the study of counterion effect on the reactivity of nucleophiles in some sn2 reactions in gas phase...

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Journal of Molecular Structure: THEOCHEM 809 (2007) 115–124

The study of counterion effect on the reactivity of nucleophilesin some SN2 reactions in gas phase and solvent media

Ali Ebrahimi *, Mostafa Habibi, Azime Amirmijani

Department of Chemistry, University of Sistan and Balouchestan, P.O. Box 98135-674, Zahedan, Iran

Received 30 June 2006; received in revised form 22 January 2007; accepted 22 January 2007Available online 6 February 2007

Abstract

The effect of counterion on the reactivity of ion pairs along the backside and frontside identity exchange reactionsNuc + CH3X fi XCH3 + Nuc (Nuc = X�,Li+X�,Na+X�,K+X�; X = F,Cl,Br) was investigated at 6-311+++G(d,p) level of theoryin the gas phase and solvent media. Single point QCISD(T) calculations were performed on all MP2 optimized structures in order todecrease the differences between theoretical and experimental values of energy in the gas phase. By intrinsic reaction coordinates(IRC) calculations, CH3X� � �M+X� complexes were confirmed along two paths. The complexation enthalpies DHcomp decrease withincreasing the diameter of counterion in the gas phase. The energy barriers (DH zovr and DH zcent) decrease with increasing the size of coun-terion in the backside attack whereas they increase in the frontside path. Solvent effect on the reaction profile has also been studied usingisodensity surface polarized continuum model (IPCM). The values of DHcomp in solvent media are smaller than gas phase and are neg-ative for some nucleophiles in the presence of solvents with high dielectric constants. The values of DH zovr and DH zcent are higher in solu-tion and grow by the increase in dielectric constant of solvent. The calculated energy values of reactants, complexes, and transition state(TS) structures in the presence of solvent are more negative than the gas phase and reduce with increasing the dielectric constant. Energydecreases in a higher rate for reactants in comparison with complexes and TS structures.� 2007 Elsevier B.V. All rights reserved.

Keywords: Methyl halide; Nucleophilic substitution reaction; Backside attack; Frontside attack; Counterion

1. Introduction

Bimolecular nucleophilic substitution (SN2) reactions atcarbon tetrahedral are among the most widely studied reac-tions of organic chemistry. An extensive amount of exper-imental [1–21] and theoretical [22–59] works has beendevoted to these reactions. A common theme in many ofthese studies has been the characterization of the potentialenergy surface along the reaction path. The effects of elec-tron correlation and basis set on optimized structures andcalculated energies have also been studied. Bohme et al.[1–3] and Brauman et al. [4–6] were the first to investigatethe gas-phase SN2 reactions experimentally. These and sub-sequent experimental studies [7–21] illustrated that the

0166-1280/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.theochem.2007.01.037

* Corresponding author. Fax: +98 541 2446565.E-mail address: [email protected] (A. Ebrahimi).

reaction can be explained by a double-well potential witha central barrier, which is responsible in the variation ofrate constants with nucleophile. Such surfaces have beenfound in ab initio molecular orbital studies, which are cur-rently one of the most useful tools for evaluating reactionpotential energy profiles [22–59].

However, the association of ions plays a central role inmany chemical and biological processes [60]. Several prop-erties of a process, such as reactivity, selectivity, and stere-oselectivity depend on the reacting species (ions or ionpairs). Some theoretical studies have been developed onthe ion pair SN2 reactions at tetrahedral carbon in thegas phase [61,62]. The mechanism of reactions has beeninvestigated and two different pathways have been pro-posed for reactions; backside attack with inversion andfrontside attack with retention. Also, the fundamentalgas–phase ion pair (Li+X�) SN2 reactions at carbon centerhave systematically been investigated by Xiong et al., in

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116 A. Ebrahimi et al. / Journal of Molecular Structure: THEOCHEM 809 (2007) 115–124

which they compared the similarities and differencesbetween the ion pair and anionic (X�) SN2 reactions [63].

Although the potential energy surface of the SN2 reac-tion has a double well form in the gas phase [7–21] it isbelieved to be unimodal in an aqueous environment [64].In the present work, the prototype SN2 reactions

Nucþ CH3X! XCH3 þNuc;

Nuc ¼ X�;LiþX�;NaþX�;KþX�;

X ¼ F;Cl;Br ð1Þ

have been considered in both gas phase and solvent mediato investigate the dependence of the reactivity of ion pairupon the nature of the counterion along the backside andfrontside paths and to reveal the effect of the solvent uponthe shapes of the potential energy surfaces by ab initiocalculations.

ΔHcomp

ΔH‡ovr

ΔH‡cent

C C

T

Nuc + CH3X

Fig. 1. The energy profile for an identity SN2 reaction in back andfrontside attacks.

2. Computational methods

A lot of calculations have been performed on the SN2reactions at tetrahedral carbon center and it has been madeclear that the computational data are very sensitive to thelevel of employed theory [22–59]. In this work, the ab initiogeometry optimizations and frequency calculations wereperformed with Gaussian98 package [65] at MP2(FC)/6-311++G(d,p) [66,67] level of theory. Frequency calculationhas been performed to check the ground and transitionstate structures and to calculate enthalpy and Gibbs freeenergy. Single point QCISD(T) [68] calculations were per-formed on all MP2 optimized structures in order todecrease the differences between calculated energy barriersand experimental results in the gas phase.

Previously, solvent effects on reaction paths have beenanalyzed by continuum model of solvation [69–77]. Trounget al. [70] studied the hydration effects on the reaction pro-file of the C1� + CH3C1 SN2 reaction using self-consistentisodensity polarizable continuum model (SCIPCM) [76].Although these hydration free energies for the Cl� anionand SN2 transition state (TS) were underestimated, the pre-dicted reaction barrier were in good agreement with othertheoretical results and experimental data. Pomelli et al.[71] presented some calculations for an SN2 reaction inambient and supercritical water performed with a contin-uum method for solvation, the polarizable continuummodel (PCM) [78]. Their results indicated that the PCMmethod is able to reproduce computer simulation resultsat a good level of accuracy, with the exception of a specificrange of P–T values of supercritical water characterized bya large isothermal compressibility. These and similar stud-ies [73–75] illustrated that although IPCM hydration ener-gies of reactants are not usually in good agreement withexperimental data, the calculated reaction barriers are.

Herein, SCRF keyword was employed to perform calcu-lations in the presence of solvents, using IPCM method.The polarizable-continuum model (PCM) uses atomicspheres with radii 1.2 times the van der Waals radii to

define the molecular cavity [78–83]. IPCM method is amodification of the PCM that defines the surface of themolecular cavity as a contour surface of constant electronprobability density of the solute molecule. Here an isoden-sity of 0.0004 electrons/bohr3 has been applied as is usuallyrecommended (although some workers recommend othervalues) [84,85]. Since the solute’s electronic wave functionchanges in each SCRF iteration, the size of the molecularcavity changes in each IPCM iteration. These calculationshave been applied on structures which optimized at MP2/6-311++G(d,p) level of theory by standard method.

The Natural Population Analysis (NPA) was also car-ried out at the mentioned level using the NBO packageincluded in the Gaussian98 suite of programs [86].

3. Results and discussion

The energy profile for a gas phase identity SN2 reaction,in which the incoming and outgoing groups are identical, isshown in Fig. 1. The reaction involves the initial formationof a pre–reaction ion– or ion pair–molecule complex (C)with a complexation enthalpy DHcomp relative to the sepa-rated reactants, which then must overcome to an activationbarrier that has been termed the central barrier, DH zcent, toreach the transition structure (T). The energy then drops asthe product ion– or ion pair–molecule complex is generatedand the later can finally dissociate into separated products.The overall activation barrier is denoted DH zovr with respectto separated reactants.

There are various conceivable structures for complexesand transition states, which are shown in Fig. 2. Herein,1C–2C, 1T–4T, and 1T 0–4T 0 correspond to complexes,transition states along backside and frontside attacks,respectively. The symmetries of the complexes and transi-tion states are depicted in this figure. There are two possi-ble conformers for ion– and ion pair–molecule complexes.In the first form, ion or ion pair is complexed with X andform a prereaction complex CH3X� � �M+X�(X�) (2C inFig. 2, M = Li, Na, K). In the second form, the X atomcoordinates with carbon and form the complex (X�)M+X�� CH3X (1C in Fig. 2). The energy of second com-plex is found to be much higher than the first for M+X�

cases [63]. To compare the curvature and geometrical

Fig. 2. Structures of probable ion– and ion pair–molecule complexes (1C

and 2C) and transition states along the backside (1T–4T) and frontside(1T 0–4T 0) SN2 reactions. 2, 3, and 4 correspond to Li+, Na+, and K+

counterions, respectively.

Fig. 4. Atomic movements along the frontside attack reaction of Li+F�.IRC for 1–6 equals 0, 1.00, 2.19, 3.23, 4.42, and 5.47, respectively.

A. Ebrahimi et al. / Journal of Molecular Structure: THEOCHEM 809 (2007) 115–124 117

change around the saddle point in more detail, andcheck the ion pair–molecule complexes along two paths,intrinsic reaction coordinates (IRCs) were calculatedat MP2/6-311++G(d,p) level of theory for backside andfrontside halide exchange reactions M+X� + CH3X fiM+X� + CH3X. The geometrical changes along the intrin-sic reaction path (IRP) for these reactions are illustrated inFigs. 3 and 4. Also, relative energies versus IRC are illus-trated in Figs. 5a and b for Li+F� in back and frontsideattacks. The points, which are specified with arrows, corre-spond to ion pair–molecule complex 2C. As can be seenfrom these figures, the first complex is obtained in theintrinsic reaction coordinate calculations for back andfrontside paths with ion pair nucleophile. This calculationand similar studies for X� [61–63] suggest that the struc-tures illustrated in Fig. 2 are favored in the reaction; 1C

and 2C for anionic and ion pair nucleophiles, respectively.In the solvent media, the reaction path can be changed

with decreasing the stability of complex. The stabilizationenergies of complexes have been calculated to determinethe potential energy surfaces of reactions in the presenceof solvents with different dielectric constants (D). Herein,the optimized structures of standard method have been

Fig. 3. Atomic movements along the backside attack reaction of Li+F�.IRC for 1–6 equals 0, 0.99, 2.18, 3.22, 4.10, and 5.40, respectively.

employed. The obtained results in the gas phase and sol-vent media are presented in the following sections,respectively.

3.1. Gas phase

Complexation enthalpies of ion– and ion pair–moleculecomplexes (DHcomp), calculated at the MP2/6-311++G(d,p) level of theory are given in Table 1. The datahave been corrected by single point calculations atQCISD(T) level in order to decrease the differencesbetween calculated result and experimental values or calcu-lated values at high levels of theory. Corrected values aregiven in the parentheses in this table.

As seen in Table 1, the DHcomp values along the backand frontside attacks decrease in the following order:

ðLiþF�Þ > ðF�Þ > ðNaþF�Þ > ðKþF�ÞðLiþCl�Þ > ðNaþCl�Þ > ðCl�Þ > ðKþCl�ÞðLiþBr�Þ > ðNaþBr�Þ > ðKþBr�Þ > ðBr�Þ

It seems that different factors such as dipole moment of ionpair and the size of M+ counterion are efficient in these or-ders. The complexation enthalpy decreases as the size ofcounterion increases. The dipole moments of ion pairs (cal-culated at mentioned level) change as follow:

KþX� > NaþX� > LiþX�

There is not a linear relationship between dipole momentof ion pair and complexation enthalpy.

The ratio of the charge (calculated by natural popula-tion analysis NAO) to the radius of Li+, Na+, and K+ cat-ions equals 1.317, 0.966, and 0.713 e/A, in M+F�, 1.269,0.939, and 0.704 e/A in M+Cl� and 1.248, 0.927, and0.702 e/A in M+Br�, respectively. The correlation coeffi-cient between complexation enthalpy and the ratio of thecharge to the radius of M+ is very close to one (0.96,0.99, and 0.99 for F, Cl, and Br cases, respectively).

The most important structural parameters of ion– andion pair–molecule complexes which were optimized at

Table 1Complexation enthalpies (DHcomp, kcal mol�1) for different nucleophiles on both paths

X� Li+X� Na+X� K+X� X�b

F �13.39 (�13.79)a �15.22 (�15.54) �12.88 (�13.07) �11.72 (�11.92) �13.81Cl �9.89 (�10.09) �14.87 (�15.03) �11.53 (�11.62) �9.95 (�9.89) �10.71Br �9.31 (�9.43) �13.73 (�13.94) �10.87 (�10.99) �9.75 (�9.64) �10.17

a The values in the parentheses corrected by single point calculation at the QCISD(T)/6-311++G(d,p) level.b These values relevant to Ref. [49] and calculated at G2(+) level.

-0.65

-0.61

-0.57

0 2 4 6 8IRC

E/h

artr

ee

-0.65

-0.61

-0.57

0 2 4 6 8IRC

E/h

artr

ee

Fig. 5. The energy of reaction system plotted as a function of intrinsic reaction coordinate (IRC) for CH3F + Li+F� fi CH3C1 + Li+F�. (a) Backsideand (b) frontside attack. The specified points with arrows correspond to complexes.


MP2/6-311++G(d,p) level are shown in Table 2. Asexpected, the optimized geometries show that the lengthof C–X bond in the complexes is larger than CH3X lonemolecules. The increasing C–X bond length in the presenceof counterion can be expressed as follow:

Liþ > Naþ > Kþ

As the size of counterion increases, the change of C–Xbond length and the complexation enthalpy decrease. Thecorrelation coefficient between complexation enthalpyand Dr(CX) (increasing C–X bond length in complexation)equals 0.96, 0.91, and 0.98 for F, Cl, and Br, respectively.These results suggest that the interaction between counter-ion and halide atom on CH3X molecule dominates the sta-bilization energy.

Overall and central barriers (DH zovr and DH zcentÞ for reac-tions with inversion (I) and retention (R) of configuration,calculated at the mentioned level are given in Tables 3 and4. The corrected values at QCISD(T) level are given in theparentheses .The results in these tables indicate that someretention energy barriers are smaller than the correspond-ing data in the inversion channel (DH zovr in Li+F�, Li+Cl�

and Na+F� cases and DH zcent in Li+X�, Na+F�, K+Cl�

and K+Br� cases). The values of DH zovr and DH zcent decreasein order Li+X� > Na+X� > K+ X� > X� along the back-side attack. Thus, the energy barrier is higher for smallercounterions. While the counterion M participates in thereaction, the barrier height would be raised by both effectsof decreasing X–C–X angle and XX distance of TSstructures. The most important structural parameters oftransition states for mentioned reactions that optimizedat MP2(FC)/6-311++G(d,p) level are shown in Table 5.As can be seen, X–X distance decreases in order

X� > K+X� > Na+X� > Li+X� along the backside attack.Therefore, the energy barrier grows by the decrease inthe X–X distance and the increase in the repulsion betweenXd� groups. On the contrary, the energy barrier decreases inorder X� > K+X� > Na+X� > Li+X� along the frontsideattack (with an exception, DH zcent is approximately equalin Na+F� and K+F� cases). The energy barrier is higherfor bigger counterions and X–X distance of TS structuresdecreases in order Li+X� @ Na+X� > K+X� > X� alongthis reaction path. The X–X distance in Li+X� is slightlydifferent from Na+X� and other factors such as theratio of the charge to the radius of counterion are moreeffective.

As expected, C–X bond length in transition state struc-tures is longer than halomethanes and complexes (seeTables 2 and 5). We can characterize the looseness of tran-sition structures by geometrical looseness parameter (%C–X) of C–X bond in a similar way to that proposed by Shaiket al. [87].

%C�Xz ¼ 100ðdzC�X � dcompðor reactantÞC�X Þ=dcompðor reactantÞ

C�X

The values of geometrical looseness of C–X bond are givenin Table 6. The larger values correspond to the frontside at-tack (with the exception of F� and Li+F�). The order ofgeometrical looseness along the back and frontside attacksis as follow: Li+X� > Na+X� > K+ X� > X�. There is anexception in the above mentioned order in which the posi-tion of K+F� is changed with F� in the backside path. Arelationship can be seen between geometrical looseness(with respect to the complexes) of C–X bonds and DH zcent,in which the correlation coefficients equal 0.91 (0.94),0.83 (0.99) and 0.97 (0.99) for F, Cl and Br classes, respec-

Tab

le2

Str

uct

ura

lp

aram

eter

so

fio

n–

and

ion

pai

r–m

ole

cule

com

ple

xes

calc

ula

ted

atM

P2/

6-31

1++

G(d

,p)

leve

l

F�

Li+

F�

Na+

F�

K+

F�

Cl�

Li+

Cl�

Na+

Cl�

K+

Cl�

Br�

Li+

Br�

Na+

Br�

K+

Br�

r C��X

2.64

63.

097

3.05

02.

987

3.19

83.

644

3.60

83.

586

3.35

93.

817

3.78

73.

761

r C-X

a1.

432

(1.3

89)a

1.43

21.

425

1.42

81.

807

(1.7

76)

1.80

31.

801

1.79

81.

966

(1.9

35)

1.95

81.

956

1.95

4r C

–H

b1.

085

1.08

9(1

.087

)1.

092

(1.0

89)

1.09

3(1

.090

)1.

084

1.08

8(1

.087

)1.

089

(1.0

87)

1.09

1(1

.087

)1.

084

1.08

6(1

.088

)1.

089

(1.0

87)

1.08

9(1

.088

)r M

-X—

1.62

9(1

.599

)2.

025

(1.9

91)

2.27

2(2

.225

)—

2.05

2(2

.022

)2.

415

(2.3

81)

2.74

(2.6

99)

—2.

223

(2.1

88)

2.57

6(2

.539

)2.

903

(2.8

61)

r M��X

—1.

901

2.32

42.

656

—2.

325

2.73

73.

196

—2.

511

2.92

13.

341

r H��X

—2.

287

2.10

32.

010

—2.

694

2.58

2.52

8—

2.82

92.

737

2.69

0hc

330.

8033

6.53

335.

8433

5.90

329.

6133

4.31

333.

8833

3.38

331.

833

5.7

335.

333

4.9

Th

eb

on

dle

ngt

hs

and

bo

nd

angl

esar

ere

po

rted

inan

gstr

om

san

dd

egre

es,

resp

ecti

vely

.a

Th

ed

ata

inth

ep

aren

thes

esco

rres

po

nd

toC

H3X

and

M+

X�

lon

esp

ecie

s.b

Th

eva

lues

inth

ep

aren

thes

esco

rres

po

nd

totw

oC

–Hb

on

ds

insy

mm

etry

pla

n.

ch

corr

esp

on

ds

tosu

mo

fth

ree

H–C

–Hb

on

dan

gles

.


tively. The data in the parentheses correspond to retentionchannel. Furthermore, there is a relationship between geo-metrical looseness (with respect to the reactants) of C–Xbonds and energy barriers (DH zovr); the correlation coeffi-cients equal 0.89 (0.87), 0.80 (0.87) and 0.81 (0.95) in theseseries, respectively. The change of energy from reactant tocomplex is related to the interaction of nucleophile withdifferent parts of reactant. The most important change(from structural viewpoint) in reactant fi product transfor-mation, which is the change of C� � �X bond length, occursin the complex fi TS step (see Tables 2 and 5). The resultsin these tables indicate that the changes of C–X bondlength are in the ranges of 0.03–0.04 and 0.4–1.2 A in reac-

tant fi complex and complex fi TS steps, respectively. Thisis in good agreement with correlation coefficients betweenDH zcent (or DH zovr) and C� � �X looseness. The correlationcoefficient of central barrier is better than the overall bar-rier. On the other hand, the correlation coefficient betweenDH zcent and C� � �X looseness along the frontside path is bet-ter than backside way. It seems that the interaction be-tween M+ ion and CH3 group in backside attack is animportant factor on this behavior.

With respect to the structures of transition states, thefollowing concepts can be deduced: the F–C–F bond anglein transition stats 2T and 2T 0 equals 90.5 and 76.5 degrees,respectively. On the other hand, the Li–F bond length of2T is bigger than 2T 0. Thus, the F–F distance in 2T

(3.044 A) is longer than 2T 0 (2.482 A). Also, this distancein 1T, 3T and 4T are longer than 1T 0, 3T 0 and 4T 0, respec-tively (see Table 5). This behavior increases the repulsionbetween Fd� groups, makes 1T 0, 3T 0 and 4T 0 more unstablethan 1T, 3T and 4T, and also causes to increase DH zovr (orDH zcent) along the frontside relative to backside attack. TheF–F distance in 2T is only 0.56 A longer than 2T 0 and thisdifference is small in comparison with other pairs (1.02–1.32 A). In this case, the predominant factor is not F–F dis-tance and the barrier energy in backside attack is largerthan frontside path. This behavior can be observed forM+Cl� and M+Br� cases in Table 5.

The difference between DH zovr (or DH zcent) values along thebackside and frontside attacks, decreases in the presence ofcounterion (100–200 kJ mol�1). Also, the barrier energyalong the frontside path is lower than backside way for somecases. Thus, counterion increases the strength of nucleophilealong the frontside attack, and the reaction with ion pairM+X� can be performed easer than X�. In addition, as theratio of charge to radius of counterion increases the ion pairbecomes a stronger nucleophile. This result is inverted alongthe backside attack on SN2 reactions.

In order to study the effect of entropy on the reactivityof nucleophiles, DG values have been calculated (see Table7). DG and DH values are in the same order with the excep-tion of X� in DGcomp. The comparison between DG dataand various DH values of Tables 1, 3, and 4 show thatall DS values (DScomp, DSzovr, and DSzcentÞ are negative.The absolute values of DSzcent are smaller than DSzovr andDScomp. Also, the absolute values of DScomp with anionic

Table 3Barrier height (DH zcent, kcal mol�1) for backside (I) and frontside (R) attacks

X� Li+X� Na+X� K+X� X�

F (I) 14.89 (13.69)a 67.38 (63.10) 54.31 (52.71) 48.02 (46.72) 11.95b

F (R) 60.98 (59.49) 51.02 (48.10) 54.55 (51.84) 54.39 (51.77) 57.60c

Cl (I) 16.89 (14.19) 55.73 (55.61) 38.26 (35.17) 32.86 (30.42) 13.72b

Cl (R) 64.28 (59.29) 55.75 (50.46) 57.26 (51.74) 58.13 (52.76) 56.84c

Br (I) 11.91 (11.60) 82.62 (78.96) 39.32 (36.61) 32.67 (30.34) 11.65b

Br (R) 59.24 (54.15) 53.17 (47.42) 54.37 (48.55) 57.68 (49.11) 52.58c

a The values in the parentheses corrected by single point calculation at the QCISD(T)/6-311++G(d,p) level.b These values are relevant to Ref. [49] and calculated at G2(+) level.c These values are relevant to Ref. [50] and calculated at G2(+) level.

Table 4Barrier height (DH zovr, kcal mol�1) for backside (I) and frontside (R) attacks

X� Li+X� Na+X� K+X� X�

F (I) 1.50 (�0.10)a 52.17 (47.55) 41.43 (39.64) 36.30 (34.79) �1.86c

23.73b 78.28 44.83 42.64

F (R) 47.59 (45.70) 35.81 (32.56) 41.68 (38.77) 42.67 (39.85) 184.51d

64.12 67.04 – 61.93

Cl (I) 7.00 (4.10) 40.90 (35.58) 35.17 (32.05) 28.86 (26.37) 3.01c

24.86 90.18 38.28 35.24

Cl (R) 54.39 (46.66) 40.92 (35.42) 45.72 (40.12) 48.17 (42.86) 193.80d

66.48 87.06 62.68 62.64

Br (I) 2.06 (1.49) 29.75 (25.27) 28.44 (23.79) 22.91 (20.69) 1.48c

21.90 86.42 50.34 29.93

Br (R) 49.93 (44.72) 39.43 (33.47) 43.49 (37.55) 44.92 (39.46) 178.90d

62.28 90.11 66.46 58.02

a The values in the parentheses corrected by single point calculation at the QCISD(T)/6-311++G(d,p) level.b These are calculated values in solvent media.c These values are relevant to Ref. [49] and calculated at G2(+) level.d These values are relevant to Ref. [50] and calculated at G2(+) level.

Table 5Structural parameters of transition states calculated at MP2/6-311++G(d,p) level

rC� � �F rM� � �F rF� � �F hFCF hFMF rC� � �Cl rM� � �Cl rCl� � �Cl hClCCl hClMCl rC� � �Br rM� � �Br rBr� � �Br hBrCBr hBrMBr

1T 1.827 — 3.654 180.0 — 2.297 — 4.594 180.0 — 2.451 — 4.902 180.0 —2T 2.143 1.789 3.044 90.49 116.60 2.466 2.260 3.994 108.2 124.2 2.554 2.476 4.384 118.2 124.63T 1.831 2.519 3.509 147.01 87.87 2.324 2.773 4.368 140.01 103.99 2.479 2.914 4.662 140.2 106.34T 1.811 2.831 3.540 153.92 76.44 3.181 3.181 4.456 153.46 88.85 2.450 3.285 4.752 151.6 92.71T 0 1.793 — 2.337 81.34 — 2.573 — 3.234 83.1 — 2.589 — 3.532 86.0 —2T 0 2.005 1.701 2.482 76.49 93.69 2.399 2.122 3.413 84.72 107.1 2.750 2.294 3.739 85.7 109.23T 0 1.969 2.141 2.489 78.46 71.12 2.547 2.487 3.441 84.95 87.51 2.722 2.294 3.746 87.0 89.64T 0 1.924 2.369 2.421 77.99 61.47 2.506 2.845 3.352 83.94 72.11 2.685 3.010 3.666 86.1 75.0

The bond lengths and bond angles are reported in angstroms and degrees, respectively.2, 3, and 4 correspond to Li+, Na+, and K+ counterions, respectively.

Table 6Geometrical looseness of C–X bond

F� Li+F� Na+F� K+F� Cl� Li+Cl� Na+Cl� K+Cl� Br� Li+Br� Na+Br� K+Br�

Relative to substrate 31 (29) 54 (44) 32 (42) 30 (38) 29 (35) 39 (45) 31 (43) 29 (41) 25 (32) 30 (40) 27 (39) 25 (37)Relative to complex 28 (25) 50 (40) 28 (38) 27 (35) 27 (33) 37 (42) 29 (41) 27 (39) 27 (34) 32 (42) 28 (41) 27 (39)

The data in the parentheses correspond to frontside attack.


Table 7Gibbs free energy values (kcal mol�1) for back (I) and frontside (R)attacks in the gas phase

DGcomp I R

DGzovr DGzcent DGzovr DGzcent

F� �7.46 9.69 17.15 54.57 62.02Li+F� �7.35 61.78 69.13 44.92 52.27Na+F� �4.99 50.17 55.16 50.79 55.78K+F� �3.95 47.09 51.04 51.78 55.73Cl� �5.32 14.66 19.98 60.72 66.04Li+Cl� �7.31 50.00 57.31 49.42 56.74Na+Cl� �4.13 44.65 48.78 54.16 58.29K+Cl� �2.89 37.84 40.73 56.58 59.47Br� �4.43 11.75 16.18 56.00 63.80Li+Br� �6.50 42.48 48.99 47.61 54.12Na+Br� �3.70 37.47 41.17 51.55 55.25K+Br� �2.76 32.35 35.11 53.01 55.77

-0.55

-0.51

-0.47

0 20 40 60 80D

-0.70

-0.65

-0.60

-0.55

E/h

artr

ee

a

b

Fig. 7. Relative energy of complex r and reactant m plotted againstdielectric constant of the solvent as calculated by IPCM method at MP2/6-311++G(d,p) level of theory along the backside path for (a)Li+Cl� + CH3Cl and (b) K+Cl� + CH3Cl.


nucleophiles are smaller than ion pairs. This behaviorchanges the situation of X� in the order of DGcomp withrespect to DHcomp.

3.2. Solvent media

Complexation enthalpies DHcomp have been calculatedin solvent media for back and frontside paths using calcu-lated energies at MP2/6-311++G(d,p) level of theory andIPCM method. The DHcomp values have been plotted ver-sus the dielectric constants of the solvents. A sample graphis shown in Fig. 6. In all cases, the absolute values of com-plexation enthalpies decrease by the increase in dielectricconstant of the solvent. Although complexation enthalpiesare positive for some reactions at low dielectric constants(2–10), they are negative until 80 for Cl�, K+Cl�, andK+Cl� cases. On the other hand, calculated dipolemoments of Cl�� CH3Cl, K+Cl�� CH3Cl, Br�� CH3Br,and K+Br�� CH3Br complexes at MP2/6-311++G(d,p)level of theory in the gas phase are equal to 8.84, 8.83,and 8.73 Debye, respectively, and are greater than othercomplexes.

In order to investigate the changes of DHcomp in solventmedia, the energies of various complexes and reactantshave been calculated at MP2/6-311++G(d,p) level usingIPCM method in solvents with different dielectric con-

-10

-8

-6

-4

-2

0 20 40 60 80

D

ΔHco

mp/

kcal

mol

-1

Fig. 6. Complexation enthalpy plotted against dielectric constant of thesolvent (D) as calculated by IPCM method at MP2/6-311++G(d,p) levelof theory along the backside path for Cl� + CH3Cl fi CH3Cl + Cl�.

stants. Two sample graphs are shown in Fig. 7. As canbe seen, the relative energies of complexes and reactantsreduce by the increase in dielectric constant of solvent.The difference between decreasing energies of complexesand reactants is small for Cl�, K+Cl�, Br�, and K+Br�

cases, in which DHcomp is negative in solvents with highdielectric constants, in comparison with other cases.

The calculated values of DH zovr increase with increasingdielectric constant of solvent for back and frontside paths.Two typical graphs are shown in Fig. 8. A maximum isshown for Na+F� and Na+Cl� cases along the back andfrontside attacks. In order to explain the changes, the rela-tive energies of TS structures and reactants have been stud-ied in the solvents with different dielectric constants. Twosample graphs are shown in Fig. 9. As can be seen, TSstructures and reactants become more stable in solventswith high dielectric constants. The energy values decreasein higher rates for reactants in comparison with TS struc-tures. Thus, DH zovr increases at higher dielectric constants.To interpret the maximum point of Fig. 8b, DER and DETS

(the difference between ER or ETS values at two adjacentdielectric constants) have been fully calculated. The resultsindicate that DER > DETS for solvents with dielectric con-stant between 1.0 and 3.0, and it is on contrary directionfor solvents with dielectric constant higher than 3. Thus,the plot of DH zovr versus D passes from a maximum in therange of 3–5. The limiting values of DH zovr in the presenceof solvent are reported in Table 4 (bold data). The valuesof DH zcent (in the cases with negative DHcomp values) growwith increasing dielectric constant of solvent (with theexception of Li+F�, Na+F�, K+F�, Na+Cl� whichdecrease along the backside attack and also Li+Cl� which

45

50

55

1 2 3 4 5

D

14

21

ΔHce

nt/k

cal m

ol-1

a

b

Fig. 10. DH zcent plotted against dielectric constant of the solvent ascalculated by IPCM method at MP2/6-311++G(d,p) level of theory alongthe backside path for (a) F� + CH3F and (b) Na+F� + CH3F.

-0.22

-0.19

-0.16

-0.13

E/h

artr

ee

-0.02

0.00

0.02

0.04

1 2 3 4 5

D

a

b

Fig. 11. Relative energy of transition state m and complex r plottedagainst dielectric constant of the solvent as calculated by IPCM method atMP2/6-311++G(d,p) level of theory along the backside path for (a)F� + CH3F and (b) Na+F� + CH3F.

41

42

43

44

45

46

0 20 40 60 80D

52

62

72

82ΔH

ovr/k

cal m

ol-1

a

b

Fig. 8. DH zovr plotted against dielectric constant of the solvent ascalculated by IPCM method at MP2/6-311++G(d,p) level of theoryalong the backside path for (a) Li+F� + CH3F and (b) Na+F� + CH3F.

-0.76

-0.71

-0.66

E/h

artr

ee

-0.04

-0.02

0.00

0.02

0.04

0 20 40 60 80D

a

b

Fig. 9. Relative energy of transition state r and reactants m plottedagainst dielectric constant of the solvent as calculated by IPCM method atMP2/6-311++G(d,p) level of theory along the backside path for (a)Li+F� + CH3F and (b) Na+F� + CH3F.


passes from a maximum along the frontside attack). Twotypical graphs are illustrated in Fig. 10. These changescan be interpreted with respect to the relative energies ofcomplexes and TS structures in solvent media. Two typicalgraphs corresponding to F� + CH3F and Na+F� + CH3Freactions are illustrated in Fig. 11. As can be seen, theenergy versus D decrease with a higher rate for complexin F� + CH3F reaction whereas decrease with a higher ratefor transition state in Na+F� + CH3F reaction. Thus, bythe increase in D, DH zcent grows in F� + CH3F and reducesin Na+F� + CH3F reaction.

4. Conclusion

The results presented in this article allow us to com-pare the potential energy surfaces, the curvature and geo-metrical changes around the saddle point, and to checkthe ion pair–molecule complexes along two paths ofsome identity SN2 exchange reactions. The IRC calcula-tions show that CH3X� � �M+X� complex participate inthe reaction along the back and frontside paths. TheDHcomp values decrease along the back and frontsideattacks with the increasing counterion diameter so that


the correlation coefficient between DHcomp values and theratio of the charge to the radius of M+ ion is very closeto one in the gas phase. The C–X bond length increasesmore for bigger counterions, so that there is a very goodcorrelation between DHcomp and increasing C–X bondlength in complexation.

The energy barriers DH zovr and DH zcent are higher for smal-ler counterions in backside attack (Li+X� > Na+X� >K+X� > X�). The order is inverted along the frontsidereaction path. These are in good agreement with X–Xdistances of transition state structures. The barrier energyincreases with decreasing X–X distance which increasesthe repulsion between Xd� groups. There is a relationshipbetween geometrical looseness of C� � �X bonds and energybarriers. The correlation coefficient between DH zcent andC� � �X looseness along the frontside path is better thanbackside way. It seems that the interaction of M+ ion withCH3 group along the backside attack is an important factoron this behavior.

In frontside attack, counterion increase the strength ofnucleophile, and the reaction with ion pair M+X� is per-formed easer than X� in the gas phase. As the ratio ofcharge to radius of counterion increases, the ion pairbecomes a stronger nucleophile. This result is invertedalong the backside attack.

Although complexes and reactants are more stable inthe solvents with higher dielectric constants, the rate of sta-bilization is bigger for reactants and result in decreasingcomplexation enthalpy with increasing dielectric constantof solvent. Also, the values of DH zovr increase with increas-ing dielectric constants of solvent. Even though the stabil-ity of TS structures and reactants increases in solvents withhigher dielectric constants, the rate of changes is bigger forreactants. In the cases with negative values of DHcomp,DH zcent usually grows by the increase in dielectric constantof solvent.

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