Jordan Journal of Chemistry Vol. 3 No.4, 2008, pp. 389-407

JJC

PES of C4H9+ Structural Isomers and Determination of the Global

Minima of XC3H6+ (X = Li to Br) via G3 Calculations

Mustafa R. Helal*, Akef T. Afaneh

Department of Chemistry, Yarmouk University, Irbid, Jordan

Received on July 30, 2008 Accepted on Oct. 22, 2008

Abstract

Three levels of theory, B3LYP/6-311+G**, MP2(full)/6-31G* and G3, had been used to

elucidate the energetic and structural relationships of XC3H6+ (X = Li to Br) isomers. The B3LYP

calculations had been replaced by MP4(SDTQ)/6-31G(d,p)//MP2(full)/6-31G(d) in the

determination of the potential energy surfaces, PES, for C4H9+ structural isomers. This had been

done to facilitate the comparison with the available published data. The relative stabilities of local

minima had been calculated. Enthalpies of formation, ∆ 298of,H , had been also determined via G3

method. Comparison of the calculated ∆ 298of,H values with the available experimental data

reveals an excellent correlation between the two sets. The obtained XC3H6+ global minima had

been compared with those of XC2H4+ and 4XCH B and the differences had been justified.

Keywords: Structural isomers; π-Bridged global minima; Cyclic global minima;

Bisected global minima; XC3H6+ (X = Li to Br); PES of C4H9

+.

Introduction The stability of the reactive intermediates in organic reactions is very important

to understand the reaction mechanisms and the structures of the products [1].

Carbocations are one the most important reactive intermediates in organic reactions.

The existence, structures, stabilities, reactivities and rearrangements of carbocations

had been experimentally and theoretically studied [1]. In recent studies [2, 3] the global

minima of substituted ethyl cations and methylboranes had been determined as

shown below.

X

CH3CH-X

X

π-Bridged

X = Groups I, II, III, SiH3 and GeH3 α-Substituted

X = CH3, NH2, OH, SH, F and Cl Cyclic

X = PH2, AsH2, SeH and Br

BH2

X

H3CBHX

C B

X

H HH

H

π-Bridged

X = Groups I and II

α-Substituted X = CH3 and Groups V, VI and

VII

Bisected X = Group III, SiH3 and GeH3

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

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The similarities and the differences between the global minima of substituted

ethyl cations and methylboranes could be attributed to the energy gap value, ∆E,

between σC-X and the empty p-orbital on the electron-deficient centers, CLP +∗ , or BLP∗ .

The higher electronegative electron-deficient center has the lower energy p-orbital.

Cationic carbon, C+, is more electronegative than B atom. MP2(full)/6-31G* energy

values of CLP +∗ and BLP∗ in H3CC+H2 and 3 2H CBH are -5.4 and +5.6 ev [4]; respectively.

The higher electronegative substituent X has the lower energy σC-X. This means that

the largest energy gap is between σC-F and BLP∗ . It should be noted that the most

electropositive X is considered as the weakest electronegative. According to the above

results[2,3], the studied substituents could be classified as follows: strong electropositive

substituents, Groups I and II, weak electropositive substituents, Group III, SiH3 and

GeH3, strong basic substituents, NH2, OH, SH, F and Cl, and weak basic substituents,

PH2, AsH2, SeH and Br. Methyl group acts as a strong base.

Let us suppose that XCH2CH2+ and XCH2BH2 exist in bisected structures. The

HC in a bisected structure is usually between σC-X and CLP +∗ or BLP∗ . This type of HC

makes σC-X bond longer while makes C C+−σ and σC-B bonds shorter. For strong

electropositive substituent X, the energy gap values are relatively small either in

XCH2CH2+ or XCH2BH2. Consequently, the HC is strong to the extent that leaving X

not bonded to C and leaving a negative charge on C. This negative charge is parallel

to CLP +∗ and BLP∗ forming π-bond. For weak electropositive X, the HC is stronger in

XCH2CH2+ leading to the formation of a π-bond, but it is not the case in XCH2BH2

which has weaker HC. Thus, XCH2BH2 species give bisected structure as global

minimum when X is a weak electropositive.

For basic X, either strong or weak, the HC is relatively small in XCH2BH2 species

because the energy gap is large. Therefore, the HC in bisected structure produces

small stabilization energy. However, the formation of a dative bond between X and B

atom produces higher stabilization energy. Consequently, CH3BHX is formed as global

minimum. Similar trend appears in XC2H4+ when X is a strong base. For weak basic X,

the energy gap is smaller and the HC produces stabilization energy more than the

formation of a dative bond. Thus, bisected structure is more stable than α-substituted.

However, the basicity of X enforces the bisected to collapse to cyclic structure.

To ensure the importance of the electrophilicity of the electron-deficient center in

gas phase, the present study is initiated. XCH2C+HCH3 and CH3C+XCH3 structural

isomers will be investigated. It is known that secondary C+ is less electrophilic than

primary C+ but stronger than B. Therefore, the structures of the global minima of 1-

substituted and 2-substituted isopropyl cation (X = Li to Br) would be theoretically

determined to check the effect of electrophilicity of secondary C+ and to cover the

deficiency in literature about 2-substituted cations.

391

Large attention had been paid to 1-substituted species [6-11], while little attention

had been given to 2-substituted species. These intermediates could be produced by

protonation of 2-substituted propenes, especially, when X has at least one lone pair of

electrons. These intermediates are facile to hydrolysis when X is a methoxy or an

amine group to give ketones [12].

The second purpose is the determination of the potential energy surface (PES)

for C4H9+ via G3 calculations. The last purpose of the present study is to determine the

enthalpies of formation, ofH∆ , of these intermediates. Comparison with published data

would be done.

Computational Details The computations have been carried out using Gaussian 03 program package,

version D.01 [13]. All species are fully geometry optimized at MP2(full)/6-31G(d) and

B3LYP/6-311+G(d,p) levels of theory. G3 energies for K to Br species were calculated

via a procedure described in Ref. 3.

Relaxed potential energy surface (PES) scans are carried out at MP2(full)/6-

31G(d) level to determine the stationary points then quadratic synchronous transit

algorithm (QST) [14] was further carried out at MP2(full)/6-31G(d) level to confirm the

transition states connect the right minima of C4H9+ molecular formula. The

MP4(SDTQ)/6-31G(d,P)//MP2(full)/6-31G(d) energies have been calculated for the

minima and transition states of C4H9+ molecular formula for comparison reason with

the published data.

RHF/6-31G(d) zero-point vibrational energy values had been scaled by 0.8929

factor for all the studied species in the present work. Natural bond orbital, NBO,

analysis had been done at MP2(full)/6-31G(d) level of theory. The uncorrected and

ZPE corrected ab initio energies, ZPE values, are present within the supporting data,

except for C4H9+ isomers. The data for these isomers are present in the text.

Results and Discussion The results indicate that the global minima of the structural isomers of XC3H6

+

are either α- or β-substituted, depending on the position of X in the periodic table.

When X is a methyl group, α-substituted, (CH3)3C+, structural isomer is the global

minimum. The structural isomers of C4H9+ (XC3H6

+; X = CH3) would be discussed first

because this system had been subjected to large number of studies with high basis set

levels but not G3 [15-19].

C4H9+ Minima

The corrected ab initio energies and the G3 enthalpy of formation, ofH∆ , values

of C4H9+ minima and transition states are presented in Table 1 while the relative

energy, Erel, values of C4H9+ minima are given in Table 2. The MP2(full)/6-31G(d)

optimized values of essential key geometrical parameters of these minima are shown

in Figure 1. The results indicate that the tert-butyl cation, M1, is the most stable

structural isomer. It is worth noting that using higher symmetry for M1 such as, C3v,

392

C3h and Cs gives one imaginary frequency. The lowest symmetry, C1, gives also one

imaginary frequency when the carbon skeleton is planar. Removing the planarity, C1

symmetry gives no imaginary frequency. ӨC6C1C4C2 Dihedral angle is 178.2o. The

stability of M1 is due to the HC between three σC-H bonds and CLP +∗ , as shown by NBO

analysis. Its G3 ofH∆ value is 171.0 kcal/mol, Table 1. This value excellently correlates

with the experimental value which is 170.1 kcal/mol [15]. The key optimized geometrical

parameters are shown in Figure 1. They are similar to those reported in Ref 16.

2-Butyl cation is the second stable minimum. Carneiro and Schleyer [17] reported

that it exists in two structures: methyl- and H-bridged structures, M2 and M3;

respectively. They reported that H-bridged is more stable than methyl-bridged at high

basis set level using correlation methods. In the present work another minimum is

found which is H-bisected, M4, structure, Table 1. The key optimized geometrical

parameters of the three minima are shown in Figure 1. The G3 ofH∆ value of H-

bridged minimum is 183.3 kcal/mol, Table 1. This value is almost the same as the

reported experimental one, 183.0 kcal/mol [18]. The G3 stability of H-bridged over

methyl-bridged is 0.8 kcal/mol, Table 1. The corresponding value obtained by Carneiro

and Schleyer is 0.3 kcal/mol at MP4(SDTQ)/6-311G(d,p)//MP2(full)/6-31G(d,p) [17].

Table 1: Corrected Ab Initio Energies of C4H9+ Structural Isomers Minima and

Transition States.

Species, Point Group

(NImag)

Ea(a.u.)

2983 of,G ( H )∆

kcal/mol MP2(FULL)/

6-31G*

MP4(SDTQ)/ 6-31G**//

MP2(FULL)/ 6-31G*

G3 (Enthalpy)

M1,C1(0) -156.84797 -156.96938 -157.35545 171.0 M2,C1(0) -156.82893 -156.94870 -157.33453 184.1 M3,C1(0) -156.82674 -156.94927 -157.33579 183.3 M4,C1(0) -156.82380 -156.94629 -157.33263 185.3 M5,C1(0) -156.78868 -156.91338 -157.30072 205.3 M6,C1(0) -156.81510 -156.93473 -157.32066 192.8 TS1,C1(1) -156.81441 -156.93490 -157.32084 192.7 TS2,C1(1) -156.82225 -156.94455 -157.33096 186.4 TS3,C1(1) -156.79378 -156.91681 -157.30304 203.9 TS4,C1(1) -156.78963 -156.912972 -157.29946 206.1 TS5,C1(1) -156.78375 -156.908594 -157.29612 208.2 TS6,C1(1) -156.81460 -156.93406 -157.32091 192.7 TS7,C1(1) -156.80772 -156.92770 -157.31391 197.1 UH,C1(0)a -156.81393 -156.93428 -157.32013 193.2 TS9,C1(1) -156.81465 -156.93509 -157.32106 192.6

a It is Up-Hill point.

393

Table 2: Relative Energy, Erel, Values of C4H9+ Structural Isomers Minima.

Species, Point Group

(NImag)

Erel(kcal/mol)

MP2(FULL)/ 6-31G*

MP4(SDTQ)/ 6-31G**//

MP2(FULL)/ 6-31G*

G3

M1, C1(0) 0.00 0.00 0.00 M2, C1(0) 11.94 12.98 13.13 M3, C1(0) 13.32 12.62 12.33 M4, C1(0) 15.17 14.49 14.32 M5, C1(0) 37.21 35.14 34.34 M6, C1(0) 20.63 21.74 21.83

ФC4C3C5 = 57.1o

tert-Butyl Cation, Species M1 Methyl-Bridged, Species M2

H-Bridged, Species M3 H-Bisected, Species M4

ӨCCCC = -87.1o (115.2o)

Cyclic 1-Butyl Cation, Species M5 Ethyl-Bridged, Species M6

Figure 1: MP2(full)/6-31G(d) Optimized Structures of the C H+4 9 isomers M1-M6.

The least stable structural isomer of C4H9+ is 1-butyl cation. It exists in two

minimal forms: cyclic 1-butyl cation, M5, and ethyl-bridged, M6, structures, Figure 1.

M5 has bridged hydrogen between the terminal carbons. M6 is more stable than M5 by

394

12.5 kcal/mol as obtained by G3 calculations, Table 2. The G3 ofH∆ of M5 and M6 are

205.3 and 192.8 kcal/mol, Table 1; respectively. The reported experimental value of

1-butyl cation is 201.9±3 kcal/mol [19]. G3 ofH∆ value is within the experimental range

when the uncertainty is included. The key optimized geometrical parameters of both

minima are shown, Figure 1.

Transition States of 2-butyl Cation

2-Butyl cation has three transition states (TS), Figure 2 and Table 3. In their

investigation of C-branching mechanisms in 2-butyl and sec-pentyl cations, Boronat,

Vireula and Comaro discussed two transition states for 2-butyl cation, TS1 and TS3[20].

TS1 is used to explain C-scrambling in M2, Reaction 1, while TS3 is used to explain

the rearrangement of M2 to M1, reaction 2 [20]. The mechanisms of both reactions are

discussed in Ref 20.

Edge-Protonated, TS1 Classical Cation, TS2 Isobutyl, TS3

ӨC1C2C6H11=19.7o

Open-Chain, TS4 Cyclic, TS5 Perpendicular, TS6

rC1-C2=1.854 Ẵ Parallel, TS7 Up-Hill point, UH Edged-bridged, TS9

Figure 2: MP2(full)/6-31G(d) Optimized Structures of the C H4 9+ isomers TS1-TS9.

395

Table 3: Activation Energy, Eact, values of C4H9+ transition states.

Species, point group

(NImag)

Eact(kcal/mol)a

MP2(FULL)/ 6-31G*

MP4(SDTQ)/ 6-31G**//

MP2(FULL)/ 6-31G*

G3 (Enthalpy)

M2, C1(1) 0.0 0.0 0.0 TS1 9.1(8.9) 8.7(8.4) 8.6 TS2 4.2(4.6) 2.6(3.0) 2.2 TS3 22.1(22.6) 20.0(20.6) 19.8

M5, C1(0) 0.0 0.0 0.0 TS4 -0.6(0.2) 0.3(1.1) 0.8 TS5 3.1(3.1) 3.0(3.0) 2.9

M6, C1(0) 0.0 0.0 0.0 TS7 4.6(4.5) 4.4(4.2) 4.2 UH 0.7(1.0) 0.3(0.6) 0.3 TS9 0.3(0.8) -0.2(0.3) -0.3

a Out of brackets values are those obtained from ZPE corrected energies while values in brackets are obtained from uncorrected energies.

C4 C5

C3

CH3H

H H11

H

HH

C3

C4 C5

H11

HH3C

H HH H

Migration of H11to C4 C4 C5

C3

H

H11 H

H

H

H

CH3

rexn(1)

M2 TS1 M2

Migration ofC5 to C3

Migration ofH from C3 to C4

CH3

C

H3C CH3

C3 C4

H

H

H3C

HH3C

C4 C5

C3

CH3H

H H11

H

HH

rexn(2)

M2 TS3 M1

The experimental value of Eact of reactions 1 and 2 are 7.5 and 18.0 kcal/mol as

reported in Ref 20. The uncorrected MP4(SDTQ)/6-31G(d,p) using MP2(full)/6-31G(d)

optimized geometry give that Eact energy values of reactions 1 and 2 are 8.4 and 20.6

kcal/mol [20]. The corresponding G3 values are 8.6 and 19.8 kcal/mol, Table 3. The

ZPE corrected MP4(SDTQ) energies give that Eact values are 8.7 and 20.0 kcal/mol,

Table 3. The results of both methods are approximately equivalent but G3 values are

slightly closer to the experimental values.

The structure of the third TS of 2-butyl cation, TS2, is the classical 2-butyl cation.

It is a transition state for the isomerization of M2 minimum to M3 minimum, reaction 3.

Widening ofC3C4C5 angle

77.4o CH3

C3

C4

C5

H

H

HH

H

H

111.2o

C4 C5

C3

CH3H

H H11

H

HH

M2 TS2 rexn(3)

Widening of C3C4C5angle continues to

be 124.9oC3 C4

H

H3C H

HCH3

TS2

M3

396

TS2 is formed by widening of C3C4C5 angle from 77.4o to 111.2o. In M3, C3C4C5

angle is 124.9o, and then one of the hydrogens on C4 becomes bridged between C3

and C4. The G3 Eact of this reaction is 2.2 kcal/mol, Table 3. This means that this

isomerization is possible at room temperature. The corresponding MP4(SDTQ) and

MP2(full) are 2.6 and 4.2 kcal/mol; respectively. Thus, the MP2(full) value is much

higher than those obtained by MP4(SDTQ) and G3 calculations.

Transition States of Cyclic 1-Butyl Cation

Cyclic 1-butyl cation minimum, M5, has two transition states: open-chain, TS4,

and symmetrical cyclic, TS5, Figure 2. TS4 can optimize to either M2 or M3, reaction 4.

The G3 Eact value for reaction 4 is 0.8 kcal/mol, Table 3. The corresponding

MP4(SDTQ) value is 0.3 kcal/mol, Table 3. Therefore, reaction 4 is smoothly taking

place at room temperature. It is known that the first reaction of primary cations is their

rearrangement to more stable ones [21]. It seems that increasing the correlation in the

method used would increase the stability of M5. Thus, MP2(full) which has the lowest

correlation among the other methods, G3 and MP4(SDTQ), gives a negative Eact

value, -0.6 kcal/mol, Table 3.

C6

H11

C4 Migration H11 to C6

M5

CH3CH2CHCH2Migration of H10to cationic carbon M2 or M3

TS4

H10

rexn(4)

TS5 is a TS for the rearrangement of M5 to M6. M5 is puckered while TS5 is

symmetrical planar. TS5 rearranges to M6 via migration of H11 either to C4 or C6 and

cleavage of C1-C2 bond with rotation of H3C-CH2 unit, reaction 5. G3 Eact value of this

reaction is 2.9 kcal/mol, Table 3. Eact arises from H//H eclipsing interaction. This means

that 1-butyl cation exists almost in ethyl-bridged structure, M6, rather than M5 due to

the low Eact value. For example, conformation of ethane activation energy is 3.0

kcal/mol [22], and it is taking place at room temperature. C2

C6

H11

C4

C1

Migration H11 to C6and C1-C2 cleavage

M5

C2

C6

H11

C4

C1

TS5

M6

rexn(5)

Transition States of Ethyl-Bridged

Ethyl-bridged minimum, M6, forms two transition states: parallel, TS7, and

edged-bridged TS9, Figure 2. The key geometrical parameters of both transition states

are shown in Figure 2. Both transition states form either methyl- or H -bridged

minimum, M2 or M3; respectively. TS7 is formed by rotation of ethyl unit to become

parallel to H2C=CH2 unit. The G3 Eact for the formation of TS7 is 4.2 kcal/mol, Table 3.

TS9 is formed by bridging of H3 (Figure 2) between C1 and C2. Eact for formation of TS9

is 0.3 kcal/mol in MP2(full)/6-31G* calculations. MP4(SDTQ) and G3 methods give

slightly negative values, -0.2 and -0.3 kcal/mol; respectively, Table 3. TS9 is four

397

membered ring. Increasing the correlation in the method would overestimate the

stability of TS9. Thus, MP4(SDTQ) and G3 give negative values for the Eact. Another

possible reason for negative value of Eact is that TS9 is not formed directly from the

M6. It is really formed from an Up-Hill, UH, point, which is less stable than M6 by 0.3

kcal/mol, as obtained from G3 calculation, Table 3. This UH point forms TS9 by

lengthening C2-H3 bond and shortening C1-H3 bond, without Eact. Migration of H3 to C1

produces 2-butyl cation minimum which exists in two conformers: H-bridged or methyl-

bridged. Thus, ethyl-bridged minimum, M6, rearranges to 2-butyl cation through two

possible transition states: TS7 with Eact of 4.2 kcal/mol and TS9 with almost zero Eact.

Consequently, the second route is mainly followed.

TS6 is symmetrical ethyl-bridged, Figure 2. The C5C2C4C1 and C5C2C1C4 are

-87.1o and 115.2o in M6. The corresponding values are -90.0o and 90.0o, which can go

to the M6 in which the C5C2C4C1 and C5C2C1C4 are -115.2o and 87.1o. Eact value for

formation of TS6 is almost zero in G3 calculations and 0.3-0.4 kcal/mol in MP2 and

MP4(SDTQ) methods, Table 2.

Groups I, II, III and IV Results

In this part of discussion, referring to group IV means SiH3 and GeH3 only

because methyl group had been previously discussed. The β-substituted species,

XCH2C+HCH3, is a global minimum, Table 4, when X is an element of groups I, II, III

and IV, while α-substituted species, (CH3)2C+X is a local minimum.

Table 4: Relative Energy, Erel, Values and Enthalpies of Formation of Minimal

XC3H6+Structural Isomers where X= Groups I, II, III and IV.

2983 of,G ( H )∆

(kcal/mol)

Erel (kcal/mol)

Species(NImag)a

G3 Enthalpy(a.u.)

MP2(FU)/6-31G*

B3LYP/6-311+G**

LiCH2C+HCH3

143.7 0.00 0.00 0.00 π-bridged,C1(0)

187.7 44.0 47.0 40.2 (CH3)2C+Li,C1,(0)

NaCH2C+HCH3

131.3 0.00 0.00 0.00 π-bridged,C1(0)

180.8 49.5 52.4 45.3 (CH3)2C+Na,C1,(0)

KCH2C+HCH3

114.7 0.00 0.00 0.00 π-bridged,C1(0)

168.7 54.0 57.2 50.2 (CH3)2C+K,C1,(0)

BeHCH2C+HCH3

208.6 0.00 0.00 0.00 π-bridged,C1(0)

232.8 24.2 26.0 21.5 (CH3)2C+BeH,Cs,(1)b

MgHCH2C+HCH3

185.8 0.00 0.00 0.00 π-bridged,C1(0)

222.9 37.2 39.0 33.2 (CH3)2C+MgH,Cs,(0)

CaHCH2C+HCH3

172.2 0.00 0.00 0.00 π-bridged,C1(0)

220.6 48.4 48.0 41.7 (CH3)2C+CaH,Cs,(0)

BH2CH2C+HCH3

398

2983 of,G ( H )∆

(kcal/mol)

Erel (kcal/mol)

Species(NImag)a

G3 Enthalpy(a.u.)

MP2(FU)/6-31G*

B3LYP/6-311+G**

204.5 0.0 0.0 0.0 b, C1,(0)

206.2 1.7 2.6 -0.8 (CH3)2CBH2+,C1,(0)

AlH2CH2C+HCH3

193.2 0.00 0.00 0.00 π-bridged,C1(0)

218.7 25.5 27.5 22.4 (CH3)2C+AlH2,C1,(0)

GaH2CH2C+HCH3

196.7 0.00 0.00 0.00 π-bridged,C1(0)

223.5 26.8 27.9 23.0 (CH3)2C+GaH2,C1,(0)

H3SiCH2C+HCH3

185.6 0.00 0.00 0.00 π-bridged, C1,(0)

200.4 14.8 16.4 12.1 (CH3)2C+SiH3,C1,(0)

H3GeCH2C+HCH3

195.2 0.00 0.00 0.00 π-bridged, C1,(0)

213.9 18.7 20.5 15.5 (CH3)2C+GeH3,C1,(0) a MP2(FULL)/6-31G. b NImag = 0 in RHF/6-31G*.

β-Substituted Global Minima

These minima have two types of structures: π-bridged and bisected structures.

BH2CH2C+HCH3 species is the only one of this class has bisected structure, Figure 3.

For comparison between π-bridged and bisected structures, KCH2C+HCH3 global

minimum is taken as an example of π-bridged, Figure 3.

π-Bridged Bisected

Figure 3 The main difference between the two structures is the shortness of H2C-C+H

bond in the π-bridged and its value is closer to the double bond length (experimental

C=C bond length is 1.339A [5]). MP2(full)/6-31G(d) NBO analysis indicates the

formation of a π-bond between methylene and cationic carbon, in the π-bridged

structure, Table 5.

399

Table 5: MP2(FULL)/6-31G* NBO Analysis of Donors and Acceptors for Main HC in

π-Bridged G3-Global Minima, XCH2C+HCH3.

X(PG) Donor Acceptor Estab

(kcal/mol) NBO Occupancy NBO Occupancy Li, C1(0) BD(C=C) 1.95772 LP*(Li) 0.03174 14.04

Na, C1(0) BD(C=C) 1.96545 LP*(Na) 0.02320 9.19 K, C1(0) BD(C=C) 1.97554 LP*(K) 0.01167 4.50

BeH, C1(0) BD(C=C) 1.83490 BD*(Be-H) 0.08344 26.41 MgH, C1(0) BD(C=C) 1.88499 BD*(Mg-H) 0.08472 25.39 CaH, C1(0) BD(C=C) 1.94521 BD*(Ca-H) 0.03412 8.62 AlH2, C1(0) BD(C=C) 1.79462 LP*(Al) 0.16678 82.29

GaH2, C1(0) BD(C=C) 1.76813 LP*(Ga) 0.18861 88.57 SiH3, C1(0) BD(C=C) 1.64186 LP*(Si) 0.34827 218.10

GeH3, C1(0) BD(C=C) 1.63129 LP*(Ge) 0.34890 200.14

In the bisected structure, NBO analysis does not show formation of a π-bond,Table 6.

In the π-bridged, π-electrons are donated to the empty p-orbital on X except when

X = BeH, MgH and CaH where the donation is to the σ*X-H, Table 5. In the bisected

structures, the HC is between σC-X and the empty p-orbital on cationic carbon.

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

Bisected 2-Substituted G3-Global and -Local Minima XCH2C+HCH3.

X Donor Acceptor Estab

(kcal/mol) NBO Occupancy NBO Occupancy Global Minima

BH2 BD(C2-B) 1.67248 LP*(C1) 0.47623 167.76 AsH2(g,in) BD(C2-As) 1.59010 LP*(C1) 0.61670 180.95

Local Minima PH2 BD(C2-P) 1.97184 LP*(C1) 0.64652 159.93

AsH2(g,out) BD*(C2-As) 0.56597 LP*(As) 0.55149 689.83 LPC1 0.87396 BD*(C2-As) 0.56597 954.16 LPC1 0.87396 LP*(As) 0.55149 743.74

The MP2(full)/6-31G(d) optimized values of essential key geometrical

parameters of all π-bridged minima are given in Figure 4. As the occupancy of πC=C

molecular orbital, MO, decreases, the C=C bond length becomes longer and more

EStab is produced. For example, the occupancy of πC=C MO in LiCH2C+HCH3 is 1.95772,

πC=C bond length is 1.353A and EStab is 14 kcal/mol. The corresponding values in

GeH3CH2C+HCH3 are 1.63129, 1.375A and 200 kcal/mol, Table 5 and Figure 4. The

πC=C length is still shorter than that of the bisected BH2CH2C+HCH3 where H2C-C+H

bond length is 1.388A, Figure 3. The HC in bisected BH2CH2C+HCH3 is responsible for

the shortness of C-C+ bond because CLP +∗ becomes occupied with π-electrons via HC.

X(PG) ( )1 2 1 4− −a

C C C Cr r ( )aC X C Xr r− −1 3 2 3 a

X C C (X C C )Φ3 2 1 3 1 2

Li, C1 1.353(1.497) 2.486(2.273) 82.3 (65.0) Na, C1 1.350(1.498) 2.804(2.641) 82.5(69.0)

K, C1 1.345(1.499) 3.244(3.111) 83.4(72.3) BeH, C1 1.372(1.478) 2.286(1.827) 90.0(53.1) MgH, C1 1.361(1.493) 2.590(2.367) 83.3(65.2) CaH, C1 1.352(1.497) 2.981(2.854) 81.9(71.4) AlH2, C1 1.365(1.488) 2.506(2.261) 83.5(63.7)

GaH2, C1 1.365(1.492) 2.449(2.308) 79.1(67.7) SiH3, C1 1.376(1.479) 2.462(2.124) 86.6(59.5)

GeH3, C1 1.375(1.487) 2.433(2.239) 80.8(65.3) a Bond Lengths in Angostromes and Angles in Degrees.

Figure 4: MP2(FULL)/6-31G* Optimized Geometrical Parameters of π-Bridged Global

Minima.

400

Formation of π-bridged could be attributed to the polarization of σC-X bond which

results in a negative charge on CH2 group. This negative charge is parallel to *CLP +

orbital which leads to the formation of a π -bond between CH2 and C+. It seems that

BH2 group is the least electropositive substituent within groups I, II, III and IV. This

means that σC-B is the least polarizable bond within this class. i.e. C=C π -bond is not

formed.

α-Substituted Local Minima

These local minima have two types of structures: carbene complexes and SS

structures. The relative energy, Erel, values of the α-substituted local minima are given

in Table 4. The local minima of (CH3)2C+X, X = GP I, MgH and CaH, are carbene

complexes. Other substituents BeH, GP III and GP IV have SS structures. It should be

noted that the most electropositive substituents form carbene complexes. In these

complexes C Xσ + − bond is highly polarized. This polarization leads to the formation of

the carbenes. The MP2(full)/6-31G(d) optimized values of essential key geometrical

parameters of carbenes are given in Figure 5. The lengths of rC1-X bonds, Figure 5,

indicate that there are no bonds between X substituents and electron-deficient

carbon.This is an indication of formation of carbene complexes.

Species(PG) ( )1 3 1 4

aC C C Cr r− −

1 2

aC Xr − ( )2 1 3 2 1 4

aX C C X C CΦ

Li,C1 1.462(1.462) 2.140 122.9(122.9) Na,C1 1.465(1.465) 2.499 123.4(123.4)

K,C1 1.469(1.469) 2.931 124.0(124.0) MgH,Cs 1.460 2.249 121.5 CaH,Cs 1.466 2.708 122.7

a Bond Lengths in Angostromes and Angles in Degrees.

Figure 5: MP2(FULL)/6-31G* Optimized Geometrical Parameters of Carbene Minima.

The NBO analysis of carbene complexes are given in Table 7. The NBO

analysis of parent carbene (H3C)2C: is included in Table 7 as reference. The results,

Table 7, indicate the presence of almost low and high occupancy p-orbitals on

electron-deficient carbon, 1

*CLP and

1CLP ; respectively, in the parent carbene. The

carbene complexes show similar results. Additionally, NBO analysis gives that these

complexes are formed of two units: X+ and parent carbene.

401

Table 7: MP2(FULL)/6-31G* NBO Analysis of Donors and Acceptors for Main HC in Carbene G3-Local Minima for Structural Isomers of XC3H6

+.

Species(PG)

Donor Acceptor Estab (kcal/mol) NBO Occupancy NBO Occupancy

(CH3)2C(C1) BD(C2-H6) 1.94614 LP*(C1) 0.12486 23.91

BD(C3-H9) 1.94613 LP*(C1) 23.92

LP(C1) 1.93406 BD*(C2-H4) 0.02578 11.47

LP(C1) BD*(C3-H7) 0.02578 11.47

(CH3)2CLi+,C1,(0) BD(C3-H5) 1.92448 LP*(C1) 0.17743 31.21

BD(C4-H8) 1.92447 LP*(C1) 31.21

LP(C1) 1.91331 LP*(Li) 0.04448 19.28

(CH3)2CNa+,C1,(0) BD(C3-H5) 1.92954 LP*(C1) 0.16541 29.45

BD(C4-H8) 1.92954 LP*(C1) 29.45

LP(C1) 1.91761 LP*(Na) 0.03776 12.52

(CH3)2CK+,C1,(0) BD(C3-H5) 1.93411 LP*(C1) 0.15425 27.90

BD(C4-H8) 1.93411 LP*(C1) 27.90

LP(C1) 1.93198 LP*(K) 0.01906 5.87

(CH3)2CMgH+,Cs,(0) BD(C4-H10) 1.92349 LP*(C1) 0.18986 29.58

BD(C5-H11) 1.92349 LP*(C1) 29.58

LP(C1) 1.83256 BD*(Mg-H) 0.11125 43.15

(CH3)2CCaH+,Cs,(0) BD(C4-H10) 1.93159 LP*(C1) 0.16763 27.23

BD(C5-H11) 1.93159 LP*(C1) 27.23

LP(C1) 1.89800 BD*(Ca-H) 0.04587 16.00

The local minima of other (H3C)2C+X species, X = BeH, BH2, AlH2, GaH2, SiH3 and

GeH3, have a general structure in which a hydrogen of each methyl group is almost

anti to X group, Figure 6. It could be designated "SS" structure, where S means

staggered. The MP2(full)/6-31G(d) optimized values of essential key geometrical

parameters are given in Figure 6. It should be noted that C1-X is much longer in

carbenes, Figure 5, than those SS species, Figure 6. In both, carbene and SS

structures, 1C+ has sp2 hybridization as indicated from the values of angles around 1C+ .

The values of these angles are given in last columns of Figures 5 and 6. It should be

noted that Erel values of local minima carbenes are much higher than those of SS

species, Table 4. This difference could be attributed to the instability of carbenes.

Species(PG) ( )aC C C Cr r− −1 3 1 4 a

C Xr −1 2 ( )

aX C C X C CΦ

2 1 3 2 1 4

BeH,Cs,(1)b 1.454 1.782 120.3 BH2,C1 1.462(1.462) 1.540 120.2(120.2) AlH2,C1 1.456(1.456) 2.071 121.4(121.4)

GaH2,C1 1.452(1.452) 2.047 121.(121.0) SiH3,C1 1.454(1.454) 1.943 120.0(120.0)

GeH3+,C1 1.450(1.450) 1.990 119.6(119.6)

a Bond Lengths in Angostromes and Angles in Degrees. b NImag=0 in RHF/6-31G*.

Figure 6: MP2(FULL)/6-31G* Optimized Geometrical Parameters of 1-Substituted

Minima.

Groups V, VI and VII Results

Elements of groups V, VI and VII give α-substituted species, (CH3)2C+X, as

global minima except X = AsH2, Table 8. The local minima have cyclic, eclipsed,

and/or bisected structures, Table 8. When X=AsH2, bisected AsH2CH2C+HCH3 species

402

is the global minimum while (CH3)2C+AsH2 is the local minimum. The global minima are

going to be discussed first.

Table 8: Relative Energy, Erel, Values and Enthalpies of Formation of Minimal Conformers of XC3H6

+ Structural Isomers, where X = NH2, PH2, GP VI, and GP VII Where G3-Global Minimum is 1-Substituted Isomer.

∆Hof

(kcal/mol)b

Ea(a.u.), Erel (kcal/mol)

Species(NImag)a

G3Enthalpy

(a.u.) MP2(FU)/

6-31G* B3LYP/

6-311+G**

NH2CH2CHCH3+

167.6 26.0 24.0 29.1 (cyc)C1,(0)

199.5 57.9 61.6 Non-existing (eC)C1,(0)

141.6 0.0 0.0 0.0 (CH3)2CNH2+,C1,(0)

PH2CH2CHCH3+

183.5 0.2 -1.9 4.3 (cyc)C1,(0)

186.3 3.0 3.7 2.1 (b)C1,(0)

183.3 0.0 0.0 0.0 (CH3)2CPH2+,C1,(0)

AsH2CH2C+HCH3

195.8 0.0 0.0 0.0 (b,g,in) C1,(0)

203.8 8.0 9.9 7.7 (CH3)2C+AsH2,C1,(0)

OHCH2CHCH3+

153.5 33.6 32.6 37.1 (cyc)C1,(0)

158.5 38.6 42.3 34.7 (eC)C1,(0)

119.9 0.0 0.0 0.0 (CH3)2COH+,C1,(0)

SHCH2CHCH3+

179.6 7.8 6.4 10.2 (cyc)C1,(0)

171.8 0.0 0.0 0.0 (CH3)2CSH+,C1,(0)

SeHCH2CHCH3+

177.5 2.1 -1.6 4.2 (cyc)C1,(0)

175.4 0.0 0.0 0.0 (CH3)2CSeH+,C1,(0)

FCH2CHCH3+

170.3 33.8) 33.0 Opt. to ecl. (cyc)C1,(0)

159.8 23.3 26.3 21.0 (eC)C1,(0)

162.3 25.8 29.1 23.3 (eH)Cs,(0)

136.5 0.0 0.0 0.0 (CH3)2CF+,C2,(0)

ClCH2CHCH3+

187.9 11.0 11.4 13.2 (cyc)C1,(0)

176.9 0.0 0.0 0.0 (CH3)2CCl+,C2,(0)

BrCH2CHCH3+

191.5 3.3 1.9 6.1 (cyc)C1,(0)

188.2 0.0 0.0 0.0 (CH3)2CBr+,C2,(0) a MP2(FULL)/6-31G*. b G3 method.

α-Substituted Global Minima

NBO analysis of these minima indicates presence of a π-bond between X and

the cationic carbon, Table 9. NBO analysis also indicates that there is a HC between *C=XBD and π-methylene orbitals (from the two methyl groups).The shortness of C+-X

bond length, Figure 7, is an additional proof for the formation of the π bond.

403

Table 9: MP2(FULL)/6-31G* NBO Analysis of Donors and Acceptors for Main HC in 1-Substituted G3-Global Minima of Structural Isomers of XC3H6

+ Species.

Species(PG)a Donor Acceptor Estab

(kcal/mol) NBO Occupancy NBO Occupancy

(CH3)2C+NH2,C1(0) BD(C4-H6) 1.96860 BD*(C1=N2) 0.10083 9.82

BD(C5-H7) 1.96860 BD*(C1=N2) 0.10083 9.82

BD(C4-H10) 1.96860 BD*(C1=N2) 0.10083 9.82

BD(C5-H11) 1.96860 BD*(C1=N2) 0.10083 9.82

(CH3)2C+PH2,C1(0) BD(C1-P2) 1.96725 BD*(C1=P2) 0.11278 12.48

BD(C4-H6) 1.96538 BD*(C1=P2) 0.11278 5.86

BD(C5-H7) 1.96538 BD*(C1=P2) 0.11278 5.86

BD(C4-H10) 1.97087 BD*(C1=P2) 0.11278 9.97

BD(C5-H11) 1.97087 BD*(C1=P2) 0.11278 9.97

BD(C1=P2) 1.96323 BD*(C1-P2) 0.04354 7.91

(CH3)2C+OH, C1(0) BD(C4-H6) 1.94975 BD*(C1=O2) 0.13009 16.86

BD(C5-H7) 1.97084 BD*(C1=O2) 0.13009 6.12

BD(C4-H10) 1.97098 BD*(C1=O2) 0.13009 6.51

BD(C5-H11) 1.95249 BD*(C1=O2) 0.13009 16.54

(CH3)2C+SH, C1(0) BD(C4-H6) 1.96179 BD*(C1=S2) 0.12496 10.52

BD(C5-H7) 1.96063 BD*(C1=S2) 0.12496 10.73

BD(C4-H10) 1.96171 BD*(C1=S2) 0.12496 10.51

BD(C5-H11) 1.96058 BD*(C1=S2) 0.12496 10.71

(CH3)2C+SeH,C1(0) BD(C4-H6) 1.96182 BD*(C1=Se2) 0.12707 10.49

BD(C5-H7) 1.95993 BD*(C1=Se2) 0.12707 10.89

BD(C4-H10) 1.96178 BD*(C1=Se2) 0.12707 10.52

BD(C5-H11) 1.95999 BD*(C1=Se2) 0.12707 10.87

(CH3)2C+F, C2(0) BD(C3-H5) 1.92937 BD*(C1-F2) 0.17726 23.81

BD(C4-H6) 1.92937 BD*(C1-F2) 0.17726 23.81

BD(C3-H7) 1.97418 BD*(C1=F2) 0.03028 6.95

BD(C4-H8) 1.97418 BD*(C1=F2) 0.03028 6.95

(CH3)2C+Cl, C2(0) BD(C3-H5) 1.93098 BD*(C1-Cl2) 0.17388 21.50

BD(C4-H6) 1.93098 BD*(C1-Cl2) 0.17388 21.50

BD(C3-H7) 1.96789 BD*(C1=Cl2) 0.02399 6.16

BD(C4-H8) 1.96789 BD*(C1=Cl2) 0.02399 6.16

(CH3)2C+Br, C2(0) BD(C3-H5) 1.93034 BD*(C1-Br2) 0.17498 21.61

BD(C4-H6) 1.93034 BD*(C1-Br2) 0.17498 21.61

BD(C3-H7) 1.96802 BD*(C1=Br2) 0.02516 6.09

BD(C4-H8) 1.96802 BD*(C1=Br2) 0.02516 6.09 a When X is bonded to hydrogen(s), C3 and C4 in Figure 5 become C4 and C5; respectively.

404

X(PG) a

C Xr −1 2 ( )aC C C Cr r− −1 3 1 4

( )a

X C C X C CΦ2 1 3 2 1 4

NH2, C1 1.295 1.484(1.484) 119.9(119.9) PH2, C1 1.667 1.494(1.494) 120.7(120.7) OH, C1 1.280 1.474(1.469) 121.8(115.5) SH, C1 1.648 1.482(1.485) 124.2(117.1)

SeH, C1 1.776 1.481(1.486) 124.5(116.8) F, C2 1.281 1.451 116.3

Cl, C2 1.638 1.465 119.4 Br, C2 1.796 1.466 119.3

a Bond Lengths in Angostromes and Angles in Degrees.

Figure 7: MP2(FULL)/6-31G* Optimized Geometrical Parameters of α-Substituted

Minima.

The driving force for the formation α-substituted global minima is the formation

of the dative π-bond between C+ and X. This formation produces large Estab,

especially, when X is a good π-donor group. AsH2 is a bad π-donor group [5]. This

means that the Estab which is produced from the dative bond between C+ and As is

relatively small. In the bisected AsH2CH2C+HCH3, the stabilization energy is produced

from the HC between σC-As and *CLP + . It seems that Estab results from HC is larger than

that results from the formation of the dative bond when X = AsH2. Consequently, the

bisected AsH2CH2C+HCH3 structure is the global minimum rather than (CH3)2C+AsH2.

In MP2(full)/6-31G(d) calculations, PH2CH2C+HCH3 and SeHCH2C+HCH3 global

minima have cyclic structures. These cyclic structures are more stable than

α-substituted ones by 1.9 and 1.6 kcal/mol as obtained by MP2(full) calculations,

Table 8. However, G3 calculations in favor of α-substituted structures to be global

minima.

It should be noted that in borane system, all elements of groups V, VI and VII

global minima are α-substituted species [3]. The only difference of borane species and

(H3C)2C+X species is when X = AsH2. Where AsH2CH2C+HCH3 global minimum is the

bisected structure. This could be attributed to the electrophilicity difference between

the secondary C+ and B atom. C+ is more electrophilic. This means HC between σC-As

and *CLP + is more effective than that between σC-As and *

BLP . i.e. Estab results from HC

in AsH2CH2BH2 is smaller than that results from the formation of the dative bond

between B and As in CH3BHAsH2. Consequently, H3CBHAsH2 is the global minimum.

The difference between XC2H4+ results [2] and those of XC3H6

+ could be

attributed to the fact that primary C+ is more electrophilic than secondary C+. This

means that the HC between σC-X and *CLP + is even more effective in XC2H4

+ than that

in XC3H6+. Consequently, for relative large substituents, X = PH2, AsH2, SeH and Br,

the bisected structures collapse to cyclic ones. Thus, the global minima for these

species have cyclic structure.

405

Bisected Global Minima(X=AsH2 and BH2)

It had been previously mentioned that the global minima of XCH2C+HCH3, X =

BH2 and AsH2, are bisected structures. The MP2(full)/6-31G(d) optimized values of key

geometrical parameters of bisected BH2CH2C+HCH3 are present in Figure 3 and those

of AsH2CH2C+HCH3 are given in Figure 8.

Figure 8 The α-substituted (CH3)2C+AsH2 is less stable than bisected by 8.0 kcal/mol as

obtained by G3 calculations, Table 8. The corresponding values when X = BH2 is 1.7

kcal/mol, Table 4. This could be attributed to the more effective HC in bisected arsenic

compound.

Groups V, VI and VII Local Minima

Some of the elements of these groups have two local minima. XCH2CH+CH3

species have cyclic and eclipsed local minima when X = NH2, OH and F. Cyclic and

bisected are local minima for PH2CH2CH+CH3. The rest of the elements of these

groups, SH, SeH, Cl and Br, have only cyclic local minima, Table 8.

It should be noted that in XCH2CH2+ species, cyclic structures are global minima

when X = PH2, AsH2, SeH and Br [2]. This could be attributed to higher electrophilicity

(electronegativity) of primary C+ than secondary one. The more electronegativity of

primary C+ makes the HC more effective and cyclic structures of XCH2CH2+ as global

minima. For strong electronegative substituents, X = NH2, OH and F, the energy gap

between C X−σ and *CLP + is large and

2CHπ becomes closer to *CLP + in XCH2C+HCH3

species. Thus, eclipsed structures which allow HC between 2CHπ and *

CLP + are the

local minima in these cases. Eclipsed FCH2C+HCH3 conformer is even more stable

than the cyclic by 10.5 kcal/mol as obtained by G3 calculations, Table 8, since the

cyclic has the smallest HC.

The optimized values of essential key geometrical parameters of cyclic local

minima are given in Figure 9 while those of eclipsed local minima are given in

Figure 10.

406

The local minimum of PH2CH2C+HCH3 has bisected structure, Figure 11.This

could be attributed to the electropositivity of PH2 group.

(PG) ( )aC C C Cr r− −1 2 1 4 ( )aC X C Xr r− −1 3 2 3

aX C C (X C C )Φ

3 2 1 3 1 2

NH2,C1 1.476(1.499) 1.495(1.506) 60.9(60.2) PH2, C1 1.518(1.512) 1.804(1.818) 65.7 (64.8) OH, C1 1.460(1.488) 1.521(1.558) 63.0(60.4) SH, C1 1.464(1.501) 1.851(1.879) 67.9(65.9)

SeH, C1 1.462(1.499) 2.004(2.034) 69.8(67.7) F, C1 1.460(1.466) 1.513(1.652) 67.5(57.8)

Cl, C1 1.457(1.486) 1.840(1.909) 69.7(64.6) Br, C1 1.456(1.487) 2.016(2.085) 71.8(66.7)

a Bond Lengths in Angostromes and Angles in Degrees

Figure 9: MP2(FULL)/6-31G* Optimized Geometrical Parameters of Cyclic Local

Minima.

Species(PG) rC1+

- C2(rC1+

-C4) rC2-X3 X3C2C1

+(X3C2C1+

C4) Angles

NH2(eC)C1(0) 1.452(1.431) 1.435 114.4(-3.2) OH(eC)C1(0) 1.444(1.430) 1.387 111.0(-1.7) F(eC)C1(0)b 1.450(1.426) 1.362 112.6(-1.2) (eH)Cs(0) 1.449(1.435) 1.361 112.4(-180.0)

a Bond Lengths in Angostromes and Angles in Degrees. b C1 had been done because Cs symmetry gives 1 Imag. Freq.

Figure 10: MP2(FULL)/6-31G* Optimized Values of Key Geometrical Parameters of

Eclipsed 2-Substituted G3-Local Minima for Structural Isomers of XC3H6+,a.

Figure 11

Conclusion The results of the present work confirm that the electronegativity of X and the

electrophilicity of the electron-deficient carbon determine the structures of the global

minima. This is due to the fact that these two factors determine the energy gap

between σC-X and *CLP + . Larger gap means less HC. The global minima of substituted

isopropyl carbocations are summarized in Figure 12. The highly electropositive

substituents give π-bridged global minima. The highly electronegative substituents give

α-substituted global minima, while BH2, AsH2 and CH3 substituents give bisected

global minima. These results are in accordance with those obtained for XC2H4+ and

XCH4B structural isomers.

407

CH3

X

(CH3)2CX

C C

X

H CH3H

H

π-Bridged

X = Groups I, II, AlH2, GaH2, SiH3 and GeH3

α-Substituted X = NH2, PH2, Groups VI

and VII

Bisected X = BH2, CH3 and AsH2

Figure 12 The potential energy surfaces, PES, of C4H9

+ structural isomers indicate that

primary carbocation rearranges to secondary at room temperature, while 2-butyl cation

is stable at room temperature. These results are in accordance with experimental

facts.

References [1] (a) Olah, G. A.; Schleyer, P. v. R., "Carbenium Ions" Vol. 2. Wiley-Interscience, New

York, London, Sydney, Toronto, 1969. (b) Olah, G. A.; Schleyer, P. v. R., "Carbenium Ions" Vol. 3. Wiley-Interscience, New York, London, Sydney, Toronto, 1971. (c) Creary, X., Chem. Rev., 1991, 91, 1625.

[2] Helal, M. R.; Afaneh, A. T., Jordan J. Chem., 2008, 3(1), 39. [3] Helal, M. R.; Afaneh, A. T.; Schleyer, P. v. R., Jordan J. Chem., 2008, 3(2), 155. [4] Helal, M. R.; Afaneh, A. T., Unpublished Data. [5] Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A., "Ab Initio Molecular Orbital

Theory" Wiley-Interscience, New York, Chichester, Brisbane, Toronto, Singapore, 1986. [6] Helal, M. R.; Jorgensen, W. L., J. Am. Chem. Soc., 1989, 111, 819. [7] Wierschke, S. G.; Chandrasekhar, J.; Jorgensen, W. L., J. Am. Chem. Soc., 1985, 107,

1496. [8] Apeloig, Y.; Stanger, A., J. Am. Chem. Soc., 1985, 107, 2806. [9] Rodriquez, C. F.; Hopkinson, A. C., J. Mol. Struct. (Theochem), 1987, 152, 69. [10] Rodriquez, C. F.; Hopkinson, A. C., J. Mol. Struct. (Theochem), 1987, 152, 55. [11] Wierschke, S. G.; Chandrasekhar, J; Jorgensen, W., J. Am. Chem. Soc., 1985, 107, 1496

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