Chemical Physics Letters 376 (2003) 524–531

www.elsevier.com/locate/cplett

A comprehensive theoretical study on the identity ion pairSN2 reactions of LiX with NH2X (X¼F, Cl, Br and I),

structure, mechanism and potential energy surface

Yi Ren a,*, San-Yan Chu b,*

a Faculty of Chemistry, Sichuan University, P.O. Box 73, Chengdu 610064, PR Chinab Department of Chemistry, National Tsing Hua University, Hsinchu 30013, Taiwan

Received 11 May 2003; in final form 5 June 2003

Published online: 5 July 2003

Abstract

Gas phase identity ion pair SN2 reactions at nitrogen LiX+NH2X!XNH2 +LiX (X¼F, Cl, Br and I) are in-

vestigated at the G2M(+) level. Two reaction mechanisms, inversion and retention, are proposed. Results indicate the

inversion mechanism is favorable for all halogens. Including Li in the anionic SN2 model will raise the overall barriers

for the LiX+NH2X (X¼F, Cl and Br) reactions and lower the overall barrier for the LiI +NH2I reaction. The sta-

bilization energies for complexes XLi� � �NH2X increase in the order: F<Cl<Br< I and show a good correlation with

halogen electronegativities.

� 2003 Elsevier Science B.V. All rights reserved.

1. Introduction

Displacement reactions at heteroatoms feature

widely in both organic and bio-organic and they

are among the most important process in me-

tabolism [1]. Recently, theoretical and experi-

mental investigations have been devoted toanionic SN2 reactions on heteroatoms in gas

phase [2–8], or in aqueous acetonitrile [9]. How-

* Corresponding authors. Fax: +86-28-85257397 (Y. Ren),

886-3-5711082 (S.-Y. Chu).

E-mail addresses: yiren57@hotmail.com (Y. Ren), sy-

chu@mx.nthu.edu.tw (S.-Y. Chu).

0009-2614/03/$ - see front matter � 2003 Elsevier Science B.V. All r

doi:10.1016/S0009-2614(03)01003-0

ever, most of SN2 reactions in the solution phase

may actually involve neutral ion-pair as reactants,

which is the source of the nucleophilic anion

species. The nucleophile of neutral ion pair are

expected to have rather different reactivity from

anion species. But the neutral nucleophilic have

received less attention. In 1995, Harder et al. [10]studied some identity ion pairs SN2 reactions at

carbon and got some interesting results. The

calculated identity reactions MX+CH3X(X¼F

and Cl; M¼Li and Na) involve preliminary en-

counter dipole–dipole complexes, then proceeds

via a cyclic inversion or retention transition

structure with highly bent X–C–X bonds behav-

ing as assemblies of ions. Streitwieser et al. [11]

ights reserved.

Y. Ren, S.-Y. Chu / Chemical Physics Letters 376 (2003) 524–531 525

extended the work to the higher alkyls and dis-

cussed some steric effects for the ion pair SN2

reactions. More recently, Leung et al. [12] re-

ported a theoretical study on ion pair SN2 reac-

tions of metal cynates and methyl halides.

Glukhovtsev et al. [2] and Ren et al. [3] hadrevealed some similarities and differences between

anionic SN2 reactions at nitrogen and carbon. In

order to investigate the generality of ion pair SN2

reaction at nitrogen, we now extend our study to

gas phase identity ion pair amino-transfer reac-

tions [Eq. (1)]. We are particularly interested in

what is the possible mechanism about the ion pair

SN2 reactions at nitrogen and whether they showsimilar patterns of behavior to the anionic SN2

reaction at nitrogen and the ion pair SN2 reactions

at carbon.

LiXþNH2X ! NH2X

þLiX ðX ¼ F; Cl; Br; and IÞð1Þ

The present work represents the first computa-

tional study of this fundamental ion pair SN2 re-

actions at such a high level and will hopefully

provide reliable energy parameters, which may be

useful for future experimental studies.

2. Computational details

Modified GAUSSIANAUSSIAN-2 theory introduced by

Mebel et al. [13], which has been extensively used

in the study of reaction mechanism [14–16], was

applied to this work. Previous study [17] indi-cated that the diffusion function is necessary in

structure optimization for the SN2 reaction.

Therefore, all geometries were fully optimized at

the B3LYP level [18,19] with the 6-311+G(d, p)

basis sets. Vibrational frequencies were employed

to characterize stationary points and the un-

scaled zero-point energies were included in com-

parison of relative energies. Electron correlationeffect was evaluated using coupled cluster calcu-

lation including triple excitations non-iteratively

[CCSD(T)]. This level of theory is termed as

G2M(+) in the present study. Full detail of pro-

cedures can be found in [13,14].

All electron basis sets were used for all first- and

second-row atoms, while Hay and Wadt [20] ef-

fective core potentials were used for the third- and

fourth-row atoms, referred as G2M(+)-ECP.

Charge were calculated by the natural population

analysis (NPA) [21–25] at the MP2/6-311+G(3df,2p) level on B3LYP/6-311+G(d,p) geome-

tries. The NPA charge of all species involved in the

title reactions were given in supporting informa-

tion. All calculation were performed with GAUS-AUS-

SIANSIAN-98 [26].

Throughout this Letter, all inter-nuclear dis-

tances are in angstroms and bond angles in de-

grees. Relative energies correspond to enthalpychanges at 0 K[DH (0 K)] in kJ/mol.

3. Results and discussions

The energy profile for Eq. (1) is described by a

symmetrical double-well potential curve. Two

possible reaction channels, corresponding to twodifferent mechanism, inversion and retention, are

proposed. The inversion mechanism involves the

initial formation of a pre-reaction dipole–dipole

complex 1. This complex must then overcome the

central barrier to reach a symmetrical inversion

transition structure 2. The latter then breaks down

to give the product dipole–dipole complex, which

subsequently dissociates into the separate prod-ucts. For the retention mechanism, the complex

and transition structure is denoted as 10 and 20,

respectively. The key energetic quantities, com-

plexation energy, DHcomp, the central barrier with

respect to complex, DH 6¼cent, and the overall bar-

rier relative to separated reactants, DH 6¼ovr, were

depicted in Scheme 1.

The main geometries of optimized reactants,

complexes and transition structures are shown in

Fig. 1. All of the energetics involved in Eq. (1) arepresented in Table 3.

Scheme 1. Schematic potential energy surface for the LiX+NH2X identity exchange reactions (X¼F–I).

Fig. 1. Main geometries of the reactants, complexes and transition structures in the reactions LiX+NH2X (X¼F–I) at the level of

B3LYP/6-311+G(d,p). The data in parentheses are the geometric looseness for the corresponding bonds.

526 Y. Ren, S.-Y. Chu / Chemical Physics Letters 376 (2003) 524–531

3.1. Reactants

Predicted properties of LiX and NH2X (X¼F,

Cl, Br and I) are compared with available experi-

mental results in Tables 1 and 2. The geometries of

LiX and NH2X at the B3LYP/6-311+G(d,p) level

generally agree well with the available experimen-

tal data and MP2/6-31+G(d) results. All fre-

quencies and dipole moment values for LiX are

reproduced by DFT method. The Li–X and N–X

bond dissociation energies compare favorably with

experimental and G2(+) values with errors lessthan about 10 kJ/mol.

3.2. Dipole–dipole complexes

There are two possible conformers for the di-

pole–dipole complexes corresponding to the dif-

Table 1

Predicted bond lengths (�AA), vibrational frequencies (cm1), dipole moment (Dye), and dissociation energies (kJ/mol) of LiX (X¼F–I)

in comparison with experiments

Species Level r(Li–X) m l DLi–X

LiF G2M(+) 1.582 900 6.354 574.4

MP2a 1.588

Exptlb 1.564 910 6.284 577.0( 21)c

LiCl G2M(+) 2.024 640 7.080 470.4

MP2 2.056

Exptl 2.021 643 7.085 469.0( 13)

LiBr G2M(+)-ECP 2.191 555 7.210 408.6

Exptl 2.170 563 7.226 418.8( 4.2)

LiI G2M(+)-ECP 2.397 496 7.338 344.4

Exptl 2.392 498 7.428 345.2( 4.2)

a From [2], at the level of MP2(full)/6-31+G(d).b From [27].c From [28].

Table 2

Main geometries for NH2X (X¼F–I) and the dissociation energies (kJ/mol) for the N–X bonds

Level r(N–X) \X–N–H DN–X

NH2 F G2M(+) 1.434 101.6 291.2

G2(+)a 1.446 100.6

Exptlb 1.436 100.9 292.0

NH2 Cl G2M(+) 1.777 104.3 253.5

G2(+) 1.780 108.9

Exptlc 1.776 108.6 252.3

NH2 Br G2M(+)-ECP 1.929 104.3 212.8

G2(+)-ECP 1.920 104.2 210.8

NH2 I G2M(+)-ECP 2.099 104.9 183.5

G2(+)-ECP 2.083 105.4 187.1

aFrom [2]. Geometries are optimized at the MP2(fc)/6-31+G(d).b From [29].c From [30].

Y. Ren, S.-Y. Chu / Chemical Physics Letters 376 (2003) 524–531 527

ferent reaction channels. In inversion mechanism,reaction of LiX with NH2X starts with the for-

mation of so called �N-philic� complexes XLi� � �NH2X(1a–d), in which the lithium cation coordi-

nates with nitrogen. The inversion complexation

energies decrease in the order I(78.8)>Br(76.4)>Cl(73.2)>F(67.1 kJ/mol) with a concomitant

continuously increase in the Li–N bond distance

from 1.994 (X¼ I) to 2.028 �AA (X¼F), in contrastto ion–molecule complexes in the anionic SN2 re-

actions at nitrogen [2], where the halide ion coor-

dinates with one hydrogen atom in NH2X and the

complexation energies increase in the orderI<Br<Cl<F. NPA analysis for these inversion

complexes show that the negative charge on ni-

trogen atom decreases dramatically from )1.104

(X¼ I) to )0.409 (X¼F) with the increase of in-

ductive effect of halogen atom in NH2X even

though the positive charge on Lithium vary from

+0.884 (LiI) to +0.957 (LiF), that indicate that the

stabilization energies for complexes XLi� � �NH2Xmay be mainly attributed to the interaction of

lithium cation and nitrogen atom. The weaker the

electronegativity of halogen in NH2X, the stronger

528 Y. Ren, S.-Y. Chu / Chemical Physics Letters 376 (2003) 524–531

the interaction between lithium and nitrogen atom.

That can explain the correlation between com-

plexation energies for the inversion complexes with

halogen electronegativities, but the slope will be

negative ðR2 ¼ 0:972Þ.For the alternative retention channel, the lith-

ium cation complexes halogen at NH2X to form

�X-philic� pre-reaction complexes H2NX� � � LiX

(10a–d), which are analogous to those found in the

reaction LiX+CH3X [10]. The effect of Li� � �Xcomplexation is 2-fold: (1) it increases the X–N

bond distance except a little bit decrease of N–I

bond in NH2I by 0.003 �AA. (2) It increases the ef-

fective positive charge on the NH2 group by about+0.09. The interactions between the lithium and

halogen atom will dominate the stabilization en-

ergies of the X-philic complexes, decreasing in the

order F(77.9)>Cl(61.9)>Br(59.4)> I(56.2 kJ/

mol). This order is also found to correlate well

with halogen electronegativities ðR2 ¼ 0:993Þ,that is analogues to one found for X� � �NH2X

complexes [2].

3.3. Transition state structures and central barrier

heights

The inversion LiX/NH2X transition structures

are found to have same C2V symmetry as the in-

version LiX/CH3X TS [10]. In the inversion LiX/

Table 3

G2M(+) Energetics of the ion pair SN2 reactions LiX+NH2X

LiX+CH3X!CH3X+LiX (entries C)a

X Pathway DHcomp DH

N C N

F Inv 67.1(114.0)b 67.8 156

Ret 77.2 200

Cl Inv 73.2(67.8) 63.6 111

Ret 61.4 210

Br Inv 76.4(58.4) 81

Ret 58.9 186

I Inv 78.8(50.0) 61

Ret 55.7 170

a From [10].b The data in parentheses are the corresponding values in the anion

NH2X TS, lithium coordinates with nitrogen and

acts as bridge connecting both halogen. The in-

version TS with inclusion Li cation show slightly

deformation from the TS geometry found in an-

ionic SN2 reactions [2]. The bridging actions of Li

cation only cause two halogen anions bent towardsit with a increase of the X–N–X angle by about

28–30�, that is much different from the inversion

transition structures LiX/CH3X [10], where there is

a remarkable deformation from the linear geome-

try found in [X� � �CH3� � �X]6¼ and the Li cation

causes a large decrease of the X–C–X angle by

about 90�. These may be the main reasons why the

inversion central barriers for the LiX+NH2X re-actions are much lower than the corresponding

values in the LiX+CH3X reactions (see Table 3).

In the retention mechanism, the coordination of

the lithium cation is on the same side of nitrogen

to both entering and leaving halide ions, which is

similar to the geometries of retention LiX/CH3X

TS [10] and there are more elongation of N–X

bond distances (0.301–0.434 �AA) and remarkabledecreases of X–N–X angles (64.0–86.2�) relative to

the inversion LiX/NH2X TS, respectively. These

geometric characteristics indicate the retention

transition structures will be much less stable than

the inversion ones.

The looseness of the inversion and retention TS

may be quantified by the looseness parameters

!NH2X+LiX (entries N) in comparison with reactions

cent DH 6¼ovr

C N C

.3(58.2) 261.1 89.2()55.8) 193.3

.4 191.6 122.6 123.8

.4(58.5) 222.6 38.2()9.3) 159.0

.6 222.6 148.7 159.0

.7(44.7) 5.3()13.7)

.3 126.8

.6(39.1) )17.2()10.8)

.4 114.2

ic SN2 reactions at nitrogen, from [2].

Y. Ren, S.-Y. Chu / Chemical Physics Letters 376 (2003) 524–531 529

(%N–X6¼ and %Li–X 6¼) in a similar way to that

proposed by Shaik et al. [31].

%N–X 6¼

¼ 100 � ½r 6¼ðN–XÞ rcompðN–XÞ =rcompðN–XÞ ð2Þ

%Li–X 6¼

¼ 100 � ½r 6¼ðLi–XÞ rcompðLi–XÞ =rcompðLi–XÞ ð3Þ

where r 6¼ðN–XÞ; r 6¼(Li–X) and rcomp(N–X), rcomp

(Li–X) are the N–X, Li–X bond-lengths in the

transition structure 2 or 20 and dipole–dipole

complex 1 or 10, respectively. In the retention

transition structures, the N–X bond are elongated

much more than the inversion TS, and the Li–X

bond lengths are almost unchanged, in contrast to

the larger %Li–X 6¼ values in the inversion LiX/

NH2X TS (Fig. 1).Calculated G2M(+) inversion central barriers,

DH 6¼cent(inv), for the reactions XLi +NH2X (X¼F,

Cl, Br and I) are significantly greater than corre-

sponding barriers in the X +NH2X (X¼F, Cl,

Br and I) reactions [2], decreasing in the order:

F(156.3)>Cl(111.4)>Br(81.7)> I(61.6 kJ/mol).

The retention central barriers are much higher

than those in the inversion TSs. The energy dif-ferences ½DH 6¼

centðretÞ DH 6¼centðinvÞ are equal to

44.1, 99.2, 104.6 and 108.8 kJ/mol for X¼F, Cl,

Br and I, respectively. This probably originates in

large part from the electrostatic repulsion between

two halide anions and more elongation of the N–X

bonds in the retention TS.

3.4. The factors that might influence the barrier

heights of TS

The inversion overall barriers, DH 6¼ovr(inv), for

the LiX+NH2X reactions are positive for X¼F,

Cl, Br, negative for X¼ I, decreasing in the or-

der F(89.2)>Cl(38.2)>Br(5.3)> I()17.2 kJ/mol),

which is different from those in anionic SN2 reac-

tions [2], where the DH 6¼ovr are negative for all hal-

ogens. The overall barriers in the retention

pathway are much higher than the ones in the in-

version pathway. The energy gaps between the two

mechanisms ½DH 6¼ovrðretÞ DH 6¼

ovrðinvÞ increase

in the order: F(33.4)<Cl(110.5)<Br(121.5)<I(131.4 kJ/mol), which predicts that the inversion

pathway are much more favorable in all of the

LiX+NH2X (X¼F, Cl, Br and I) reactions. So, in

the following discussion, we just focus on somefactors that might influence the barrier heights of

inversion TS.

NPA analysis for the inversion transition

structures show a substantial positive charge on

the NH2Li moiety and can be readily modeled as

triple ion valence bond configuration [X� � �(NH2Li)þ� � �X] 6¼, although there is no doubt that

the covalency plays a significant role in bondingto the entering and leaving groups in SN2 tran-

sition state. This suggests that the contribution of

electrostatic interaction may be one of the factors

for stabilizing the inversion TS. Meanwhile, the

Li–X bonds in inversion TS are much more

elongated than the retention TS, the looseness

parameters %Li–X 6¼ decrease in the order

F(45.2)>Cl(22.1)>Br(18.1)> I(14.1). The inver-sion overall barriers in Table 3 show that the

roles of Li–X bond dissociation energies seem to

override the electronic interactions and may play

dominant role in determining the barrier heights,

leading to the highest DH 6¼ovr (inv) for inversion

LiF/NH2F TS because of the strongest Li–F

bond and the largest %Li–F 6¼ value. The weakest

Li–I bond and the smallest %Li–I 6¼ value may beresponsible for the lowest overall barrier for the

inversion LiI/NH2I TS. As for the difference be-

tween the overall barriers for the ion pair and the

anionic reactions, the lower overall barriers for

inversion [F� � �NH2� � �F]6¼ and [LiI/NH2I]6¼ are

consistent with the much larger complexation

energies for complexes F � � �HNHF and

ILi� � �NH2I.

4. Conclusions

Application of G2M(+) theory to gas-phase

identity ion pair exchange reactions on nitrogen

[Eq. (1)] leads to the following conclusions:

(1) There are two possible reaction channels viadifferent complexes and transition structures.

Predicted inversion reaction pathway is

530 Y. Ren, S.-Y. Chu / Chemical Physics Letters 376 (2003) 524–531

LiX þ NH2X ! XLi � � �NH2X

! ½X � � �LiNH2 � � �X 6¼

! XH2N � � �LiX

! XNH2 þ LiX

The retention reaction pathway is different

from inversion one, as following:

LiX þ NH2X ! NH2X � � �LiX

! ½H2N � � �X2Li 6¼

! NH2X � � �LiX

! NH2Xþ LiX

(2) The large energy gaps between retention and

inversion TSs ½DH 6¼ovrðretÞ DH 6¼

ovrðinvÞ ¼ 33:4(X¼F),110.5 (X¼Cl), 121.5 (X¼ Br) and

131.4 kJ/mol (X¼ I)] imply that the inversion

pathway are much more favorable for all hal-

ogens.

(3) The introduction of lithium cation will raise

the overall barriers for the LiX+NH2X(X¼F,Cl and Br) reactions and lower the

overall barrier for the LiI +NH2I reaction,

that suggests that the ion pair reaction

LiI +NH2I may be more facile process than

the anionic reaction I +NH2I.

(4) Inversion complexation energies for dipole–di-

pole complexes XLi� � �NH2X increase in the

order: F<Cl<Br< I and are found to showa good correlation with halogen electroneg-

ativities.

Supporting information

NPA charge distributions for the species in-volved in the ion pair SN2 reactions at nitrogen are

available from the author upon request or via

internet.

Acknowledgements

We are very thankful to the National Center for

High-Performance Computing of Taiwan for

generous amounts of computing time. We alsothank the National Science Council and the Min-

istry of Education (Contract 89-FA-04-AA) of

Taiwan for their financial support.

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