A theoretical study on the mechanism of a novel one-carbon ... - Springer

0 downloads 0 Views 500KB Size Report
Mar 17, 2011 - pound (e.g., benzimidazolium) and Grignard reagent has been investigated ... sponding reaction mechanism has been given by the potential.

Struct Chem (2011) 22:901–907 DOI 10.1007/s11224-011-9776-1

ORIGINAL RESEARCH

A theoretical study on the mechanism of a novel one-carbon unit transfer reaction Haiyan Zhu • Jing Zhang • Zhenyi Wen Yongning Liu



Received: 17 November 2010 / Accepted: 4 March 2011 / Published online: 17 March 2011 Ó Springer Science+Business Media, LLC 2011

Abstract The mechanism of one-carbon unit transfer reaction between tetrahydrofolate coenzymes model compound (e.g., benzimidazolium) and Grignard reagent has been investigated employing the DFT and B3LYP/6-31G* levels of theory. Three consecutive reactions leading to major products N,N0 -dimethyl-ophenylenediamine and acetone have been proposed and discussed. For these reactions, the structure parameters, vibrational frequencies, and energies for each stationary point have been calculated, and the corresponding reaction mechanism has been given by the potential energy surface, which is drawn according to the relative energies. The calculated results show that the corresponding major products N,N0 -dimethyl-ophenylenediamine and acetone are in agreement with experimental findings, which provided a new illustration and guidance for these reactions. Keywords Tetrahydrofolate coenzyme  One-carbon unit transfer  Benzimidazolium salt  DFT  Nucleophiles H. Zhu  Y. Liu (&) State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, People’s Republic of China e-mail: [email protected] H. Zhu (&) Department of Chemistry and Chemical Engineering, Weinan Teacher’s University, Weinan 714000, Shaanxi, People’s Republic of China e-mail: [email protected] J. Zhang The 213th Research Institute of China Ordnance Industry, Xi’an 710061, Shaanxi, People’s Republic of China Z. Wen Institute of Modern Physics, Northwest University, Xi’an 710069, People’s Republic of China

Introduction Tetrahydrofolic acid, or tetrahydrofolate (THF), is a derivative of folic acid. In the process of synthesizing purines, thymidine, amino acids, and certain nucleic acids, it acts as not only a coenzyme but also results in the delivery of a group with one-carbon atom [1]. When the one-carbon unit is at the formic acid oxidation level, the imidazoline with a five-ring structure is the active site [2–4] (Chart 1). Various derivatives of N,N0 -diarylethylenediamines and structurally related compounds have been investigated as THF models to imitate the function of the one-carbon fragment transfer [5, 6]. Using imidazoline or benzimidazolium compounds as tetrahydrofolate coenzyme models, Shi et al. have successfully synthesized aldehydes, ketones, large-ring cycloalkanones, and other organic compounds [7–13]. In the process of these biomimetic reactions, the one-carbon unit transfers from the THF models to the nucleophilic reagents at the formic acid oxidation level. The reaction formula is shown on Scheme 1. In order to grasp more substantial and comprehensive understandings about those crucial experiments mentioned above, we need to collect more details at the molecular level. The rationality in the explanation of their observations remains to be supported by the accurate potential energy surfaces (PESs), which indicates the necessity for the further theoretical studies. Extensive theoretical studies can, on the one hand, regulate experimental suggestions, and on the other provide new findings that could not be reached experimentally under considered conditions. Therefore, we provide here a further representation about the theoretical study for this kind of one-carbon unit transfer reaction. As is shown in Scheme 1, the functional groups R and R0 only change their locations without being

123

902

Struct Chem (2011) 22:901–907 O O N

OH

C

H N

C

O

C

H

CH2

N N

CH2 N

H2N

C

N H

Results and discussion O

O

Reactant, equilibrium states, and transition states

Chart 1 The structure with active site of THF

involved in the process of reactions, therefore the reactions above must have been governed by the similar reaction mechanism. In the present quantum chemical study, we will take one representative reaction (e.g., R = CH3 and R0 = CH3) as an example and analyze the possible reaction mechanism in the view of hybrid density functional theory (B3LYP). In addition, every stationary point of the whole reaction has been discussed, respectively, from the perspectives of thermodynamics and dynamics.

Computational details Applied as a practical and effective computational tool, density functional theory (DFT) was employed with the Becke three-parameter Lee–Yang–Parr functional (B3LYP) [14, 15], which was proved to offer the possibility of calculating reaction energies with reasonable accuracy [16, 17]. The sufficient complete basis set 6-31G* including moderately diffuse d orbital was used to optimize the structures of all the stationary points (reactants, intermediates, transition states, and products). R. Q. Zhang et.al have proved the fact that this basis set can lead to accurate calculation and even comparable to the lager basis set, e.g., cc-PVDZ, 6-311??G** and cc-PVTZ, when used to calculate the geometric structures and vibrational frequencies for a general large system [18]. The transition states were ascertained by vibrational analysis with only one imaginary frequency mode. In the case of TS, the vibration associated with the imaginary frequency was checked to correspond with a movement in the direction of the reaction coordinate. Intrinsic reaction coordinates (IRC) [19]

CH3 N

I 1. RMgX 2.H+ ,H2O

H N CH3

O

R' N CH3

R'

C

R

+ N CH3 H

Scheme 1 The reaction formula of the one carbon unit transfer reaction. R = CH3, X = I: R0 = CH3, CH3CH2, C6H5, p-O2NC6H4, p-CLC6H4, p-CH3OC6H4, p-CH3C6H4R; or R = C6H5CH2, X = Cl: R0 = CH3,CH3CH2, CH3CH2CH2CH2, (CH3)2CH, (CH3)3C, C6H5, C6H5CH2, c-C6H11, p-O2NC6H4, p-CLC6H4, p-CH3OC6H4, p-CH3C6H4

123

starting from the transition state was calculated to find minimum-energy points (MEP). All the calculations are performed using the Gaussian 03 program package [20].

The optimized structures of THF and its model compound benzimidazolium salt calculated at the B3LYP/6-31G* level are shown in Fig. 1. The corresponding parameters of bond lengths and bond angles are summarized in Table 1. From Fig. 1 and Table 1, it can be seen that the active part, i.e., the quinary-ring of the benzimidazolium salt (R1) is quite similar to which of the THF in structure. The bond lengths and bond angles of R1 are all a little bit higher than those of the tetrahydrofolate, beside the angles of N2–C1– N3. The B3LYP/6-31G* optimized structures of reactant and products are listed in Table 2, while the optimized structures of intermediates (IM) and transition states (TS) are shown in Table 3. The reaction pathways The whole process of the one-carbon unit transfer begin with the reactants benzimidazolium salts (R1) and nucleophile Grignard reagent (R2), three consecutive reactions involved. In the first reaction, two different pathways have been revealed that are named as pathway a and pathway b. Pathway a As shown in Table 3, the ethyl group (C2H5–) of R2 attacks the atom C1 on the quinary-ring of the benzimidazolium salt, through Van der Waals force to form the pre-reactive complex (denoted as 1-IM1a). In 1-IM1a, the C5-C1 bond distance is 0.3403 nm and the ethyl group is almost parallel to the benzimidazolium salt molecular. With the approaching of ethyl group of R2 close to benzimidazolium salt, the reactant only passes one transition state 1-TS1a to form an intermediate 1-IM2a at last. The C5–C1 bond length of 1-IM2a is 0.1553 nm, while the bond between C5 and Mg7 breaks simultaneously. This pathway contains a nucleophilic addition reaction and represents a substitution mechanism. Pathway b Pathway b started from 1-IM1b via one transition state 1-TS1b then formed 1-IM2b. All structures in both pathway a and pathway b contain two independent parts, one part is [MgBr]?, the other part is benzimidazoline (the

Struct Chem (2011) 22:901–907

903

Fig. 1 B3LYP/6-31G* optimized sructures of tetrahydrofolate (a) and benzimidazolium salts (b)

Table 1 The B3LYP/6-31G* calculated parameters of tetrahydrofolate (a) and benzimidazolium salts (b) Species

a b

Bond length (nm)

Bond angles (°)

R(1,2)

R(1,3)

R(1,4)

A(2,1,3)

A(2,1,4)

A(3,1,4)

0.13 0.13

0.13 0.13

0.11 0.11

113.26 110.82

123.85 124.58

122.88 124.58

principal part of the whole reaction). Compared with the corresponding structures in pathway a, the principal parts are virtually the same, while the [MgBr]? parts of all structures in pathway b have a large deflection, and the deflection angles are all about 30°. Moreover, the experimental result shows that the existence of benzimidazoline has been testified [7], therefore, our theoretical results are in good agreement with the experimental results available. Two steps have been revealed for the second reaction trough calculations. In the first step, one H? cation attacks atom C1 of benzimidazoline to form an intermediate (2-IM1). Subsequently, the five-membered ring opens with

the C1–N2 bond fracture to form 2-IM2 via a transition state (2-TS1). The bond length of C1–H10 of 2-IM1 and 2-IM2 are 0.3857 nm and 0.1090 nm, respectively. In the second step, 2-IM2 isomerizes to 2-IM3 via 2-TS2, i.e., the H? cation transfers from C1 to N2. The old C1–H10 bond breaks and a new N2–H4 bond forms simultaneously. Two possible mechanisms have been revealed in the second reaction. One is the insertion mechanism, and the other is an intramolecular rearrangement mechanism. The third reaction is an addition–hydrolysis reaction, which consists of three steps. Firstly, the oxygen atom (O11) in water attacks the active part C1, meanwhile H13 gets away from O11. The C1–O11 bond length of 3-IM1, 3-TS1, and 3-IM2 shortens from 0.32, 0.18, to 0.15 nm, respectively. However, the H12–O11 bond length of 3-IM1, 3-TS1, and 3-IM2 elongate from 0.10, 0.14, and 0.30 nm, respectively. This process is known as the nucleophilic addition reaction and displays a substitutional mechanism. Secondly, the bond length of C1–O11 shortens while the bond length of H13–O11 elongates; in the mean time H5 gradually circumrotates and comes near to N3, the dihedral

Table 2 The main structure parameters of reactants and products by B3LYP/6-31G* calculated

Species

R1

Structure Parameters

Species

Bond

Bond

Dihedral

Bond

Bond

Dihedral angle

R(1,2)

A(3,1,2)

D(1,2,3,4)

R(5,6)

A(6,5,7)

D(5,6,7,8)

0.14

106.75

-0.00

0.15

115.30

-180.00

R(1,3)

A(4,1,2)

R(5,7)

A(5,7,8) 178.87

0.14

126.62

0.21

R(1,4)

A(4,1,3)

R(7,8)

0.11

126.62

R(1,9)

A(9,1,5)

D(9,1,5,6)

R(2,3)

A(3,11,2)

D(3,11,10,2)

0.12

124.00

180.00

0.27

95.7154

-92.23

R(1,5)

A(1,5,6)

R(3,11)

A(3,10,2)

0.15

113.26

0.10

95.7123

R2

R(5,6) P1

Structure Parameters

0.15

0.24

R(2,10) P2

0.10

Unit (bond length: nm; bond angle, dihedral angle º)

123

904

Struct Chem (2011) 22:901–907

Table 3 The main structure parameters of intermediates and transition states by B3LYP/6-31G* calculated

Species

1-IM1a

1-TS1a

1--

1-IM2a

2-IM1

2-IM2

2-IM3

3-TS1

3-TS2

3-TS3

Bond length

Bond angle

Dihedral angle

R(1,5)

A(1,5,6)

0.34

104.36

R(5,7)

A(6,5,7)

Bond length

Bond angle

Dihedral angle

D(1,2,3,4)

R(1,5)

A(1,5,6)

D(1,2,3,4)

-0.62

0.34

106.67

-12.88

D(5,6,7,8)

R(5,7)

A(6,5,7)

D(5,6,7,8)

0.66

43.513

7.26

0.61

79.59

-153.79

R(1,4)

A(4,1,2)

D(1,2,5,6)

R(1,4)

A(4,1,2)

D(1,2,5,6)

0.13

126.08

62.60

R(1,5)

A(1,5,6)

D(1,2,3,4)

1-IM1b

0.13

125.43

104.25

R(1,5)

A(1,5,6)

D(1,2,3,4)

0.23

107.95

-12.99

0.23

108.47

-12.98

R(5,7)

A(6,5,7)

D(5,6,7,8)

R(5,7)

A(6,5,7)

D(5,6,7,8)

0.64

65.232

20.85

0.59

87.90

-161.32

R(1,4)

A(4,1,2)

D(1,2,5,6)

R(1,4)

A(4,1,2)

D(1,2,5,6)

0.11

123.79

100.04

R(1,5)

A(1,5,6)

D(1,2,3,4)

1-TS1b

0.11

122.66

105.80

R(1,5)

A(1,5,6)

D(1,2,3,4)

0.16

114.47

-31.20

0.16

114.93

-31.64

R(5,7)

A(6,5,7)

D(5,6,7,8)

R(5,7)

A(6,5,7)

D(5,6,7,8)

0.63

76.583

19.94

0.59

96.44

-171.82

R(1,4)

A(4,1,2)

D(1,2,5,6)

R(1,4)

A(4,1,2)

D(1,2,5,6)

0.11

110.47

114.62

R(1,3)

A(3,1,2)

D(1,3,2,10)

1-IM2b

0.11

109.38

117.51

R(1,3)

A(3,1,2)

D(1,3,2,10)

0.15

101.45

21.22

1.48

101.40

6.90

R(1,2)

A(10,1,3)

D(3,1,5,6)

R(1,2)

A(10,1,3)

D(3,1,5,6)

0.15

152.63

73.55

0.15

170.16

107.60

R(1,10)

A(10,1,2)

D(2,1,5,6)

R(1,10)

A(10,1,2)

D(2,1,5,6)

0.39

93.81

-171.82

R(1,3)

A(3,1,2)

D(1,3,2,10)

2-TS1

0.23

84.63

-136.70

R(1,3)

A(3,1,2)

D(1,3,2,10)

0.14

78.58

28.94

0.14

84.31

-15.64

R(1,2)

A(10,1,3)

D(3,1,5,6)

R(1,2)

A(10,1,3)

D(3,1,5,6)

0.28

114.64

-168.19

0.25

99.00

-175.48

R(1,10)

A(10,1,2)

D(2,1,5,6)

R(1,10)

A(10,1,2)

D(2,1,5,6)

0.11

78.95

-64.02

R(1,3)

A(3,1,2)

D(1,3,2,10)

2-TS2

0.13

19.28

-64.83

R(1,11)

A(11,1,3)

D(13,11,1,5)

0.15

80.63

-17.08

0.32

97.13

65.98

R(1,2)

A(10,1,3)

D(3,1,5,6)

R(1,3)

A(11,1,5)

D(13,11,1,3)

0.27

104.65

179.49

0.14

125.27

-157.75

R(1,10)

A(10,1,2)

D(2,1,5,6)

R(11,12)

A(3,1,5)

D(1,11,13,12

0.10

78.95

-68.70

R(1,11)

A(11,1,3)

D(13,11,1,5)

3-IM1

0.10

120.91

146.65

R(1,11)

A(11,1,3)

D(13,11,1,5)

0.18

104.24

48.43

0.15

107.07

78.54

R(1,3)

A(11,1,5)

D(13,11,1,3)

R(1,3)

A(11,1,5)

D(13,11,1,3)

0.14

110.87

177.53

0.15

112.30

-154.76

R(11,12)

A(3,1,5)

D(1,11,13,1

R(11,12)

A(3,1,5)

D(1,11,13,12

0.14

118.92

165.06

R(1,11)

A(11,1,3)

D(13,11,1,5)

3-IM2

0.30

114.66

129.85

R(1,11)

A(11,1,3)

D(13,11,1,5)

0.15

111.10

149.41

0.15

111.09

149.06

R(1,3)

A(11,1,5)

D(13,11,1,3)

R(1,3)

A(11,1,5)

D(13,11,1,3)

0.15

108.48

149.41

0.15

108.52

-84.30

R(11,12)

A(3,1,5)

D(1,11,13,1

R(11,12)

A(3,1,5)

D(1,11,13,12

0.10

114.48

-63.46

R(1,11)

A(11,1,3)

D(13,11,1,5)

3-IM3

0.10

114.44

-63.65

R(1,11)

A(11,1,3)

D(13,11,1,5)

0.14

92.37

-135.72

0.12

23.93

179.21

R(1,3)

A(11,1,5)

D(13,11,1,3)

R(1,3)

A(11,1,5)

D(13,11,1,3)

0.16

118.14

-11.67

0.40

124.83

0.61

R(11,12)

A(3,1,5)

D(1,11,13,1

R(11,12)

A(3,1,5)

D(1,11,13,12

0.14

118.29

-67.85

0.19

148.75

-129.17

Unit (bond length: nm; bond angle, dihedral angle º)

123

Species

3-IM4

Struct Chem (2011) 22:901–907

905

angel of D(12,11,1,3) is from 154.76° (3-IM2), 84.30° (3-IM3), and finally to 0.61° (3-IM4). 3-IM4 includes two independent parts, one is N,N0 -dimethyl-ophenylenediamine, and the other is target compound acetone.

-3309.30

R1+R2

IM2b

Energy/a.u.

-3309.40

Thermodynamic and kinetic analyses Thermodynamic and kinetic analyses can be resorted to for the further illustration of the reliability and possibility of the reaction. A lot of reports about theoretical research of thermodynamic and kinetic properties are available today [21–24]. The thermodynamic and kinetic calculations have carried out on the basis of the B3LYP/6-31G* optimized parameters. Some data of the thermodynamic and dynamics are shown in Table 4. The schematic energy profiles of all structures are displayed in Figs. 2, 3, and 4, respectively. Thermodynamic analyses As shown in Table 4, Gibbs free energy change (DrGhm) and enthalpy change (DrHhm) of the two pathways in the first reaction are all negative, that means the first reaction is a spontaneous, exothermic process. DrGhm and DrHhm values in

TS1b

IM1b

-3309.35 TS1a

IM1a

IM2a

-3309.45 -3309.50 -3309.55 -3309.60

P1+P2

Reaction 1

-3309.65

Reaction Coordinate Fig. 2 Schematic energy profiles for the reaction 1

the pathway a are all smaller than those of the pathway b, respectively, therefore the pathway a can take place more easily than the pathway b. The two steps of the second reaction have different thermodynamics properties. DrGhm and DrHhm in the first step are all negative, however, those in the second step are all positive, that is to say, the first step of this reaction is a spontaneous, exothermic reaction

Table 4 Thermodynamic parameters of all species and activation energies of reaction paths Species

Enthalpy, H (a.u.)

Gibbs free energy, G (a.u.)

Total energy, E (a.u.)

Enthalpy change, Dr Hmh (a.u.)

Gibbs free energy change, Dr Ghm (a.u.)

21.004

-73.514

-55.136

39.382

-10.502

-31.506

Activation energy, Ea (kJ mol-1)

R1 ? R2

-3309.309

-3309.397

-3309.328

1-IM1a

-3309.364

-3309.440

-3309.384

1-TS1a

-3309.358

-3309.427

-3309.376

1-IM2a

-3309.392

-3309.461

-3309.410

1-IM1b

-3309.365

-3309.441

-3309.366

1-TS1b

-3309.332

-3309.408

-3309.351

1-IM2b

-3309.369

-3309.443

-3309.387

R3 ? H?

-537.886

-537.939

-537.900

2-IM1

-538.169

-538.230

-538.185

2-TS1 2-IM2

-538.148 -538.199

-538.202 -538.255

-538.162 -538.214

60.386

-78.765

-65.638

2-TS2

-538.185

-538.241

-538.200

3 6.757

34.132

34.132

2-IM3

-538.186

-538.242

-538.201

94.518

126.024

133.900

42.008

-63.012

-73.514

178.534

-55.136

-78.765

2-IM3 ? H2O

-614.547

-614.625

-614.566

3-IM1

-614.583

-614.648

-614.602

3-TS1

-614.509

-614.568

-614.525

3-IM2

-614.535

-614.597

-614.553

3-TS2

-614.533

-614.596

-614.537

3-IM3

-614.536

-614.598

-614.553

3-TS3

-614.468

-614.530

-614.485

3-IM4

-614.557

-614.628

-614.577

P1 ? P2

-614.256

-614.333

-614 .272

R3 is benzimidazoline

123

906

Struct Chem (2011) 22:901–907

Conclusions

-537.85 + R3+H

-537.90

Energy/a.u.

-537.95 -538.00 -538.05 -538.10 TS3

-538.15 -538.20

TS4

IM4

IM3

P3

Reaction 2 -538.25

Reaction Coordinate Fig. 3 Schematic energy profiles for the reaction 2

-614.25

P4+P5

Energy/a.u.

-614.30 -614.35 -614.40 -614.45

TS7

-614.50 -614.55

TS5 R4+R5

-614.60

TS6 IM6

Tetrahydrofolate coenzymes assume the function of the carriers of one-carbon unit transfer on biosynthesis and cell metabolize. Its model compound benzimidazolium salt has been used to synthesize organic compounds such as aldehydes, ketenes, large-ring cycloalkanone, and so forth. In order to study the mechanism of this kind of one-carbon unit transfer reaction, the synthesis reaction of acetone has been taken as a representative example in this paper. Moreover, fourteen equilibrium structures and seven transition states have been located on the DFT/B3LYP (6-31G*) level of theory. Besides, three consecutive reactions have been involved in the whole process from benzimidazolium salt with Grignard reagent to acetone. The first reaction is a formylation reaction which consists of two possible pathways; the second reaction is made up of a nucleophilic addition process and a intramolecular rearrangement process of H? cation; while the third reaction is a stepwise addition–hydrolysis reaction including three steps, among which the third step decides the speed of the whole reaction with the biggest activation energy of 178.53 kJ mol-1.

IM7

IM8 IM5

Reation 3

-614.65

Reaction Coordinate

References

Fig. 4 Schematic energy profiles for the reaction 3

while the second step is on the contrary. In the first step of the third reaction, DrGhm and DrHhm are all bigger and positive. While which of the two following steps 3-IM2 ? 3-TS2 ? 3-IM3 and 3-IM3 ? 3-TS3 ? 3-IM4 are all negative and the absolute values are all bigger. Hence the second and the last step are spontaneous, exothermic processes. Kinetic analysis As displayed in Fig. 2 and Table 4, the activation energy Ea of the pathway a and pathway b are both relatively low, and the Ea of pathway a is a little less than that of the pathway b. Thus the reaction speeds of two pathways are all slow, pathway a will be faster than that of the latter. However, the following reaction of benzimidazoline with one H? cation has a higher energy base of 60.39 kJ/mol, therefore, it is more difficult to realize. In the third reaction, Ea of the first step and the last step are all much higher than that of the other reactions. The last step Ea is 178.53 kJ/mol is the biggest activation energy of the whole reaction, therefore the last step decides the speed of the whole reaction.

123

1. Kompis IM, Islam K, Then RL (2005) Chem Rev 105:593–620 2. Biera¨ugel H, Plemp R, Hiemstra HC, Pandit UK (1983) Tetrahedron 39:3971–3979 3. Huizenga RH, Vawiltenburg J, Biera¨ugel H, Pandit UK (1991) Tetrahedron 47:4165–4174 4. Biera¨ugel H, Brands KMJ, Pandit UK (1988) Heterocycles 27:1589–1593 5. Kulkowit S, McKervey MA (1978) J Chem Soc Chem Commun 23:1069–1070 6. Meyers AI, Collingt EW (1970) J Am Chem 92:6676–6678 7. Jiang JL, Shi Z (1998) Synth Commun 28:4137–4142 8. Shi Z, Gu H (1997) Synth Commun 27:2789–2791 9. Shi Z, Gu H (1997) Synth Commun 27:2701–2707 10. Guo Y, Shi Z (2004) Synth Commun 34:3183–3189 11. Guo Y, Wu XL, Li JL, Xu RQ, Shi Z (2005) Synth Commun 35:2489–2494 12. Bai YJ, Lu J, Shi Z, Yang BQ (2001) Synlett 4:544–546 13. Li JL, Yin WT, Zhang J, Guo Y, Wu XL, Bai YJ, Shi Z (2008) Chem J Chinese 29:100–103 14. Becke AD (1993) J Chem Phys 98:1372–1377 15. Gill PMW, Johnson BG, Pople JA, Frisch MJ (1992) Int J Quantum Chem 44:319–331 16. Riemer-Sorensen S, Zioutas K, Hansen SH, Pedersen K, Dahle K, Liolios A (2007) Phys Rev Lett 8:1313011–1313014 17. Klontzas E, Mavrandonakis A, Tylianakis E, Froudakis GE (2008) Nano Lett 8:1572–1576 18. Zhang RQ, Wong NB, Lee ST, Zhu RS, Han KL (2000) Chem Phys Lett 319:213–219 19. Garrett ER, Gurkan T (1979) J Pharm Sci 68:26–32 20. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA Jr, Vreven T, Kudin KN, Burant

Struct Chem (2011) 22:901–907 JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P,

907

21. 22. 23. 24.

Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA (2003) GAUSSIAN03 Revision B.03. Gaussian Inc., Pittsburgh, PA Binderbauer MW, Guo HY, Tuszewski M, Putvinski S, Sevier L, Barnes D (2010) Phys Rev Lett 105:0450031–0450034 Steckler R, Truhlar DG (1990) J Chem Phys 93:6570–6577 Liu YP, Lu DH, Lynch GC, Truong TN, Gonzalezlafont A, Truhlar DG (1993) Abstr Am Chem Soc 206:244 Schenter GK, Garrett BC, Truhlar DG (2003) J Chem Phys 119:5828–5833

123

Suggest Documents