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DFT Studies of Homogeneous Catalysis in the Gas Phase: Dehydration Kinetics of Several Tertiary Alcohols With Hydrogen Chloride JOSE R. MORA,1 DAVID J. MARQUEZ,2 EDGAR MARQUEZ,2 ˜ O,2 TANIA CORDOVA,3 GABRIEL CHUCHANI1 MARCOS LORON 1

Centro de Quı´mica, Instituto Venezolano de Investigaciones Cientı´ficas (I.V.I.C.), Apartado 21827, Caracas, Venezuela 2 Departamento de Quı´mica, Escuela de Ciencias, Universidad de Oriente Nućleo Sucre, Cumana, Venezuela 3 Department of Medicinal Chemistry, College of Pharmacy, University of Florida, Gainesville, Florida 32610 Received 6 April 2011; accepted 12 April 2011 Published online 7 December 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/qua.23145

ABSTRACT: The mechanisms for the acid-catalyzed gas-phase dehydration of the tertiary alcohols 2-methyl-2-propanol, 2-methyl-2-butanol, and 2-methyl-2-pentanol were examined at B3LYP/6-31G(d), B3LYP/6-31G(d,p), B3LYP/6-31G(2d,p), B3LYP/6-31G(2d,2p), B3PW1/6-31G(d), B3PW1/6-31G(d,p), B3PW1/6-31G(2d,p), B3PW1/6-31G(2d,2p), MPW91PW91/6-31G(d), MPW91PW91/6-31G(d,p), MPW91PW91/6-31G(2d,p), and MPW91PW91/6-31G(2d,2p) levels of theory. Calculation results suggest that the dehydration processes catalyzed by hydrogen chloride to give the corresponding olefin and water occur with the formation of Van der Waals complexes between the alcohol and hydrogen chloride. The transition states are six-membered cyclic structures involving one molecule of HCl and one of the alcohol. These reactions appear to be molecular in nature. Analysis of the progress along the reaction coordinate, in terms of bond orders, NBO charges, and geometrical parameters suggest these reactions to be moderately polar and nonsynchronous and are dominated by the breaking of the HACl bond, together with an important cleavage of CAO C 2010 Wiley Periodicals, Inc. Int J Quantum Chem 112: 78–88, 2012 bond in the transition state. V Key words: tertiary alcohols; gas-phase kinetics; DFT calculations; mechanism

Correspondence to: T. Cordova; e-mail: taniacsintjago@ufl. edu

International Journal of Quantum Chemistry, Vol 112, 78–88 (2012) C 2010 Wiley Periodicals, Inc. V

DFT STUDIES OF HOMOGENEOUS CATALYSIS

1. Introduction

T

he gas-phase dehydration kinetics of alcohols has been found to be complex and difficult to study. Alcohols are known to decompose from a free radical chain to molecular mechanism, when changing from primary to tertiary structures [1]. The temperatures required for gas-phase dehydration of alcohols are from 500 C and up. The OH of alcohols is a bad leaving group in thermal decomposition processes. However, a few of these substrates have shown to undergo a homogeneous, unimolecular elimination under maximum catalysis of HCl or HBr gas [2–10]. The acid-catalyzed bimolecular dehydration of some alcohols may be carried out well below 100 C compared with the uncatalyzed elimination of water, implying a reduction of the energy of activation by about 125 kJ/mol. The transition state (TS) for the acid-catalyzed dehydration of tertbutyl alcohol was first postulated by Maccoll and Stimson as described in Scheme 1 [2]. Steric acceleration was considered to be the probable factor in the rate enhancement of the gas phase elimination kinetics of acid-catalyzed alkylbranched tertiary alcohols [8, 9]; however, the electronic effect was not ignored. A later work [10] considered the electronic factor to be responsible for the rate increase. This conclusion was derived from kinetic data of 2-phenyl-2-propanol and 3-methyl-1-buten3-ol, where the allylic and benzylic substituents stabilize the positive carbon in the polarization of CdþOHd in the TS through electron donation, increasing the rate. Electronic structure calculations have been used successfully in the study of the mechanisms of organic reactions. In this direction, we have studied several unimolecular reactions such as

SCHEME 1. elimination reactions of 2,2-diethoxy-ethylamine and 2,2-diethoxy-N,N-diethyl-ethylamine, which proceed by a complex mechanism involving parallel and consecutives reactions [11]. Computational studies of bimolecular reactions, such as SN2 reactions, have demonstrated these reactions proceed through a van der Walls complex, more stable than the reactants, and that this complex continues to the TS in the reaction path [12]. In a recent work on the study of the 1,3dipolar cycloaddition between diphenylnitrone and maleimidebisamide complexes, the authors have evaluated the potential energy surface, both in the gas phase and in dichloromethane, and they concluded the reaction to occur through van der Waals complex (vdW complex) in a highly asynchronous process, involving energy changes of about 20 kcal mol1 [13]. The informations described about the acid-catalyzed dehydration of tertiary alcohols [9] (Table I) suggested an interesting study of these gas-phase elimination reactions through theoretical calculations to support or modify the proposed reaction mechanism. In this respect, the potential energy surfaces (PESs) of the dehydration reaction of 2methyl-2-propanol, 2-methyl-2-butanol, and 2methyl-2-pentanol under hydrogen chloride gas catalyst were studied at several density functional theory (DFT) levels of theory. In this way, it is possible to obtain the kinetic and thermodynamic

TABLE I Experimental kinetic and thermodynamic parameters of R(CH3)2COH gas-phase elimination reaction catalyzed by HCl at 4308C.a Substrate

k (cm /mols)

Rel. rate per H

Ea (kJ/mol)

Log A (cm3/mols)

DH= (kJ/mol)

DS= (J/mol K)

DG= (kJ/mol)

Ref.

3.1 136.5 183.7 290.9

1 44 59 94

– 136.8 142.2 145.3

– 12.30 12.83 13.26

– 125.1 130.5 133.6

– 33.16 23.01 14.78

– 148.5 146.7 144.0

[4] [3] [6] [9]

H CH3 CH3CH2 CH3CH2CH2

3

DS=, DH=, and DG= values were not reported in Refs. [3, 6, 9]. Therefore, we have estimated these parameters and included in this work.

a

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MORA ET AL. TABLE II Enthalpy changes from isolated reactants to van der Waals Complexes at 4308C (703.15 K) and 0.1316 atm. t-Butanol

2-Methyl-2-butanol

2-Methyl-2-pentanol

Method

Basis

DHvdW (kJ/mol)

DHvdW (kJ/mol)

DHvdW (kJ/mol)

B3LYP

6–31G(d) 6–31G(d,p) 6–31G(2d,p) 6–31G(d) 6–31G(d,p) 6–31G(2d,p) 6–31G(2d,2p) 6–31G(d) 6–31G(d,p) 6–31G(2d,p) 6–31G(2d,2p)

29.8 30.4 30.1 27.7 28.6 27.5 27.0 31.2 32.0 30.9 30.3

22.6 23.2 23.0 20.8 21.7 20.8 20.2 22.3 23.2 22.0 21.5

21.0 21.7 21.3 19.3 20.2 18.7 18.2 18.3 19.1 18.1 17.5

B3PW91

MPW1PW91

parameters for a reasonable understanding of the process of decomposition of these alcohols.

2. Computational Methods and Models The kinetics and mechanism for the gas-phase dehydration of several tertiary alcohols catalyzed by hydrogen chloride were investigated by means of electronic structure calculations using DFT methods. The calculations at this level of theory were performed by using the Becke’s three-parameter formulation from the Lee, Yang, and Parr correlation functional B3LYP/6-31G(d), B3LYP/6-31G(d,p), B3LYP/6-31G(2d,p), B3LYP/6-31G(2d,2p) [14–16],

the Perdew–Wang 1991 correlation functional B3PW1/6-31G(d), B3PW1/6-31G(d,p), B3PW1/631G(2d,p), B3PW1/6-31G(2d,2p), MPW1PW91/631G(d), MPW1PW91/6-31G(d,p), MPW1PW91/ 6-31G(2d,p), and MPW1PW91/6-31G(2d,2p) [17], as implemented in Gaussian 03 [18]. The structures of all stationary points were fully optimized using the default options in Gaussian for convergence with the Berny analytical gradient optimization, that is, density matrix was 109 atomic units [19], threshold ˚ , and value for maximum displacement 0.0018 A maximum force was 0.00045 Hartree/Bohr. Stationary points, minimum energy, and TSs were verified using frequency calculations at all level of theories mentioned above. The vdW complexes were located and characterized. These complexes are more stable than the isolated reactants (alcohol þ HCl). Therefore,

TABLE III Kinetic and thermodynamic parameters for dehydration of t-butanol at 430 8C (703.15 K) and 0.1316 atm. Method B3LYP

Basis

6–31G(d) 6–31G(d,p) 6–31G(2d,p) 6–31G(2d,2p) B3PW91 6–31G(d) 6–31G(d,p) 6–31G(2d,p) 6–31G(2d,2p) MPW1PW91 6–31G(d) 6–31G(d,p) 6–31G(2d,p) 6–31G(2d,2p) Experimental

80

Ea (kJ/mol) Log A (cm3/mols) DS= (J/K mol) DH= (kJ/mol) DG= (kJ/mol) k (cm3/mols) 145.7 142.0 137.2 136.5 151.0 146.7 141.8 140.9 156.9 152.3 147.5 146.4 136.8

13.16 13.05 12.92 12.85 13.17 13.05 12.92 12.82 13.23 13.09 12.98 12.89 12.30

16.78 18.91 21.33 22.61 16.50 18.77 21.33 23.32 15.36 18.06 20.19 21.90 33.16


134.0 130.3 125.5 124.8 139.3 135.0 130.1 129.2 145.2 140.6 135.8 134.7 125.1

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145.8 143.6 140.5 140.7 150.9 148.2 145.1 145.6 156.0 153.3 150.0 150.1 148.5

216.0 314.7 534.8 516.9 90.3 143.3 243.5 223.5 37.7 59.9 105.3 103.5 136.5

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DFT STUDIES OF HOMOGENEOUS CATALYSIS TABLE IV Kinetic and thermodynamic parameters for dehydration of 2-methyl-2-butanol at 4308C (703.15 K) and 0.1316 atm. Method

Ea (kJ/mol) Log A (cm3/mols) DS= (J/Kmol) DH= (kJ/mol) DG= (kJ/mol) k (cm3/mols)

Basis

B3LYP

6–31G(d) 6–31G(d,p) 6–31G(2d,p) B3PW91 6–31G(d) 6–31G(d,p) 6–31G(2d,p) 6–31G(2d,2p) MPW1PW91 6–31G(d) 6–31G(d,p) 6–31G(2d,p) 6–31G(2d,2p) Experimental

141.4 137.7 133.0 146.5 142.3 137.6 136.7 152.1 147.7 143.1 142.1 142.2

13.31 13.21 13.03 13.19 13.14 12.99 12.91 13.32 13.25 13.09 12.99 12.83

we have estimated the kinetics and thermodynamic parameters using these complexes as reference at all level of theories. TS structures were located using the quadratic synchronous transit protocol [20]. The TS structures were identified by means of normal-mode analysis by having a single imaginary frequency and the corresponding transition vector. The intrinsic reaction coordinate (IRC) calculations [21] were carried out to confirm that the minimum energy path connects the calculated TS with the vdW complexes and products. Thermodynamic quantities such as zero-point vibrational energy (ZPVE), temperature corrections (E(T)) and absolute entropies (S(T)), were obtained from frequency calculations. Temperature corrections and absolute entropies were procured assuming ideal gas behavior from the

13.94 15.79 19.20 16.21 17.21 20.05 21.47 13.65 15.08 18.06 20.05 23.01

129.7 126 121.3 134.8 130.6 125.9 125 140.4 136 131.4 130.4 130.5

139.5 137.1 134.8 146.2 142.7 140 140.1 150 146.6 144.1 144.5 146.7

634.6 956.8 1418.0 201.7 367.1 582.6 572.7 105.3 188.4 288.9 269.8 183.7

harmonic frequencies and moments of inertia by standard methods [22] at average temperature and pressure values within the experimental range. Scaling factors for frequencies and zero point energies were taken from the literature [23, 24]. The first-order rate coefficient k was calculated using the TS theory TST [25] assuming that the transmission coefficient is equal to 1 as expressed in the following Eq. (1):

k ¼ rðkB T=C hÞ expðDG‡ =RTÞ

(1)

where DG‡ is the Gibbs free energy change between the reactant and the TS, r is the symmetry number, kB and h are the Boltzmann and Planck constants, respectively, and C is the standard state (1 mol cm3). In these reactions, reactants and TSs are

TABLE V Kinetic and thermodynamic parameters for dehydration of 2-methyl-2-pentanol at 4308C (703.15 K) and 0.1316 atm. Method

Ea (kJ/mol) Log A (cm3/mols) DS= (J/K mol) DH= (kJ/mol) DG= (kJ/mol) k (cm3/mols)

Basis

B3LYP

6–31G(d) 6–31G(d,p) 6–31G(2d,p) 6–31G(2d,2p) B3PW91 6–31G(d) 6–31G(d,p) 6–31G(2d,p) 6–31G(2d,2p) MPW1PW91 6–31G(d) 6–31G(d,p) 6–31G(2d,p) 6–31G(2d,2p) Experimental

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135.9 133.0 129.3 128.8 141.3 137.9 134.0 133.3 147.0 143.4 139.5 138.7 145.3

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13.17 13.06 12.91 12.79 13.19 13.17 13.05 12.94 13.28 13.25 13.14 13.03 13.26

16.50 18.63 21.62 23.89 16.21 16.64 18.91 20.88 14.36 14.93 17.07 19.20 14.78

124.2 121.3 117.6 117.1 129.6 126.2 122.3 121.62 135.3 131.7 127.8 127 133.6

135.8 134.4 132.8 133.9 141 137.9 135.6 136.3 145.4 142.2 139.8 140.5 144.0

1195.1 1518.4 1996.4 1654.0 491.0 834.4 1236.7 1097.1 231.3 399.9 602.9 534.8 290.9


81

MORA ET AL. where the subscript ab refers to the basis set of the complex AB, and the subscripts a and b correspond to the basis set of fragments A and B, respectively.

3. Results and Discussions 3.1. KINETIC AND THERMODYNAMIC PARAMETERS

SCHEME 2. asymmetric; therefore, the symmetry number is 1 [26, 27]. DG‡ was calculated using the following relations [Eqs. (2) and (3)]: DG‡ ¼ DH‡ TDS‡

(2)

DH‡ ¼ V ‡ þ DZPVE þ DEðTÞ

(3)

and

where V‡ is the potential energy barrier, and DZPVE and DE(T) are the differences of ZPVE and temperature corrections between the TS and the reactant, respectively. Entropy values were estimated from vibrational analysis. In calculations involving week associations such as vdW complex, DE are corrected for BSSE, using counterpoise correction (CP): DEcorr ¼ DE DECP with DECP ¼ EðAÞab þ EðBÞab EðAÞa EðBÞb

The acid-catalyzed gas-phase dehydration of the tertiary alcohols: 2-methyl-2-propanol, 2methyl-2-butanol, and 2-methyl-2-pentanol have been studied to gather further information on the reaction mechanisms proposed under the experimental conditions. Theoretical calculation at DFT levels of theory allowed the localization of the TS of the elimination reaction catalyzed by hydrogen chloride in the gas phase. The relative stability of vdW complexes with respect to isolated reactants was determined by calculation of enthalpy changes of isolated reactants to vdW complexes (DHvdW), results are shown in Table II. The vdW complexes are 20–30 kJ mol1 more stable than the isolated reactants; the most stable is that of t-butanol. The enthalpy of activation and, consequently, the energy of activation were calculated considering the differences in potential energy from the lowest stationary point in the PES, that is, the vdW complex, and the highest potential energy in the minimum energy path, that is, the TS [12, 13]. The reaction rates were estimated using the TST equation above, including the entropy changes in the pre-exponential factor [Eqs. (1) and (2)].

FIGURE 1. Optimized structures for reactant (R), transition state (TS), and products (P) at B3PW1/6-31(2d,2p) level of theory for gas-phase elimination reaction of t-butanol in the presence of HCl. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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FIGURE 2. Optimized structures for reactant (R), transition state (TS), and products (P) at B3PW1/6-31(2d,2p) level of theory for gas-phase elimination reaction of 2-methyl-2-butanol in presence of HCl. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] The TS configuration is a six-membered cyclic structure in which one hydrogen chloride molecule and the alcohol participate. In the TS, the hydrogen of HCl approaches the oxygen of the alcohol transferring a hydrogen atom to form water. HCl is regenerated in the process as the olefin is formed. Detailed description of the TS and the changes throughout the reactions are given in the following sections. Thermodynamic and kinetic parameters calculated at different theory levels for each substrate are shown in Tables III–V. Thermodynamic quantities were obtained from frequency calculations, and the estimated activation parameters were compared with the experimental values [3, 6, 9]. Temperature corrections were carried out at the average experimental conditions (T ¼ 430 C). In the gas-phase dehydration of t-butanol, reasonably good agreement was found for the energy

and enthalpy of activation calculated at B3LYP/ 6-31G(2d,p), B3PW91/6-31G(2d,2p) levels, when compared with the experimental values. The MPW1PW91/6-31G(2d,2p) method produced small overestimation of the energy and enthalpy of activation. Using the polarized function such as (d,p), (2d,p), and (2d,2p) improved the calculated parameters. Calculated entropy of activation was better estimated using B3PW91/6-31G(2d,p). In the case of 2methyl-2-butanol, good estimated values for energy and enthalpy of activation were obtained with B3PW91/6-31G(d) and MPW1PW91/6-31G(d,p). The B3LYP gave underestimated parameters when increasing the size of the basis set. Both B3PW91/631G(d) and MPW1PW91/6-31G(d,p) calculations gave reasonable values of entropy of activation. For 2-methyl-2-pentanol, better values for energy and enthalpy of activation were obtained by using the MPW1PW91/6-31G(d) level of theory; B3LYP and

FIGURE 3. Optimized structures for reactant (R), transition state (TS), and products (P) at B3PW1/6-31(2d,2p) level of theory for gas-phase elimination reaction of 2-methyl-2-pentanol in presence of HCl. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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MORA ET AL. TABLE VI Selected structural parameters of reactant (R), transition state (TS), and products (P) for dehydration of t-butanol, 2-methyl2-butanol, and 2-methyl-2-pentanol at 4308C (703.15 K, 0.1316 atm) at B3PW1/6–31(2d,2p) level of theory. t-Butanol

bond C1AC2 C2AH3 H3ACl4 Cl4AH5 H5AO6 O6AC1

R 1.53 1.09 3.34 1.33 1.73 1.46

2-Methyl-2-butanol

TS 1.43 1.19 1.89 2.01 1.00 2.28

O6AC1AC2AH3 H3ACl4AH5AO6

P 1.34 – 1.29 – 0.97 –

9.79 30.83

221.35

2-Methyl-2-pentanol

Atomic Length (A˚) bond R TS P C1AC2 1.53 1.43 1.34 C2AH3 1.10 1.19 – H3ACl4 3.19 1.86 1.28 Cl4AH5 1.32 2.01 – H5AO6 1.70 1.00 0.96 O6AC1 1.45 2.27 – Dihedral angles (degrees) O6AC1AC2AH3 22.14 H3ACl4AH5AO6 24.38 Imaginary frequency (cm1) 235.59

B3PW91 functional gave parameters with some deviation from the experimental values. With regard to the entropy of activation, all methods gave reasonable value although more negative when compared with experimental. Overall, B3PW91/631G(2d,p) and MPW1PW91 gave better parameters for the HCl-catalyzed elimination of these substrates. The energies of activation for 2-methyl-2-butanol and 2-methyl-2-pentanol are similar and slightly higher than that of t-butanol, as shown in the calculated parameters. Experimentally, the entropy of activation is more negative for t-butanol (about 33 J/K mol), implying a tight TS structure. This value increases for 2-methyl-2-butanol (approximately 23 J/K mol) and more for 2-methyl-2-pentanol approximately 15 J/Kmol). Calculated entropy values are in reasonable agreement to the experimental values of t-butanol at B3PW1/6-31(2d,2p) and

bond C1AC2 C2AH3 H3ACl4 Cl4AH5 H5AO6 O6AC1

R 1.54 1.10 2.85 1.49 1.34 1.51

TS 1.40 1.26 1.75 2.15 1.01 2.46

O6AC1AC2AH3 H3ACl4AH5AO6

P 1.34 – 1.31 – 0.99 –

2.72 41.44

178.25

MPW1PW91/6-31G(2d,2p); however, the calculated values deviate from experimental for 2methyl-2-butanol and more so for 2-methyl-2-pentanol, suggesting the contribution of low frequency modes, mainly anharmonic in the latter substrates, as the alkyl substituent at the beta carbon increases in size (R ¼ CH3 and R ¼ CH2CH3, Scheme 2). 3.2. TS AND MECHANISM The TS structures for the gas-phase HCl-catalyzed dehydration reactions of t-butanol; 2methyl-2-butanol and 2-methyl-2-pentanol were estimated. The optimized geometries for reactant, vdW complexes, products, and TSs are similar in all DFT methods. The entropy of activation suggests the arrangement of the atoms in the TS, that is, the very tight

TABLE VII NBO charges at selected atoms of complex (R), transition state (TS), and products (P) for dehydration of t-butanol, 2-methyl-2-butanol and 2-methyl-2-pentanol at B3PW1/6–31(2d,2p) level of theory. t-Butanol Atom C1 C2 H3 Cl4 H5 O6

84

2-Methyl-2-butanol

2-Methyl-2-pentanol

R

TS

P

Atom

R

TS

P

Atom

R

TS

P

0.287 0.715 0.252 0.366 0.295 0.766

0.338 0.777 0.315 0.628 0.498 0.927

0.010 0.455 0.284 0.284 0.472 0.944

C1 C2 H3 Cl4 H5 O6

0.287 0.507 0.261 0.374 0.300 0.768

0.343 0.587 0.328 0.635 0.501 0.939

0.023 0.238 0.290 0.290 0.476 0.953

C1 C2 H3 Cl4 H5 O6

0.240 0.508 0.279 0.350 0.307 0.642

0.275 0.508 0.307 0.554 0.458 0.852

0.027 0.235 0.280 0.280 0.419 0.839


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DFT STUDIES OF HOMOGENEOUS CATALYSIS TABLE VIII Wiberg bond index of reactant (R), transition state (TS), and products (P) from dehydration of t-butanol at the B3PW91/6–31G(2d,2p) level of theory.

BiR BiTS BiP dBi dBav Sy %Ev

C1AC2

C1AO6

C2AH3

H3ACl4

Cl4AH5

H5AO6

1.0046 1.2685 1.9302 0.1831

0.8612 0.2041 0.0000 0.7630

0.9201 0.6184 0.0000 0.3279

0.0001 0.2461 0.9218 0.2669

0.8188 0.1502 0.0000 0.8166

0.0980 0.6058 0.7801 0.7445

0.5170 0.7009 18.31

76.30

32.79

structures will have more negative values, while more positive values are expected for structures of more loose character with more degrees of freedom. Consequently, it is expected that a reasonable description of the TS is obtained from the method giving the best fitting with experimental values for the entropy of activation. With this criterion, we have selected the method with closer agreement to the experimental entropy of activation as the most representative structure for the TS. The TS configuration and atom numbering are shown in Scheme 2. Optimized structures for vdW complexes, TS, and products for these reactions are shown in Figures 1–3 for t-butanol, 2-methyl-2-butanol, and 2methyl-2-pentanol, respectively. Geometrical parameters of the optimized vdW complex, TS, and products are given in Table VI. The geometrical parameter’s atom numbering is shown in Scheme 2 and Figures 1–3. For the three alcohols considered in this study, the Cl4AH5 distance is increased in the TS com˚ in the pared with the vdWcomplex (from 1.3 A ˚ in the TS), being more imreactant to 2.0–2.1 A portant in the case of 2-methyl-2-pentanol. Also, an increase in O6AC1 distance is observed indicat-

26.69

81.66

74.45

ing bond breaking, and again more advanced for ˚ in the reactant to 2-methyl-2-pentanol (from 1.5 A ˚ in the TS). The C1AC2 distance is short2.3–2.5 A ened indicating the formation of the olefin C¼ ¼C ˚ in the complex to double bond (from 1.52–1.53 A ˚ in the TS). The six-centered TS config1.43–1.40 A uration including atoms C1, C2, H3, Cl4, H5, and O6 shows deviations from planarity as seen in the dihedrals. The imaginary frequency that characterizes the TS is mainly associated with a rocking vibration of hydrogen H5 approaching oxygen O6 and leaving Cl4. The nature of the TS of the mechanism described above was verified by means of IRC calculations. To gain more insight in the proposed mechanisms, further analysis of NBO charges and bond indexes were carried out. The results are discussed in the following sections. 3.3. NBO CHANGES The changes in electron distribution throughout these reactions were followed by means of NBO analysis. NBO charges for the relevant atoms of reactant, TS, and products in the dehydration reactions of t-butanol, 2-methyl-2-butanol, and 2-

TABLE IX Wiberg bond index of reactant (R), transition state (TS), and products (P) from dehydration of 2-methyl-2-butanol at the B3PW91/6–31G (2d,2p) level of theory.


C1AC2

C1AO6

C2AH3

H3ACl4

Cl4AH5

H5AO6

0.9832 1.2683 1.8649 0.1532

0.8643 0.1937 0.0000 0.7759

0.8984 0.5809 0.0000 0.3534

0.0030 0.2612 0.9186 0.2820

0.8118 0.1454 0.0000 0.8209

0.1013 0.6066 0,7755 0.7495

0.5225 0.7019 15.32

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35.34

28.20

82.09

74.95


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MORA ET AL. TABLE X Wiberg bond index of reactant (R), transition state (TS), and products (P) from dehydration of 2-methyl-2-pentanol at the B3PW91/6–31G(2d,2p) level of theory.


C1AC2

C1AO6

C2AH3

H3ACl4

Cl4AH5

H5AO6

0.9950 1.3798 1.8718 0.4389

0.8168 0.1129 0.0000 0.8618

0.8902 0.4818 0.0000 0.4588

0.0088 0.3746 0.9225 0.4004

0.6248 0.0898 0.0000 0.8563

0.2789 0.6998 0.8244 0.7716

0.6313 0.8113 43.89

86.18

45.88

methyl-2-pentanol are shown in Table VII. NBO charges for dehydration of the three alcohols (Table VII) show an increase in electron density of the chlorine atom Cl4 from the reactant to the TS. Changes in charges at C1 and C2 are small. The hydrogen H5 being transferred from HCl to the alcoholic oxygen becomes more positive, while changes in the hydrogen being abstracted by the Chlorine atom, H3 are smaller. In these reactions, hydrogen chloride is acting simultaneously as general base catalyst abstracting hydrogen H3 at C2, and as general acid catalyst by protonating oxygen O6 to form a better leaving group. These changes illustrate the involvement of HCl in the gas-phase dehydration reaction of the alcohols in this study. 3.4. BOND ORDER ANALYSIS NBO bond order calculations have been used to follow the changes along the reaction coordinates [28–30]. For this purpose, Wiberg bond indexes [31] were computed using the natural bond orbital NBO program [32] as implemented in Gaussian 03W. These indexes can be used to estimate bond orders from population analysis. Bond breaking and making processes involved in the reaction mechanism are described by means of the Synchronicity (Sy) concept proposed by Moyano et al. [33] defined by the expression [Eq. (4)]: " Sy ¼ 1

n X

# jdBi dBavj=dBav =2n 2

(4)

i¼1

n is the number of bonds directly involved in the reaction, and the relative variation of the bond index is obtained from Eq. (5):

86

40.04

85.63

77.16

dBi ¼ ½Bi TS Bi R =½Bi P Bi R

(5)

where the superscripts R, TS, and P represent reactant, TS, and product, respectively. The evolution in bond change is calculated as in Eq. (6): %Ev ¼ dBi 100

(6)

The average value is calculated from equation (7): dBave ¼ 1=n

n X

dBi

(7)

i¼1

Wiberg bonds indexes Bi were calculated for those bonds involved in the gas-phase hydrogen chloride-catalyzed elimination reaction of t-butanol, 2methyl-2-butanol, and 2-methyl-2-pentanol, that is, C1, C2, H3, Cl4, H5, O6 shown in Scheme 2. Other bonds were not considered. The synchronicity parameter has been used to describe if a reaction occurring in a concerted fashion shows equal progress along the different reaction coordinates or not. This parameter varies from 1 in the case of concerted synchronic reaction to 0 in the case of asynchronous process. Although global synchronicity is a general concept, analysis of bond order in the different reaction coordinates describe the extension to which any particular bond involved in the reaction is formed or broken in the TS. In this sense, the reaction can be described more advanced in some reaction coordinates than others. Analysis of bond order changes given as Wiberg indexes states that the most advanced reaction coordinate is the breaking of Cl4AH5 bond for all three substrates. Less progress is observed in other events. However, this is the


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DFT STUDIES OF HOMOGENEOUS CATALYSIS general case, there are differences among the three substrates. For 2-methyl-2-pentanol the breaking of Cl4AH5 is as advanced (86%) as the breaking of C1AO6 bond (86 %), contrary to the other two compounds where the breaking of Cl4AH5 dominates by a small margin over the breaking of C1AO6 bond (82% vs. 76–78%). Another important distinction is the formation of C1AC2 double bond, which is more advanced for 2-methyl-2-pentanol (44%) than for the other two substrates (15–18%). Other reaction coordinates, C2AH3 bond breaking (46 %) and H3ACl4 bond formation (40%) are also more advanced for 2methyl-2-pentanol compared with t-butanol and 2-methyl-2-butanol (Table VIII–X). The above described differences account for a more synchronic process in the case of 2-methyl2-pentanol (Sy ¼ 0.81) as opposed to t-butanol and 2-methyl-2-butanol dehydration reaction (Sy ¼ 0.70). In the former, both HCl and CAO bond breaking are advanced in the TS to the same extent and also other reaction coordinates are more advanced compared with the other two substrates (Table VIII–X).

HACl through concerted mechanisms, with different synchronicity values implying that the reaction progress is different along the reaction coordinate involved. The 2-methyl-2-pentanol acid-catalyzed dehydration reaction in the gas phase is a more synchronous process compared with t-butanol and 2-methyl-2-butanol

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4. Conclusions The kinetics and mechanism for the HCl-catalyzed dehydration of some tert-alcohols in the gasphase were investigated using DFT calculations. The formation of vdW complexes between the reactant and HCl, before the elimination reaction, was verified for all substrates. These complexes show the necessary orientation of the reactant for the formation of the TS. This work confirms the assistance of hydrogen chloride in the TS for the gas-phase dehydration of alcohols. In the reaction, hydrogen chloride acts both as general base catalyst in the abstraction of a beta hydrogen, and as general acid catalyst in the protonation of the alcoholic oxygen, thus decreasing considerably the energy of activation of this reaction channel compared with the uncatalyzed process. These results support the consideration of a six-membered cyclic TS type of mechanism. The Sy values for elimination of water and the corresponding olefin from the alcohols imply a semipolar concerted process, and the reaction is less nonsynchronic for 2-methyl-2-pentanol where the breaking of HCl and CAO bonds is very advanced in the TS structure. The rate-determining step of these reactions involves the breaking of

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