Jordan Journal of Chemistry Vol. 3 No.1, 2008, pp. 39-55

JJC

G3-Global and -Local Minima of XC2H4+ Structural Isomers

where X = Li to Br

Mustafa R. Helal* and Akef T. Afaneh

Chemistry Department, Yarmouk University, Irbid, Jordan

Received on Oct. 16, 2007 Accepted on Feb. 4, 2008

Abstract

B3LYP/6-311+G** and G3 levels of theory reveal that cyclic and 1-substituted isomers

are either global or local minima for XC2H4+ structural isomers when X is CH3 or an element of

groups V, VI and VII. π-bridged structures are global minima when X is an element of groups I, II

and III, SiH3 and GeH3. The large electrophilicity of C+ in substituted ethyl cations and the

position of X in the periodic table are the main factors that determine the structure of the global

minima.

Keywords: G3-Global and -Local Minima; Substituted ethyl cation; π-bridged;

Electrophilicity; NBO analysis.

Introduction

In a recent study of CH4BX structural isomers [1a]

, G3 calculations reveal that π-

bridged structure is the global minimum when X is an element of either GP I or GP II.

The bisected open-chain structure of XCH2BH2 is the global minimum when X = BH2,

AlH2, GaH2, SiH3 and GeH3. However, when X is CH3 or an element of groups V, VI

and VII, the global minimum is 1-substituted isomer. It is worth to note that cyclic

structure does not appear as global minimum for any species of substituted

methylboranes. However, cyclic structure is a local minimum when X = NH2, OH, SH,

SeH, Cl or Br [1]

.

π-bridged bisected 1-substituted

Ethyl cation and methylborane are isoelectronic. However, 1o C

+ is more

electrophilic than B atom. Therefore, cyclic structure is expected to be global minimum

for several 2-substituted ethyl cations. Bromination of either cis- or trans-2-butene in

acetic acid gives only anti addition [2]

which means the formation of bromonium ion as

an intermediate in these reactions.

* Corresponding author. E-mail: mustafa_helal@yahoo.com

40

Substituted ethyl cations had been subjected to large number of theoretical

studies [3-10]

. In a recent study [3]

, a corner-protonated cyclopropane had been found to

be a pathway for dissociation of isopropyl cation to allyl cation and H2. Previous

theoretical studies reveal that +

3CH CHX are the global minima when X = F [4]

and X = Cl

[5], while the bromonium ion is the global minimum when X = Br

[6]. This means that

experiment and theory are in agreement with each other.

Rodriquez and Hopkinson [7, 8]

investigated the formation of cyclic structures of

substituted ethyl cations when the substituent is an element of either GP V or GP VI.

Unfortunately, the basis sets that had been used in the above studies are either 3-

21G//3-21G or 6-31G*//3-21G. Even for+

2 2 2AsH CH CH , the investigators used

MINI1//MINI1 basis set [8]

. Accordingly, the present study is initiated.

The main purpose of the present work is finding out the G3-global and -local

minima for substituted ethyl cations, +

2 4XC H , where X = Li to Br. The obtained data

would be compared with the corresponding substituted methylboranes to check the

importance of the electrophilicity difference between C+ and B atom in determining the

global minima. The obtained minima would be also compared with published data. The

enthalpy of formation, o

fΔH , values of studied species would be calculated via G3

method and compared with the available experimental and calculated values by other

methods of calculations.

Computational Methods

The optimized geometries of the studied species had been determined by

MP2(full)/6-31G* method [11]

using Gaussian 03 revision-D.01 [12]

and Pentium IV PC at

Yarmouk University. This was the choice because G3 calculations usually used

MP2(full)/6-31G* optimized geometries [13]

. When the substituent is an element from

the third period, G3 enthalpies had been manually calculated as described in Ref. 13.

For comparison reason, B3LYP/6-311+G** calculations [14]

had been also done. The

MP2(full)/6-31G* optimized structures of the global and local minima had been

elucidated by NBO analysis [15]

. The corrected zero-point energy values are present in

the supporting data. They had been obtained from the RHF/6-31G* values multiplied

by 0.8929 factor [13]

. The uncorrected and corrected Hartree-Fock energies of all

species studied in this work are present in the supporting material.

Results and Discussion

Through the whole discussion, minimum and NBO analysis mean that it is G3-

minimum and MP2(full)/6-31G* NBO analysis; respectively.

The structures of the global minima of +

2 4XC H isomers depend on the position of

the substituent X in the periodic table. To facilitate the discussion, the substituents are

grouped according to the structures of the global minima. When X is an electropositive,

41

e.g. group I, II and III, SiH3 and GeH3, π-bridged global minima are obtained. When the

substituent has one electron-pair or more, the global minimum is either 1-substituted or

cyclic structure isomer. Thus, when X = NH2, OH, SH, F, Cl in addition to CH3 group,

the global minima are 1-subsitiuted isomers. However, when X = PH2, AsH2, SeH and

Br, the global minima are cyclic structures. It seems that the more polarized X, i.e.

larger X, decreases the strain energy of the formed 3-membered ring. Consequently,

cyclic structure becomes more stable than 1-substituted isomer. The global minimum

structure of ethyl cation has cyclic structure but it is H-bridged rather than π-bridged.

The relative energy, Erel, values of different isomers of 2 4

XC H are present in Table 1, 3

and 5. It is worth to comment on the obtained Erel values by different methods of

calculations. Generally speaking, the density functional, B3LYP, theory gives the

lowest Erel values for open-chain isomers and the highest values for cyclic isomers,

Table 1, 3 and 5. This is in contrast to the perturbation, MP2, theory where Erel values

are the lowest for the cyclic isomers and the highest for the open-chain ones. This is

known from the literature that MP2 enhances the formation of the rings [1]

. G3 Erel

values are in between those obtained by B3LYP and MP2 calculations, (Tables 1, 3

and 5).

H-bridged Global Minima

Ethyl cation is the only species that has H-bridged global minima, Table 1.

Table 1: Relative Energy, Erel, Values and Enthalpies of Formation of XC2H4

+ Structural isomers where X is GP I, GP II, GP III, SiH3,

and GeH3 and G3-Global Minima are H- and π -Bridged.

o

f ,G ( H )298

3

(kcal/mol)

Erel (kcal/mol)

Species(NImag)a

G3 MP2(FU)/

6-31G* B3LYP/

6-311+G**

CH3C+H2

216.35(215.4)b 0.00 0.00 0.00 H-bridged,Cs(0)

216.50(215.4)b 0.15 0.3 0.3 H-bridged,C2V(0)

222.30 5.95 6.2 3.6 e,Cs(1) LiCH2C

+H2

154.37 0.00 0.00 0.00 π-bridged,C2V(0) 220.99 66.62 71.2 62.0 e,Cs(1) 206.42 52.05 55.8 48.7 CH3C

+HLi,Cs(1)

NaCH2C+H2

123.9 0.00 0.00 0.00 π-bridged,C2V(0) 204.5 74.17 79.7 69.3 e,Cs(2)

c

185.5 57.41 61.1 54.0 CH3C+HNa,Cs(1)

KCH2C+H2

108.26 0.00 0.00 0.00 π-bridged,C2V(0) 188.87 80.61 87.2 76.1 e,Cs(2)

c

169.87 61.61 65.6 58.6 CH3C+HK,Cs(1)

BeHCH2C+H2

226.1 0.00 0.00 0.00 π-bridged,Cs(0) 259.7 33.6 36.5 29.3 e,Cs(1) 256.4 30.3 33.1 26.0 CH3C

+HBeH;Cs(1)

MgHCH2C+H2

199.0 0.00 0.00 0.00 π-bridged,Cs(0) Table 1: Cont’d

252.4 53.4 56.2 49.5 e,Cs(1) 243.4 44.4 47.2 40.8 CH3C

+HMgH,Cs(1)

CaHCH2C+H2

185.2 0.00 0.00 0.00 π-Bridged,Cs(0) 251.5 66.3 70.0 56.8 e,Cs(1)

42

o

f ,G ( H )298

3

(kcal/mol)

Erel (kcal/mol)

Species(NImag)a

G3 MP2(FU)/

6-31G* B3LYP/

6-311+G**

238.3 53.1 55.2 45.2 CH3C+HCaH,Cs(1)

BH2CH2C+H2

220.9 0.00 0.00 0.00 π-bridged(XCC)Csd(0)

229.1 8.2 7.9 10.0 π-bridged,(XH)eCs(1)

243.2 22.3 23.6 20.0 ee,Cs(1) 245.1 24.2 26.2 21.7 eb,Cs

f(2)

228.8 7.9 9.4 2.2 CH3C+HBH2,Cs

g(1)

AlH2CH2C+H2

207.9 0.00 0.00 0.00 π-bridged(XCC)Csd(0)

208.5 0.6 0.00 0.7 π-bridged(XH)Cse(0)

248.2 40.3 42.9 37.6 ee,Cs(1) 249.8 41.9 45.0 39.2 eb,Cs

f(2)

241.1 33.2 35.9 28.7 CH3C+HAlH2,Cs

g(1)

GaH2CH2C+H2

210.4 0.00 0.00 0.00 π-bridged(XCC)Csd(0)

211.2 0.8 1.1 0.9 π-bridged(XH)Cse(1)

254.7 44.3 44.9 41.2 ee,Cs(1) 256.1 45.7 47.4 42.6 eb,Cs

f(2)

246.0 35.6 37.9 31.0 CH3C+HGaH2,Cs

g(1)

SiH3CH2C+H2

202.0 0.4 0.00 0.00 π-bridged(XH)e,Cs(0)

201.6 0.00 0.1 0.1 π-bridged(XCC)d,Cs(1)

231.6 30.0 31.9 27.0 es,Cs(1) 231.0 29.4 32.1 26.9 ee,Cs(2) 221.3 19.7 21.0 17.1 CH3C

+HSiH3,C1(0)

GeH3CH2C+H2

210.4 0.5 0.00 0.0 π-bridged(XH)e ,Cs(0)

209.9 0.00 0.1 0.0 π-bridged(XCC)d,Cs(1)

245.8 35.9 37.4 32.9 es,Cs(1) 245.1 35.2 37.5 32.7 ee,Cs(2) 235.1 25.2 26.1 22.6 CH3C

+HGeH3,C1(0)

a MP2(FULL)/6-31G*.

b Ref. 18.

c NImag = 1 in RHF/6-31G* calculations.

d XCC is

the symmetry Plane. e

XH is the symmetry plane. f CH2

+ has eclipsed configuration,

XH2 has bisected configuration, reversing the situation gives bridged structure. g

XH2 has bisected configuration with respect to C-C

+ bond.

The MP2(full)/6-31G* optimized values of key geometrical parameters of ethyl

cation global minimum are shown in Figure 1.

C2v(0)

oC-Cr =1.380A

(bridged)

oC-Hr =1.305A

(bridged)

oCCHΘ =58.1

Figure 1: H-Bridged Global Minima.

NBO analysis indicates that the occupancy of p-orbital on each carbon is 0.686,

while the occupancy of s-orbital on the H-bridged is 0.637, Table 2. The total

occupancy of the three orbitals is 2.009. This means that a 3-centers-2-electrons bond

is formed. Methyl borane global minimum has an open chain structure [1]

. The effect of

the electrophilicity of C+ in ethyl cation is clear and profound in making H-bridged as

global minimum.

43

The enthalpy of formation, o

fΔH , for +

3 2CH CH , had been calculated to be 216.5

kcal/mol (Table 1) as obtained from G3 method. Several experimental and theoretical

reported values are available [16-18]

. The closest reported value is 215.4 kcal/mol [18]

,

which is in good agreement with the present calculated value.

π-bridged Global Minima

Except ethyl cation, other species included in Table 1 have π-bridged global

minima. XCH2BH2 species have also π-bridged global minima, but only when X is an

element of either GP I or GP II [1]

. This difference could be attributed to the higher

electrophilicity (electronegativity) of C+ than B atom. This difference allows formation of

a π-bond between the two carbon atoms when X has less metallic character than

those in groups I and II. Thus, +

2 2XCH CH species have π-bridged global minima when

X is an element of GP III, SiH3 or GeH3. The higher electropositivity of GP I and GP II

elements is behind the formation of π-bonds between C-C+ and C-B in the two

systems.

Cs optimized geometries of+

2 2XCH CH , X = BH2, AlH2, GaH2, SiH3 and GeH3,

have two possible symmetry planes: XH and XCC planes. Both cases give π-bridged

structures but with different energies. G3 results, Table 1, reveal that XCC symmetry

plane gives lower energy with zero imaginary frequency than XH symmetry plane,

when X is an element of GP III. The opposite is found when X = SiH3 or GeH3 i.e. XH

symmetry plane gives zero imaginary frequency while XCC symmetry plane gives one

imaginary frequency with 0.4-0.5 kcal/mol lower energy, Table 1. The MP2(full)/6-31G*

optimized values of key geometrical parameters of π-bridged global minima are given

in Figure 2.

X PG aC-C

r 21

aC -XC -X

r (r ) 2 11 2

aXC CXC C

Θ (Θ )

Li C2v 1.349 2.400 73.7 Na C2v 1.346 2.743 75.8 K C2v 1.342 3.226 78.0 BeH Cs 1.361 2.025(2.024) 70.4(70.03) MgH Cs 1.355 2.499(2.499) 74.3(74.3) CaH Cs 1.348 2.988(2.988) 77.0(77.0) BH2 XCC; Cs 1.376 1.813(1.813) 67.7(67.7) AlH2 XCC; Cs 1.358 2.389(2.389) 73.5(73.5) GaH2 XCC; Cs 1.360 2.413(2.413) 73.6(73.6) SiH3 XH; Cs 1.365 2.275 72.5 GeH3 XH; Cs 1.367 2.356 73.1 a Bond Lengths in Angstroms and Angles in Degrees.

Figure 2: MP2(full)/6-31G* Optimized Values of Key Geometrical Parameters of π-Bridged Global Minima.

The G3- o

fΔH values of the π-bridged global minima are present in the last

column of Table 1. Unfortunately, the corresponding experimental values are

unavailable to be compared with those calculated values. NBO analysis indicates that

the main hyperconjugation (HC) is between πC-C and *

XLp except for GP II elements,

(Table 2).

44

Table 2: MP2(FULL)/6-31G* NBO Analysis of Donors and Acceptors for Main HC in H-bridge and π-Bridged G3-Global Minima of Structural Isomers of XC2H4

+ Species.

X(PG) Donor Acceptor EStabilization

kcal/mol NBO Occupancy NBO Occupancy

H-bridged Species

H,C2v(0) 1

*CLp 0.68634

2

*HLp 0.63677 1008.65

3

*CLp 0.68634

2

*HLp 0.63677 1008.65

π-bridged Species

Li(C2v) C-Cπ 1.96529 *LiLp 0.03428 15.11

Na(C2v) C-Cπ 1.97423 *NaLp 0.02561 10.02

K(C2v) C-Cπ 1.98589 *KLp 0.01360 5.13

BeH(Cs) C-Cπ 1.82393 *Be-Hσ 0.08477 26.45

MgH(Cs) C-Cπ 1.88958 *Mg-Hσ 0.08621 26.35

CaH(Cs) C-Cπ 1.95097 *Ca-Hσ 0.03714 10.35

BH2(XCC; Cs) C-Cπ 1.50985 *

BLp 0.50846 532.96

AlH2(XCC; Cs) C-Cπ 1.79865 *AlLp 0.17175 85.59

GaH2(XCC; Cs) C-Cπ 1.78262 *GaLp 0.18148 84.72

SiH3(XH)Cs C-Cπ 1.65674 *SiLp 0.33289 204.00

GeH3(XH)Cs C-Cπ 1.65387 *GeLp 0.33088 70.88

In this group, the main HC is between πC-C and*

Be-Hσ , *

Mg-Hσ and*

Ca-Hσ . NBO analysis

also indicates that *

XLp is sp2-orbital for GP III and it is vacant p-orbital for X = SiH3 and

GeH3.

1-Substituted Global Minima

In addition to CH3 group, substituents with at least one lone-pair and have

relatively small size, i.e. less polarizable, the global minima are 1-substituted

structures. This is applied to the substituents X = NH2, OH, SH, F and Cl, Table 3. The

bonds pattern in isopropyl cation is different from those of other species. Therefore, it

would be first discussed.

Table 3: Relative Energy, Erel, Values and Enthalpies of Formation of 1-Substituted G3-Global Minima (CH3CHX) and Conformers of XCH2C

+H2 Where X = CH3, NH2, OH, SH, F and Cl.

2983 o

f ,G ( H )

(kcal/mol)

Erel (kcal/mol)

Species(NImag)

a G3

MP2(FU)/ 6-31G*

B3LYP/ 6-311+G**

193.5(193.1)b 0.00 0.00 0.00 CH3C

+HCH3,C1(0)

193.5(193.1)b 0.00 0.00 0.00 CH3C

+HCH3,C2(0)

CH3CH2C+H2

201.5(201.1)b 7.9 6.0 12.1 (cyc;XCC)

c,d,Cs(0)

201.0(201.1)b 7.5 6.1 12.2 (cyc;XH)

c,eCs(1)

212.7 19.2 20.1 20.9 (es)Cs(1) 213.2 19.7 21.3 21.6 (ee)Cs(2) 159.5 0.00 0.00 0.00 CH3C

+HNH2 (eX)Cs(0)

180.46 21.0 18.8 23.7 NH2CH2C+H2 (cyc)Cs(0)

230.73 71.19 76.22 68.20 (egg,in)Cs(1) 228.86 69.32 73.72 66.52 (egg,out)Cs(2)

f

142.27 0.00 0.00 0.00 CH3C+HOH (eXa)Cs(0)

45

2983 o

f ,G ( H )

(kcal/mol)

Erel (kcal/mol)

Species(NImag)

a G3

MP2(FU)/ 6-31G*

B3LYP/ 6-311+G**

142.77 0.49 0.50 0.74 (eXe)Cs(0) 170.01 27.73 26.64 31.36 OHCH2C

+H2 (cyc)C1(0)

170.01 27.73 26.64 31.36 (cyc,XH)Csc(0)

185.21 42.94 42.77 44.05 (cyc,XCC)Csc(1)

187.52 45.52 50.82 42.65 (ea)Cs(1) 190.14 47.87 55.10 45.76 (ee)Cs(2) 190.00 0.00 0.00 0.00 CH3C

+HSH (eXa)Cs(0)

190.00 0.00 0.00 0.00 (eXe)Cs(0) 192.79 2.79 1.34 5.41 SHCH2C

+H2 (cyc)C1(0)

192.79 2.79 1.34 5.40 (cyc,XH)Csc(0)

223.22 33.22 36.21 34.36 (b,XCC)c,g

Cs(1) 234.60 44.60 48.50 40.0 (ea)Cs(1) 234.61 44.61 48.38 41.01 (ee)Cs(2) 164.37 0.00 0.00 0.00 CH3C

+HF (eF)Cs(0)

192.82 28.45 25.96 30.93 FCH2C+H2 (cyc)C2V(0)

191.69 27.31 30.54 24.86 (e)Cs(1)h

200.06 0.00 0.00 0.00 CH3C+HCl (eCl)Cs(0)

204.85 4.79 4.94 7.82 ClCH2C+H2 (cyc)C2V(0)

227.56 27.50 29.47 25.68 (e)Cs(1) a MP2(FULL)/6-31G*.

b Ref. 19.

c XH means that XH plane is the symmetry plane

while XCC means that the symmetry plane is XCC Plane . d

It is CH3-bridged via 2-electrons-3-centers (C atoms) bond rather than Pi-bond as in case of X = SiH3 orGeH3.

e It is corner-protonated cyclopropane.

f NImag =1 in RHF/6-31G*

calculations. g

The corresponding OHCH2CH2+ conformer optimizes to cyclic

structure. h

NImag = 0 in RHF/6-31G* calculations.

The MP2(full)/6-31G* optimized values of key geometrical parameters of isopropyl

cation are shown in Figure 3 which is similar to those reported [19]

. Figure 3 shows that

one of hydrogens of each of the methyl groups is almost perpendicular to +

1 2CC H plane.

The value of the dihedral angles, 5 3 1 2H C C HΦ and

6 4 1 2H C C HΦ is 76.9o. The main HC is

between the perpendicular C-Hσ (

3 5C -Hσ and4 6C -Hσ ) and

1

*

CLp , (Table 4).

C2

1 2C Hr = o1.093 A

3 5C -Hr = o1.117 A

3 7C -Hr = o1.089 A

3 9C -Hr = o1.094 A

1 4C -Cr = o1.437 A

5 3 1H C CΘ = o100.9

3 1 4C C CΘ = o125.4

5 3 1 2H C C HΦ = o76.9

9 3 1 2H C C HΦ = o-33.7

7 3 1 2H C C HΦ = o-167.3

Figure 3: MP2(full)/6-31G* Optimized Values of Key Geometrical Parameters of Isopropyl Cation.

46

Table 4: MP2(FULL)/6-31G* NBO Analysis of Donors and Acceptors for Main HC in 1-Substituted G3-Global Minima of Structural Isomers of XC2H4

+ Species.

X(PG) Donor Acceptor EStabilization

kcal/mol NBO Occupancy NBO Occupancy

CH3,C2(0) BD(C3-H5) 1.90063 1

*CLp 0.24815 38.15

BD(C4-H6) 1.90063 1

*CLp 0.24815 38.15

NH2,Cs(0) BD(C2-H6) 1.96489 *C-Nπ 0.05790 10.68

BD(C2-H7) 1.96489 *C-Nπ 0.05790 10.68

OH,Cs(0) BD(C2-H6) 1.95318 *C-Oπ 0.07559 13.62

BD(C2-H7) 1.95318 *C-Oπ 0.07559 13.62

SH,Cs(0) BD(C2-H6) 1.95460 *C-Sπ 0.07928 11.97

BD(C2-H7) 1.95460 *C-Sπ 0.07928 11.97

F,Cs(0) BD(C2-H6) 1.93769 *C-Fπ 0.10522 16.63

BD(C2-H7) 1.93769 *C-Fπ 0.10522 16.63

Cl,Cs(0)a BD(C2-H6) 1.93659

1

*C -Clσ 0.10673 16.19

BD(C2-H6) 1.93659 *C-Clπ 0.01280 3.64

BD(C2-H7) 1.93659 1

*C -Clσ 0.10673 16.19

BD(C2-H7) 1.93659 *C-Clπ 0.01280 3.64

a HC is Mainly with

1

*C -Clσ because is lower energy than *

C-Clπ .

The o

fΔH of +

3 3CH CHCH had been calculated to be 193.5 kcal/mol as obtained

via G3 calculations. The most recent experimental reported value is 193.1 kcal/mol [20]

.

The experimental relative energy of n-propyl cation with respect to isopropyl cation is 8

kcal/mol [20]

which is in agreement with G3 value, (Table 3).

The MP2(full)/6-31G* optimized values of key geometrical parameters of 1-

substituted global minima are shown in Figure 4. The shortness of +

C-X indicates

formation a double bond between X and C+. NBO analysis for these species indicates

also formation of C=X bond, Table 4. NBO analysis of these global minima, Table 4,

indicates that the main HC is between 2CHπ molecular orbital and *

C-Xπ bond.

However, in +

3CH CHCl , HC is between 2CHπ and

1

*

C -Clσ is more effective than that

between 2CHπ and *

C-Clπ , (Table 4).

47

X PG 1 2

aC -C

r 1 4

aC -X

r 4 1 2

aX C C

Θ

Global Minima NH2 Cs (0) 1.471 1.289 123.7 OH Cs (0) 1.452 1.270 119.5 SH Cs (0) 1.469 1.636 122.5 F Cs (0) 1.431 1.263 121.3 Cl Cs (0) 1.446 1.614 124.6

Local Minima PH2 Cs (0)

b 1.488 1.649 125.9

AsH2 Cs (0) 1.485 1.747 125.6 SeH Cs (0) 1.470 1.763 122.4 Cs (0) 1.469 1.761 129.0 Br Cs (0) 1.448 1.768 124.5 a Bond Lengths in Angstroms and Angles in Degrees.

Figure 4: MP2(full)/6-31G* Optimized Values of Key Geometrical Parameters of 1-Substituted Ethyl Cation.

+

3 2CH CHNH , +

3CH CHOH and +

3CH CHSH are protonated ethanimine, acetaldehyde and

thioacetaldehyde; respectively. The proton affinity values of these protonated species

had been calculated from their o

fΔH values, Table 3. o

fΔH values of H+ = 368.55

kcal/mol [21]

, CH3CHO = -40.8 kcal/mol [22]

, CH3CHS = 11.95 kcal/mol [23]

and

CH3CHNH = 5.74 kcal/mol [24]

. The calculated proton affinity values, according to eq.1,

are 185.5, 190.5 and 214.8 kcal/mol, for CH3CHO, CH3CHS and CH3CHNH;

respectively. The experimental proton affinity of acetaldehyde is 184.1 kcal/mol [25]

.

H3C

XH

H H3C

X

H

+ H

eq.1

Cyclic G3-Global Minima

+

2 2XCH CH , X = PH2, AsH2, SeH and Br have cyclic G3-global minima (Table 5).

However, the corresponding XCH2BH2 have 1-substituted G3-global minima [1]

. It

seems that the larger electrophilicity of C+ is the driving force for formation of cyclic

global minima in carbocations. Another factor that helps the formation of cyclic minima

is the size of X. The larger size decreases the strain energy in the formed 3-membered

ring. Consequently, cyclic structure becomes more stable than 1-substituted one.

However, the relative energies of 1-substituted isomers are between 2.5-5 kcal/mol

higher than the corresponding cyclic ones, (Table 5).

48

Table 5: Relative Energy, Erel, Values and Enthalpies of Formation of XCH2C

+H2 Cyclic G3-Global Minima, and its

Conformers and CH3C+HX, X = PH2, AsH2, SeH, and Br.

o

f ,G ( H )298

3

(kcal/mol)

Erel (kcal/mol) Species (NImag)

a

G3

MP2(FU)/ 6-31G*

B3LYP/ 6-311+G**

PH2CH2C+H2

193.76 0.00 0.00 0.00 (cyc)Cs(0) 235.77 42.01 46.87 36.37 (egg,in)Cs(1) 234.90 41.14 46.01 35.49 (egg,out)Cs(2)

CH3C+HPH2

199.07 5.31 6.56 2.14 (eX)C1(0)b

AsH2CH2C+H2

217.54 0.00 0.00 1.54 (cyc)Cs(0) 248.50 30.96 35.27 25.33 (eggin)Cs(1) 247.69 30.15 35.30 24.73 (egg,out)Cs(2)

CH3C+HAsH2

221.67 4.13 6.06 0.00 (eX)C1(0)b

SeHCH2C

+H2

190.36 0.00 0.00 0.00 (cyc)Csc(0)

216.81 26.45 30.11 24.81 (b)Csd(1)

234.91 44.55 52.09 37.40 (ea)Cs(2) 235.01 44.65 53.66 38.07 (ee)Cs(2)

CH3C+HSeH

193.54 3.18 6.34 0.46 (eXa)Cs(0) 193.54 3.17 6.57 0.45 (eXe)Cs(0)

BrCH2C+H2

207.64 0.00 0.00 0.93 (cyc)C2V(0) 239.78 32.14 31.91 25.07 (e)Cs(1)

CH3C+HBr

210.25 2.62 4.30 0.00 (eBr)Cs(0) 211.46 3.83 5.79 1.64 (eH)Cs(1)

a MP2(FULL)/6-31G*

b C1 had been done because Cs Gives one

imaginary frequency. c

XH is the plane of symmetry (X is the hetero atom).

d CCX plane is the symmetry plane(X is the hetero atom).

The MP2(full)/6-31G* optimized values of key geometrical parameters of cyclic

global minima are given in Figure 5. The shown optimized values confirm the formation

of cyclic structures.

X PG aC-C

r 21

aC -XC -X

r (r ) 2 11 2

aXC CXC C

Θ (Θ )

Global Minima PH2 Cs 1.517 1.803(1.803) 65.1(65.1) AsH2 Cs 1.510 1.914(1.914) 66.8(66.8) SeH

b Cs 1.461 2.005 68.6

Br C2V 1.454 2.026 69.0

Local Minima

NH2 Cs 1.474 1.494(1.494) 60.5(60.5)

OHb Cs 1.458 1.525 61.4

SHb Cs 1.464 1.851 66.7

F C2V 1.457 1.552 62.0

Cl C2V 1.456 1.848 66.8 a Bond Lengths in Angstroms and Angles in Degrees.

b XH is the symmetry plane.

Figure 5: MP2(full)/6-31G* Optimized Values of Key Geometrical Parameters of Cyclic Structure.

NBO analysis of cyclic global minima shows that the donor molecular orbitals for

the main HC are 1C -Xσ and

2C -Xσ , while the acceptors are 2

*

C -Xσ and 1

*

C -Xσ ;

respectively (Table 6).

49

Table 6: MP2(FULL)/6-31G* NBO Analysis of Donors and Acceptors for Main HC in XCH2C

+H2

Cyclic G3-Global Minima.

X, PG (NImag)

Donor Acceptor EStabilization

kcal/mol NBO Occupancy NBO Occupancy

PH2,Cs(0) BD(C1-P) 1.97374 2

*C -Pσ 0.02229 6.42

BD(C2-P) 1.97374 1

*C -Pσ 0.02229 6.42

AsH2,Cs(0) BD(C1-As) 1.96666 2

*C -Asσ 0.03263 7.18

BD(C2-As) 1.96666 1

*C -Asσ 0.03263 7.18

SeH,Cs(0)a BD(C1- Se) 1.93746

2

*C -Seσ 0.06059 26.16

BD(C2- Se) 1.93746 1

*C -Seσ 0.06059 26.16

Br,C2V(0) BD(C1-Br) 1.93215 2

*C -Brσ 0.06761 32.07

BD(C2-Br) 1.93215 1

*C -Brσ 0.06761 32.07

a SeH plane is the symmetry plane.

It is worth to note that as the size of X increases, the stabilization energy, Estab,

results from HC becomes larger. For example, Estab results from HC between

1C -Pσ and 2

*

C -Pσ is 6.42 kcal/mol, while for Br substituent, Estab value is 32.07 kcal/mol,

(Table 6).

Carbenes Intermediates

When X substituent is an element of groups I, II and III, there is only one

minimum, π-bridged. However, the isomers that have higher energies than the global

minima but lower than other isomers are 1-substituted isomer,+

3CH CHX , Table 1. When

X = Li, Na, K, MgH and CaH, 1-substituted isomers look-like carbenes.

The MP2(full)/6-31G* optimized values of key geometrical parameters of singlet

carbene, ••

3CH CH , are shown in Figure 6.

ecl, Cs(1)

anti, Cs(1)

1 3C -Hr = °1.109A

C-Cr = °1.483A

3CCHΘ = °107.9

1 3C -Hr = °1.110A

C-Cr = °1.482A

3CCHΘ = °104.4

Figure 6: MP2(full)/6-31G* Optimized Values of Key Geometrical Parameters of Methylcarbene.

50

The singlet state was chosen because the resulted carbenes from MP2(full)/6-

31G* optimizations of 1-substituted species are singlet carbene. The main HC in

parent carbene is between 2CHπ and *Lp on methyne carbon (Table 7).

Table 7: MP2(FULL)/6-31G* NBO Analysis of Donors and Acceptors for Main HC in Carbenes Formed upon Optimization of CH3CH and CH3C

+HX Where X = Li, Na, K, MgH and CaH.

X, PG (NImag)

a

Donor Acceptor EStabilization kcal/mol NBO Occupancy NBO Occupancy

CH3C(1)H

anti,Cs(1)b BD(C2-H5) 1.97187

1

*CLp 0.05285 10.43

BD(C2-H6) 1.97187 1

*CLp 0.05285 10.43

1CLp 1.97486

2 3

*C -Hσ 0.01982 2.70

1CLp 1.97486

2 5

*C -Hσ 0.00891 3.27

1CLp 1.97486 2 6

*C -Hσ 0.00891 3.27

ecl,Cs(1)c BD(C2-H5) 1.96739

1

*CLp 0.05843 11.47

BD(C2-H6) 1.96739 1

*CLp 0.05843 11.47

1CLp 1.97281 2 3

*C -Hσ 0.02579 12.08

Li,e,Cs(1) BD(C2-H6) 1.94999 1

*CLp 0.09406 16.49

BD(C2-H7) 1.94999 1

*CLp 0.09406 16.49

1CLp 1.93756 *

LiLp 0.04572 19.42

Na,e,Cs(1) BD(C2-H6) 1.95435 1

*CLp 0.08574 15.33

BD(C2-H7) 1.95435 1

*CLp 0.08574 15.33

1CLp 1.94596 *NaLp 0.03675 12.04

K,e,Cs(1) BD(C2-H6) 1.95855 1

*CLp 0.07790 14.16

BD(C2-H7) 1.95855 1

*CLp 0.07790 14.16

1CLp 1.96230 *

KLp 0.01865 5.64

MgH,e,Cs(1) BD(C2-H6) 1.93841 1

*CLp 0.11556 19.48

BD(C2-H7) 1.93841 1

*CLp 0.11556 19.48

1CLp 1.85218 *

Mg-Hσ 0.11275 45.02

CaH,e,Cs(1) BD(C2-H6) 1.94759 1

*CLp 0.09876 17.07

BD(C2-H7) 1.94759 1

*CLp 0.09876 17.07

1CLp 1.92131 *

Ca-Hσ 0.04858 17.01

a In all CH3CHX

+ studied species, X is eclipsed with one hydrogen of the CH3 group.

b The hydrogen on C1 is anti to one hydrogen of the CH3 group.

c The hydrogen on

C1 is eclipsed with one hydrogen of the CH3 group.

51

The MP2(full)/6-31G* optimized values of geometrical parameters of resulted

carbenes from +

3CH CHX are shown in Figure 7.

X PG 1 2

aC -C

r 11

aC -XC -H

r (r ) 1 21 2

aXC CHC C

Θ (Θ )

Li Cs(1) 1.452 1.098(2.147) 108.9(130.4) Na Cs(1) 1.456 1.100(2.499) 107.9(132.0) K Cs(1) 1.461 1.102(2.939) 106.7(132.5) MgH Cs(1) 1.441 1.097(2.257) 117.3(129.4) CaH Cs(1) 1.450 1.099(2.714) 108.3(129.8) a Bond Lengths in Angstroms and Angles in Degrees.

Figure 7: MP2(full)/6-31G* Optimized Values of key Geometrical Parameters of Substituted Methylcarbene.

Their geometries are similar to those of parent carbenes but with shorter C-C

bonds. NBO analysis shows that the C-C bond length is directly proportional to the

occupancy of the nonbonding MO on C (1CLp ). As the population of

1CLp decreases,

C-Cr length decreases. For example, 1CLp occupancy in

3CH CH(anti) and +

3CH CHMgH is

1.97486 and 1.85218; respectively, Table 7. This means that there are more

hyperconjugation from 2CHπ to

1

*

CLp in +

3CH CHMgH species which leads to longer C-Hr

and shorter C-Cr bond, Figures 6 and 7.

Although 3CH CH

and X are electron-deficient species, NBO analysis show

existence of HC between the two species. Separation energies that are required for a

complete separation between the two species, calculated according to eq.2, are

present in Table 8.

•• + ••+

3 3CH CHX CH CH+X eq.2

Table 8: Separation Energy, ESeparation,

Values for + ••

+

3 3CH CHX CH CH+X

Species G3-enthalpy Eseparation

(kcal/mol) ••

3CH CH (anti) -78.383723

Li+ -7.264432 43.47

Na+ -161.913872 32.29

K+ -599.565858 22.61

MgH+ -200.194259 62.65

CaH+ -677.723881 38.33

G3-Local Minima for GP IV

The structure of n-propyl cation is C-bridged as shown in Figure 8. One of the

hydrogen that is bonded to bridged carbon is eclipsed with 1 2C -C bond. The G3

calculated o

fΔH , of this species is 201.5 kcal/mol, which correlate well with the reported

experimental value, 201.1 kcal/mol [20]

.

52

Cs

1 2C -Cr = o1.391A

2 3C -Cr = o1.791A

1 3C -Cr = o1.706A

1 2 3C C CΘ = o63.4

2 1 3C C CΘ = o69.8

Figure 8: MP2(full)/6-31G* Optimized Values of key Geometrical Parameters of n-Propyl Cation.

NBO analysis shows that this species is composed of two units: 2 4C H and

3CH .

The occupancies of the p-orbitals on C1 and C2 are 0.56764 and 0.73054; respectively,

while the occupancy of sp3 orbital on C3 is 0.83735. Overlapping of these three

molecular orbitals produces a 3-centers-2-electrons bond.

The results, Table 3, indicate presence of a species which have lower energy

(0.4 kcal/mol) than the C-bridged species, with one imaginary frequency. NBO analysis

shows that this species is a corner-protonated cyclopropane, as suggested by Hudson

et al [3]

. It is a transition state for dissociation of isopropyl cation to allylic cation and

H2[3]

.

The G3-local minima of +

2 4XC H is 1-substituted species when X is either SiH3 or

GeH3, Table 1. The structures of these local minima are shown in Figure 9. The

electropositivity of SiH3 and GeH3 increases the electrophilicity of C+. To compensate

the electron deficiency on C+, one of the hydrogens of the methyl group makes a

bridge with C+; Figure 9 This type of bridging is not observed in isopropyl cation. It is

worth to note that this type of bridging is not formed in B3LYP/6-311+G** calculations.

3SiH 3GeH

1 2C -Cr = o1.390A o1.388A

1C -Xr = o1.947A o1.999A

1 (bridged)C -Hr = o1.327A o1.323A

2 (bridged)C -Hr = o1.278A o1.281A

1 2XC CΘ = o125.8 o125.8

(bridged) 1 2H C CΘ = o56.1 o56.4

(bridged) 2 1H C CΘ = o59.5 o59.3

Figure 9: MP2(full)/6-31G* Optimized Values of key Geometrical Parameters of 1-Substituted Ethyl Cation, where X = SiH3 and GeH3.

53

1-Substituted G3-Local Minima

+

3 2CH CHPH ,+

3 2CH CHAsH , +

3CH CHSeH and +

3CH CHBr are local minima for +

2 4XC H

structural isomers. As previously discussed in 1-substitiuted G3-global minima, NBO

analysis indicates formation of a π-bond between C+ and X-substituent. The

MP2(full)/6-31G* optimized values of key geometrical parameters of these local

minima are shown in Figure 4.

Cyclic G3-Local Minima

+

2 2XCH CH has cyclic local minima when X =2

NH , OH, SH, F and Cl. To form

cyclic structure, an additive bond is formed between X and C+ atom. However, X

substituents have relatively small sizes; strain energies are expected to be relatively

large. Consequently, cyclic structure is a local rather than a global minimum. The

MP2(full)/6-31G* optimized key geometrical parameter values confirm the formation of

3-membered rings (Figure 5).

Comparison between +

2 4XC H and 4

XCH B Global Minima

To demonstrate the importance of the effect of the electronegativity of C+ on the

structures of the global minima, it is necessary to make a general comparison between

+

2 4XC H and 4XCH B global minima. When X is a methyl group,

3 3H CCHCH

and

3 3H CBHCH are the global minima due to the fact that both C+ and B are electron-

deficient centers while methyl is an electron-donating group in these species.

When X is an element of either groups V, VI or VII, 3

H CBHX are the global

minima due to the formation of the dative bond between X and B atom. This factor

works in substituted ethyl cation isomers only when X has a small size and it is a

strong base, X = NH2, OH, SH, F and Cl. For larger size and weaker base substituents,

X = PH2, AsH2, SeH and Br, the hyperconjugation between C X and the empty P-

orbital on C+ produces more stabilization energies than the formation of the dative-

bond. Consequently, cyclic structures are the global minima rather than 1-substituted

isomers. As had been previously discussed, the larger size of PH2, AsH2, SeH and Br

decreases the strain energies of the formed three-membered rings. In case of borane

compounds, it seems that the hyperconjugation between C X with PB produces less

stabilization energies than the formation of the dative-bond. Consequently, CH3BHX

are the global minima for all elements of groups V, VI and VII. The above discussion

confirms the importance of the electronegativity of C+. This factor decreases the

energy gap between C X and C

P which makes the hyperconjugation between these

interacting orbitals is more effective and important in determining the structures of the

global minima.

54

The electronegativity of C+ is behind the formation of π-bridged global minimum

with less electropositive substituents, X = group III, SiH3 and GeH3, where bisected

structures are the global minima in case of borane. The electropositivity of C+

leads to

stronger hyperconjugation between C X and *

CLp

as had been previously discussed.

This strong hyperconjugation leads to the formation of π-bridged rather than bisected

in case of substituted ethyl cations.

Conclusion

To summarize, the global minima for +

2 4XC H structural isomers are π-bridged, 1-

substituted and cyclic. Electropositive X gives π-bridged global minimum. 3

CH and

small size X with at least one electron-pair gives 1-substituted global minimum. Larger

size X with electron-pairs gives cyclic structure as global minimum. The stability of the

π-bridged is due to the formation of a π-bond between the two carbons. The stability of

1-substituted isomers arises from the dative bond between X and *

CLp

. The

hyperconjugation between C X and *

CLp

is responsible for the stability of the cyclic

global minima.

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