h

aAt the B3LYP/6-311�G(d,p) level.bAt the MP2(fc)/6-31�G(d), from ref. 26.cRef. 27.dRef. 28.eRef. 29.fRef. 30.gRef. 42, 9-18–9-21.hRef. 43, at 0 K.


2.448 Å (2c) or 2.315 Å (2�c) and 2.440 to 2.666 Å (2d) or2.523 Å (2�d), respectively.

The looseness of the inversion and retention TS may be quan-tified by the looseness parameters (%C—X� and %Li—X�) in asimilar way to that proposed by Shaik et al.2

%C—X� � 100�rC—X� � rC—X

comp /rC—Xcomp (3)

%Li—X� � 100�rLi—X� � rLi—X

comp /rLi—Xcomp (4)

where rC—X� , rLi—X

� and rC—Xcomp , rLi—X

comp are the C—X, Li—X bondlengths in the transition structure 2 and the dipole–dipole complex1, respectively.

The %C—X� values for inversion mechanism lie within in alarger range (varying from 31.7 for 2d to 50.9 for 2a) thancorresponding values for retention mechanism (varying from 43.0for 2�a to 46.5 for 2�b). The %Li—X� values in both of the TSvary in a small range, about 9.5 for inversion TSs and 3.9 for theretention TSs. All of the looseness index are presented in Figure 2.

The calculated central barrier heights for the reactions X� �CH3X with backside or frontside attack at the present level of theG2M(�) theory are also close to the available experimental da-ta34–37 or other high levels of theory13,26 (see Table 3).

For the identity ion-pair reactions XLi � CH3X 3 CH3X �LiX (X � F, Cl, Br, and I), the inversion central barriers at 0 Kspan a larger range of about 112 kJ mol�1, decreasing in the orderF (263.6 kJ mol�1) � Cl (203.3 kJ mol�1) � Br (174.7 kJmol�1) � I (150.7 kJ mol�1) with an increase of the X–C–X angleand decrease of the looseness index %C—X� from X � F to X �I. This large barrier range is significantly greater than values in thecorresponding anionic SN2 reactions (varying from 41.6 kJ mol�1

for X � I to 56.5 kJ mol�1 for X � Cl) where the angle X–C–X

Table 3. Energeticsa (kJ mol�1) of Identity SN2 Reactions X� � CH3X 3 CH3X � X� in the Gas Phase.

X Method �Hcomp

�Hcent� �Hovr

�

inv ret inv ret

F G2M(�) �56.2 (�57.0) 50.1 (47.7) 242.3 �6.2 (�9.2) 186.0G2(�)b �56.5 (�57.1) 48.5 (46.1) 241.0 �8.0 (�11.0) 184.5W1c �57.2 55.6 �1.6

Cl G2M(�) �43.9 (�43.7) 56.5 (54.5) 229.8 12.7 (10.9) 185.9G2(�) �44.0 (�43.7) 55.5 (53.5) 237.8 11.5 (9.8) 193.8W1 �44.1 56.9 12.8Exptl �43.5d 57.2f 11.9h

Br G2M(�)-ECP �40.7 (�40.2) 47.9 (46.0) 223.9 7.2 (5.8) 183.3G2(�)-ECP �41.5 (�40.5) 46.9 (45.0) 220.0 5.8 178.9W1-core �42.0 45.1 4.3exptl �46.9d 48.9g 7.2i

I G2M(�)-ECP �36.0 (�35.4) 41.6 (39.8) 208.5 5.6 (4.4) 172.2G2(�)-ECP �36.0 (�35.3) 42.5 (40.8) 207.4 6.5 (5.5) 171.4exptl �37.7 � 0.8e

aCalculated energetics at 0 K are listed, with 298 K values given in parentheses, in which the enthalpies of reactants areassumed to be 0.0 kJ/mol.bRef. 26.cRef. 13.dRef. 31.eRef. 37.fRef. 34.gRef. 36.hRef. 32.iRef. 35.

Figure 3. Plot of gas phase G2M(�) complexation energies[�Hcomp(0K)] of the dipole–dipole complexes 1 vs. Mulliken electro-negativity (in Pauling units, taken from ref. 33) of the halogen atom.�Hcomp values are listed in Table 4.


is 180° and the geometrical looseness for the transition state varyin a small range (from 23.2 for X � I up to 28.0 for X � Cl).26 Thecentral barriers of retention TS [�Hcent

� (ret)] are found to besurprisingly similar for the entire system with X � F, Cl, Br, I,ranging from 195.8 kJ mol for I up to 207.7 kJ mol for Cl.Interestingly, the sequence (Cl � F � Br � I) does not followgroup ordering; such disordering is also observed in the anionicSN2 reactions. The smaller barrier range is accord with the similargeometric looseness of the C—X bond in the retention transitionstructures.

Calculated central barriers (�Hcent� ) for the LiX � CH3X reac-

tions at the G2M(�) theory are slightly different from the previousresults by Harder et al.4 At the MP4/6-31�G(d)//HF/6-31�G(d)�ZPE level, �Hcent

� values are 261.1 kJ mol�1 for 2a and191.6 kJ mol�1 for 2�a, respectively, which are a little bit smallerthan ours. For the LiCl � CH3Cl reaction, Harder et al. obtainedthe same barriers (222.6 kJ mol�1) 4 for both of 2b and 2�b. OurG2M(�) results are different for two pathway and smaller thanHarder’s results by 17 kJ mol�1 averagely.

Overall Barrier Heights and the Factors That MightInfluence the Reaction Mechanism

Harder et al.4 pointed out the bending of the entering and leavinghalogen in the LiX/CH3X TS can be modeled as triple ion LiX2

�,interacting with a methyl cation. The ionic character may play adominant role, although there is no doubt that the covalency alsocontributes.

The overall barriers for inversion pathway [�Hovr� ( inv)] in the

reactions of LiX � CH3X (X � F–I) are all positive and muchhigher than the corresponding values in the identity anionic SN2reactions, decreasing in the order: F (204.7 kJ mol�1) � Cl (146.9kJ mol�1) � Br (119.0 kJ mol�1) � I (97.3 kJ mol�1) at 0 K, incontrast to those for the anionic SN2 reactions with a negativevalue for F and smaller positive values for other halogens (seeTable 4). For the retention channel, the overall barriers are foundto decrease in the order Cl (151.3 kJ mol�1) � Br (143.8 kJmol�1) � I (142.4kJ mol�1 ) F (142.1 kJ mol�1) at 0 K, which

are smaller than corresponding values in anionic SN2 reactionswhere the �Hovr

� values vary from 172.2 kJ mol�1 for I up to 186.0kJ mol�1 for F. All of these shows the presence of Li in the anionicSN2 reactions will lower the energy of retention TS by the tripleion LiX2

� stabilization despite the electrostatic repulsion ofX� . . . X�, but increase the inversion barrier heights by stronglydeformation of its idea linear geometry. Therefore, LiX is lessreactive than X� for the inversion reaction with CH3X. Theopposite is true for the retention reaction.

Meanwhile, NPA analysis shows that introduction of the Lication in the anionic SN2 reaction clearly affects the ionicity of theion-pair reaction. In the inversion LiX/CH3X TS, NPA chargedistributions on the CH3 group increase from �0.59 to �0.84e for2a, �0.46 to �0.68e for 2b, �0.41 to �0.59e for 2c , and �0.34to �0.49e for 2d, respectively. For the retention TS, the charge onthe CH3 group increase from �0.51 to 0.75e for 2�a , �0.58 to�0.74e for 2�b, �0.55 to 0.71e for 2�c, and �0.52 to 0.68e for2�d.

The H–C–H angle 117.0° and the high charge (�0.75e) of CH3

group in the retention LiF/CH3F transition structure 2�a indicate ahigh degree of carbocation character. Obviously, the orientation ofCH3 cation and the shorter C—F bond distance in 2�a make theinteraction between CH3

� and LiF2� more favorable, which can

explain why the overall barrier for 2�a is lower than the one in 2a.As the increase of the size of halogen from fluorine to iodine,following three factors may lead to shift from retention to inver-sion mechanism: (1) the distances between carbon and halogenatom in the retention TS become longer with the increase ofhalogen atom size and the differences of distance [rc—x(ret) �rc—x(inv)] increase in the following order: F (�0.115 Å) � Cl(0.102 Å) � Br (0.187 Å) � I (0.270 Å); (2) in the retentionLiX/CH3X TS, the charge distributions on the CH3 cation groupdecrease from �0.75e for 2�a to �0.68e for 2�d with the decreaseof electronegativity of halogen; (3) the angle X–C–X in the inver-sion TS increases from 88.8° in 2a to 111.5° in 2d. The first andsecond factor will decrease the electrostatic interactions of CH3

�

with LiX2�, and the role of the covalency seems to be gradually

Table 4. Energetics (kJ mol�1) of the Ion Pair SN2 Reactions LiX � CH3X 3 CH3X � LiXin the Gas Phase.

X Method �Hcomp

�Hcent� �Hovr

�

inv ret inv ret

F G2M(�)a �58.9 (�60.2) 263.6 (261.9) 200.9 (199.6) 204.7 (201.7) 142.1 (139.5)MP4b �67.8 261.1 191.6 193.3 123.8MP2c �77.9 283.5 205.6

Cl G2M(�) �56.4 (�56.3) 203.3 (201.6) 207.7 (207.0) 146.9 (145.3) 151.3 (150.7)MP4 �61.5 222.6 222.6 161.1 161.1MP2 �67.8 234.8 167.0

Br G2M(�) �55.8 (�55.1) 174.7 (173.1) 199.6 (199.1) 119.0 (118.0) 143.8 (144.0)I G2M(�) �53.4 (�52.4) 150.7 (148.9) 195.8 (195.6) 97.3 (96.5) 142.4 (143.3)

aCalculated enthalpies at 0 K, with 298 K values given in parentheses.bAt the level of MP4/6-31�G(d)//HF/6-31�G(d)�ZPE(HF/6-31�G(d)), from ref. 4.cAt the level of MP2(full)/6-31�G(d), from ref. 5.


dominant from 2�a to 2�d. The third factor will reduce the strainenergies in the inversion transition states. The above explanationsmay rationalize the energy gap [�Hovr

� (ret) � �Hovr� (inv)] or

[�Hcent� (ret) � �Hcent

� (inv)] increasing from about �63 kJ mol�1

for the LiF � CH3F reaction to 45 kJ mol�1 for the LiI � CH3Ireaction. In other words, the inversion mechanism is more favor-able for the halogen atom with larger size in the ion-pair SN2reactions LiX � CH3X(X � F, Cl, Br, and I).

High-level computational study of Glukhovtsev et al.38 for theidentity SN2 reactions at nitrogen X� � NH2X 3 NH2X � X�

(X � F, Cl, Br, and I) suggests that the lower overall barrierheights, the more facile for the SN2 reactions. Following this idea,we can predict the reactivity sequence for the identity ion-pair SN2reactions LiX � CH3X (X � F, Cl, Br, and I) will decrease in theorder with the increase of the overall barriers: LiI (97.3 kJmol�1) � LiBr (119.0 kJ mol�1) � LiF (142.1 kJ mol�1) � LiCl(146.9 kJ mol�1).

Solvent Effects

The anionic SN2 reaction profiles are expected to be unimodalwhether in protic solvent C2H5OH or aprotic solvent CH3COCH3.This is attributed to the more solvation energy for halide ion,which has a localized charge, than the transition state, whichcarriers very dispersed charge. The strength of solvation variesfrom one anion to another. Fluorine is the smallest halide, with themost concentrated charge, and binds strongly to the solvent viaion–dipole interaction, which leads to the largest difference be-tween the calculated overall barrier in solvent and in vacuo(��Hovr

� ). Moreover, we notice that the �Hovr� and ��Hovr

� valuesin protic solvent are usually larger than in aprotic solvent becausethe protic solvent acts as the hydrogen bond donor, decreasing withthe electronegativity of X. For example, the �Hovr

� values follow inthe order: 139.5 kJ mol�1 (X � F) � 112.4 kJ mol�1 (X � Cl) �100.1 kJ mol�1 (X � Br) � 90.9 kJ mol�1 (X � I) in C2H5OH,and 129.9 kJ mol�1 (X � F) � 103.9 kJ mol�1 (X � Cl) � 93.2kJ mol�1 (X � Br) � 81.7 kJ mol�1 (X � I) in CH3COCH3 for

the reactions X� � CH3X with the inversion mechanism, respec-tively, which imply the reactivity of halide ions in solution will beopposed to the order in the gas phase, decreasing in the series:I� � Br� � Cl� � F�.

To check the reliability of computational method, we compareour theoretical results with available experimental data. The sol-vation free energy of the Cl� ion in water is calculated to be�318.0 kJ mol�1, which is slightly less than the experimentalvalue of �313.8 kJ mol�1. 39 PCM predicts for �Hovr

� the value of115.6 kJ mol�1 for the Cl� � CH3Cl reaction in water, which isin good agreement with experiment estimated by Albery andKreevoy to be 110.9 kJ mol�1.40

The shape of potential energy profiles in solution for ion-pairSN2 reactions are not significantly changed, and most of them arestill double-well except the reaction LiI � CH3I in protic solvent.The results in Table 5 indicate that the complexation energies forLiX � CH3X in solvents are still negative for most of reactionseven though they are much lower than that calculated in gas phase,in contrast to the anionic SN2 reactions where all of the complex-ation energies are positive in solution. The lower complexationenergies originates from the dipole–dipole interactions betweenreactants, complexes, and solvents with large dielectric constantand sizable dipole moment. In Table 5, it can be seen that thecomplexation energies in solution decrease with the size of halo-gen. In the protic solvent, the energy of complex CH3I . . . LiI ishigher than the reactants, the complexation energies become pos-itive, and the potential profile will be unimodal for the LiI � CH3Ireaction in C2H5OH.

The ��Hovr� values in the ion-pair SN2 reactions are smaller

than that in the anionic reactions because the reaction speciesremain overall neutral throughout the ion-pair reaction. The sol-vation free energies for ion-pair reactions increase with the size ofhalogen. The ��Hovr

� values are found to lie within a relativelymarrow range, increasing in the following order: 48.8 kJ mol�1

(X � F) � 51.1 kJ mol�1 (X � Cl) � 52.8 kJ mol�1 (X � Br) �62.3 kJ mol�1 (X � I) in C2H5OH, 39.8 kJ mol�1 (X � F) � 42.4

Table 5. Calculated Energeticsa in Different Solvents at 298 K for the Reactions X� � CH3X 3CH3X � X� and LiX � CH3X 3 CH3X � LiX (X � F, Cl, Br and I).

X Solvent �Hcomp

�Hcent� �Hovr

�

inv ret inv Ret

F Ethanol �15.3 (31.2)b 265.8 (108.4) 214.0 250.5 (139.5) 198.7Acetone �27.3 (36.0) 268.8 (93.9) 212.5 241.5 (129.9) 185.2

Cl Ethanol �13.0 (13.6) 209.3 (98.8) 222.2 196.4 (112.4) 209.2Acetone �23.0 (9.3) 210.6 (94.6) 219.3 187.7 (103.9) 196.3

Br Ethanol �8.7 (15.9) 179.5 (84.2) 214.3 170.8 (100.1) 205.6Acetone �19.6 (9.6) 180.3 (83.7) 211.6 160.7 (93.2) 192.0

I Ethanol 3.6 (14.8) 155.3 (76.0) 210.1 158.8 (90.9) 213.7Acetone �11.8 (9.1) 155.3 (72.6) 207.9 143.5 (81.7) 196.1

aWith B3LYP/6-311�G(d,p) geometries, the solvation energy is defined as SE � ��Gsol[B3LYP/6-311�G(d,p)],�H(solvent) � �H[G2M(�)(298 k)] � SE.bThe data in parentheses are �H(solvent) values for anionic reactions.


kJ mol�1 (X � Cl) � 42.7 kJ mol�1 (X � Br) � 47.0 kJ mol�1

(X � I) in CH3COCH3 for the reactions LiX � CH3X with theinversion mechanism, respectively. The overall barriers in acetone�Hovr

� (CH3COCH3) are calculated to be 143.5 kJ mol�1 (X �I) � 160.7 kJ mol�1 (X � Br) � 185.2 kJ mol�1 (X � F) � 187.7kJ mol�1 (X � Cl), which is consistent with experimental re-sults.44

Correlations of Barrier Heights with Energetic andGeometrical Characteristics of the Transition State

There has been considerable discussion in the literature as to whatfactors might influence the barrier heights in the gas phase anionicSN2 reaction.2,26,38,41 In this context, we will briefly discuss therelationship between the central barrier with geometrical charac-teristics of the transition state for ion-pair SN2 reactions at carbon,and check whether the reactions of LiX with CH3X show a similarpattern of behavior to the anionic one. Because the ion-pair SN2 atcarbon involves the breaking of bonds C—X and Li—X, it will bealso interesting to observe the relationship between the centralbarrier and dissociation energy of bonds C—X and Li—X. Thereare two possible reaction channels for entire set of reaction systemLiX � CH3X (X � F, Cl, Br, and I), these correlations will bediscussed, respectively.

The calculation of the anionic SN2 reactions X� � CH3X (X �F, Cl, Br, and I) at the G2(�) level showed that there was areasonable correlation between the inversion central barrier(�Hcent

� ) and the looseness of the MP2 transition structure geom-etries for all halogens (R2 � 0.939).26 It was also found that theG2(�) central barriers correlate the bond dissociation energiesDC—X (X � Cl, Br, and I), but fail to X � F.

In the ion- pair SN2 reactions LiX � CH3X, good correlationsbetween the central barriers with the looseness of the SN2 transi-tion structures %C—X� (R2 � 0.998, Fig. 4), the bond dissocia-tion energies DC—X (R2 � 0.999, Fig. 5) and DLi—X (R2 � 0.990,

Fig. 6) for the entire set of system with X � F, Cl, Br, and I,respectively, are observed for the inversion mechanism.

For the retention pathway, good correlation between �Hcent�

and %C—X� exist only for X � Cl, Br, I (R2 � 1.000, Fig. 7), butbreaks down for X � F. There are also reasonably correlationsbetween �Hcent

� with DC—X (R2 � 0.972, Fig. 8) and DLi—X (R2 �0.953, Fig. 9), respectively, both of these correlations fail for X �F. These phenomena may be attributed to the shorter C—F bondand lower central barrier in the retention LiF/CH3F TS.

Figure 4. Plot of gas phase G2M(�) central barriers [�Hcent� (0K)] of

the inversion pathway for reaction 1 vs. the geometric looseness indexof inversion LiX/CH3X TS (%C—X�) [see eq. (2)]. The B3LYP/6-311�G(d, p) values of %C—X� are presented in Figure 2. �Hcent

�

values are listed in Table 4.


the inversion pathway for reaction 1 vs. the G2M(�) dissociationenergies of C—X bond in CH3X (DC—X). The G2M(�) DC—X valuesare listed in Table 2.


the inversion pathway for reaction 1 vs. the G2M(�) dissociationenergies of the Li—X bond (DLi—X). The G2M(�) DLi—X values arepresented in Table 1.


Conclusions

Application of the G2M(�) theory to the identity ion-pair ex-change reactions at saturated carbon LiX � CH3X 3 CH3X �LiX (X � F, Cl, Br, and I) leads to the following conclusions:

1. There are two possible reaction channels via the same LiX/CH3X complex and different transition structures. The energyprofile for the identity exchange reactions are described by asymmetric double-well curve, with the following pathway:

CH3X � LiX 3 CH3X · · · LiX 3 �LiX/CH3X�� 3

XLi · · · XCH3 3 LiX � CH3X

2. The inversion central barriers for ion-pair substitution at carbonfor X � F–I span a range of 113 kJ mol�1, much larger than therange of 15 kJ mol�1 for anionic substitution at carbon, con-tinuously decreasing from 263.6 kJ mol�1 for X � F to 150.7kJ mol�1 for X � I. The retention central barrier heights forreactions LiX � CH3X are scattered within a small range ofabout 12 kJ mol�1, which is close to the corresponding value(34 kJ mol�1) in anionic SN2 reactions with retention of con-figuration.

3. The energies gaps [�Hcent� (ret) � �Hcent

� (inv)] between twodifferent channels increase in the following ordering: F (�62.6kJ mol�1) � Cl (4.4 kJ/mol�1) � Br (24.8 kJ mol�1) � I (45.1kJ mol�1). These results indicates the retention mechanism isfavorable for the LiF � CH3F reaction and can compete withthe inversion mechanism for the LiCl � CH3Cl reaction. Theinversion mechanism is favorable for the LiX � CH3X (X � Brand I) reactions. The reactivity for the identity ion-pair nucleo-philic substitution reactions LiX � CH3X will fall in thefollowing order based on the magnitude of the overall barriers:I � Br � F � Cl.

4. Complexation energies for dipole–dipole complexes CH3X � � �LiX do not show a stronger variation with halogen, and arecalculated to be 58.9 kJ mol�1 (X � F), 56.4 kJ mol�1 (X �Cl), 55.8 kJ mol�1 (X � Br), and 53.4 kJ mol�1 (X � I), whichare found to correlate with halogen electronegativity.

5. There are good correlations between G2M(�) inversion centralbarriers for ion-pair substitution at carbon with the geometriclooseness of the transition state (%C—X�), bond dissociationenergies DC—X and DLi—X for all of the halogen, respectively.For the retention mechanism, these correlations break down forF.

6. In contrast to the anionic SN2 reactions, the potential energyprofiles for ion-pair reactions in solution are still double-wellshape except the LiI � CH3I reaction with the unimodalenergetic profile in protic solvent.

Figure 7. Plot of G2M(�) central barriers [�Hcent� (0K)] of the reten-

tion pathway for reaction 1 vs. the geometric looseness index ofretention LiX/CH3X TS (%C—X�) [see eq. (2)]. The B3LYP/6-311�G(d, p) values of %C—X� are presented in Figure 2.

Figure 8. Plot of G2M(�) central barriers [�Hcent� (0K)] of the reten-

tion pathway for reaction 1 vs. the G2M(�) dissociation energies ofthe C—X bond in CH3X (DC—X). The G2M(�) DC—X values arelisted in Table 2.

Figure 9. Plot of the gas phase G2M(�) central barriers [�Hcent� (0K)]

of the retention pathway for reaction 1 vs. the G2M(�) dissociationenergies of the Li—X bond (DLi—X). The G2M(�) DLi—X values arepresented in Table 1.


Acknowledgments

We are very thankful to the National Center for High-PerformanceComputing of Taiwan for generous amounts of computing time.We express our gratitude to the referee of their valuable comments.

Supplementary Material

NPA charge of species involved in the anionic SN2 reactions andion-pair SN2 reactions is available via the Internet http://journals.wiley.com/jcc.

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Documents

Modified Gaussian-2 level investigation of the identity ion-pair SN2 reactions of lithium halide and methyl halide with inversion and retention mechanisms