GAS PHASE DECOMPOSITION OF T-BUTYL METHYL ETHER

CATALYZED BY DIFFERENT HYDROGEN HALIDES: A DFT STUDY

Cuesta et al., 65–79

GAS PHASE DECOMPOSITION OF T-BUTYL

METHYL ETHER CATALYZED BY DIFFERENT

HYDROGEN HALIDES: A DFT STUDY

Sebastián Cuesta1,2,3*, Edgar Márquez4&José Mora 1,2,*

Recibido: 9 de abril 2022 / Aceptado: 16 de junio 2022

DOI 10.26807/ia.v10i2.237

KEYWORDS: catalysis, DFT, hydrogen halide, reaction mechanism

ABSTRACT

The gas phase decomposition of t-butyl methyl ether catalyzed by hydrogen ha-

lides is studied. Four different hydrogen halides (fluorine, chlorine, bromine,

and iodine) were evaluated to determine the electronic influence of the halogen

in the reaction mechanism. To describe the mechanism, the ωB97XD/LANL2DZ

level of theory was used. The reactivity order found was F<Cl<Br<I. Interes -

tingly, the activation free energy estimated for the HCl model was 133.9 kJ/mol,

which is in good agreement with the experimental one (134.3 kJ/mol). Further-

1Universidad San Francisco de Quito, Departamento de Ingeniería Química, Grupo de Química Com-

putacional y Teórica (QCT-USFQ), Quito, Ecuador (*correspondencia: sebastian_cuesta@yahoo.

com)

2Universidad San Francisco de Quito, Departamento de Ingeniería Química, Instituto de Simulación

Computacional (ISC-USFQ), Quito, Ecuador. (sebastian_cuesta@yahoo.com, *correspondencia:

jrmora@usfq.edu.ec)

3University of Manchester, Department of Chemistry, Manchester Institute of Biotechnology, Manches-

ter, UK (sebastian_cuesta@yahoo.com)

4Universidad del Norte, Facultad de Ciencias Exactas, Departamento de Química y Biología, Grupo

de Investigaciones en Química y Biología, Barranquilla, Colombia (ebrazon@uninorte.edu.co)

InfoANALÍTICA 10(2)

Julio 2022

INTRODUCTION

more, a correlation above 0.804 was noticed when the electronegativity, the

hydrogen-halide distance, and the pKa of the hydrogen halides were compared

to the thermodynamic parameters (activation free energy, enthalpy, and en-

tropy). Analyzing the mechanism in depth through the intrinsic reaction coor-

dinate, reaction force, and reaction electronic flux plots, it was observed that

though the reaction occurs in a one-step concerted way. The mechanism could

be divided into two events; the first one composed by a proton transfer from

the halide to the oxygen and the carbon-oxygen bond cleavage, and the second

one being the rate-limiting event which includes the proton transfer from the t-

butyl to the halide and the double bond formation.

The decomposition of several organic

compounds containing an oxygen

atom such as alcohols and ethers can

be catalyzed by hydrogen halides

(Failes & Stimson, 1962; Stimson &

Watson, 1966b). VR Stimson and EJ

Watson studied the gas phase de-

composition of t-butyl methyl ether

catalyzed by hydrogen chloride

(Stimson & Watson, 1966a) and in a

subsequent work, authors studied the

gas phase decomposition of t-butyl

ethyl ether using the same hydrogen

halide (Stimson & Watson, 1966b).

Several studies have been performed

since then, including the decomposi-

tion mechanism of t-butyl isopropyl

ether (Daly & Steele, 1972), t-butyla-

mine (Maccoll & Nagra, 1971), 2,2-

dimethoxypropane (Stimson & Tilley,

1972), 1,l-dimethoxyethane, and

acetaldehyde dimethyl acetal (Stim-

son, 1971). Experimental mechanistic

studies suggest the decomposition of

these compounds using hydrogen ha-

lides as catalyst is molecular and ho-

mogenous (Stimson & Watson,

1966a), being the basicity of the oxy-

gen atom a key factor in the reaction

rate of the mechanism. In this sense,

alcohols present lower reaction rates

compared to ethers (Maccoll &

Nagra, 1971). By comparing different

functional groups the following reac-

tivity was found acid<ester<alco-

hol<ether (Stimson & Tilley, 1972).

GAS PHASE DECOMPOSITION OF T-BUTYL METHYL ETHER

CATALYZED BY DIFFERENT HYDROGEN HALIDES: A DFT STUDY

Cuesta et al., 65–79

In 2012, Mora et al studied the

hydrogen chloride catalyzed dehy-

dration reaction mechanism of seve-

ral tertiary alcohols (Jose R. Mora et

al., 2012); while, in 2015, Julio et al

worked on elucidating the gas phase

elimination kinetics of aliphatic un-

saturated aldehydes catalyzed by

hydrogen chloride (Julio, Mora, Mal-

donado, & Chuchani, 2015). Their re-

sults suggest these reactions are

homogeneous and unimolecular. Ter-

tiary alcohol dehydration occurs

through a six membered transition

state, where the chloride transfers a

proton to the oxygen (Maccoll &

Nagra, 1971). Furthermore, the ther-

mal deamination of primary amines

catalyzed by HBr also follows the

same six-membered transition state

(Monascal, Cartaya, Álvarez-Aular,

Maldonado, & Chuchani, 2018). The-

refore, the same is believed to hap-

pen in ethers thermal decomposition

where an important influence of the

halide is mostly noticed. At the best

of our knowledge, no studies have

been performed to evaluate the in-

fluence of different halides in the gas

phase thermal decomposition me-

chanism.

In this work, we present a computa-

tional study on the gas phase decom-

position of t-butyl methyl ether

catalyzed by hydrogen halides. The

aim of this investigation is to get in-

sights about the reaction mechanism

while analyzing the electronic effect

of changing the halide in the energy

barriers and reaction rates.

Scheme 1. T-butyl methyl ether gas phase decomposition catalyzed

by hydrogen halides

InfoANALÍTICA 10(2)

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To characterize the gas phase decom-

position of t-butyl methyl ether ca-

talyzed by different hydrogen halides,

the DFT long-range dispersion-co-

rrected Head-Gordon hybrid functio-

nal wB97XD (Chai & Head-Gordon,

2008b, 2008a; Grimme, 2006; Mora,

Cervantes, & Marquez, 2018), as im-

plemented in Gaussian 16 (Frisch et

al., 2016) software, was used. Moreo-

ver, a LanL2DZ basis set was emplo-

yed to describe the system as it has a

wider application being able to co-

rrectly describe atoms from Na-La

and Hf-Bi (Check et al., 2001; Fars-

hadfar, Chipman, Yates, & Ariafard,

2019; Ganji & Ariafard, 2019; Wadt

& Hay, 1985). T-butyl methyl ester,

hydrogen fluoride, hydrogen chlo-

ride, hydrogen bromide, and hydro-

gen iodide were optimized in the gas

phase. Furthermore, a frequency

analysis was done at 656.15 K, which

is the average temperature reported

in the experiments. Berny analytical

gradient optimization algorithm was

employed to optimize transition state

structures. Frequency calculations

were later run to confirm whether the

TS structure is correct by identifying

only one negative frequency descri-

bing the decomposition.

To get an insight in all the changes

occurring as the decomposition pro-

ceeds, the intrinsic reaction coordi-

nate (IRC) plot was obtained

(Gonzalez & Bernhard Schlegel,

1989; H. P. Hratchian & Schlegel,

2005; Hrant P. Hratchian & Schlegel,

2004). From the IRC calculation, the

reaction force (RF) molecular descrip-

tor is obtained taking the negative de-

rivative of the energy over the

normalized reaction coordinate as

described in equation 1.

The RF profile is key to extract infor-

mation about all the geometrical

changes and electronic ones that

occur as the reaction is taking place

(Herrera & Toro-Labbé, 2007; Martí-

nez & Toro-Labbé, 2009; José R.

Mora et al., 2018; Toro-Labbe, 1999).

In a unimolecular, concerted mecha-

nism, the RF profile presents three

zones i.e the reagents region going

from the reagents (R) to x1; the tran-

sition state region (from x1 to x2); and

the products region (from x2 to the

COMPUTATIONAL METHODS

(1)

GAS PHASE DECOMPOSITION OF T-BUTYL METHYL ETHER

CATALYZED BY DIFFERENT HYDROGEN HALIDES: A DFT STUDY

Cuesta et al., 65–79

products). By integrating each zone

four reaction “works” can be estima-

ted giving information about the elec-

tronic and geometrical contributions

to reach the TS and during the relaxa-

tion process in the products forma-

tion (equation 2).

Finally, the reaction electronic flux

(REF) plot was also obtained. As its

name suggest, the REF describes the

different electronic rearrangements

happening during the reaction where

positive values means spontaneous

events while negative ones non-spon-

taneous (Duarte & Toro-Labbé, 2011;

Giri, Parida, Jana, Gutiérrez-Oliva, &

Toro-Labbe, 2017). Furthermore, ne-

gative values imply bond weakening

while positive values bond strengthe-

ning. This descriptor is obtained using

the chemical potential (μ) as de-

scribed in equation 3 (Flores-Mora-

les, Gutiérrez-Oliva, Silva, & Toro-

Labbé, 2010; Herrera & Toro-Labbé,

2007).

To obtain the chemical potential, the

finite difference approximation and

the theorem of Koopmans were used

to be able to define in terms of the

fron tier molecular orbitals LUMO

(Lowest Unoccupied Molecular Or-

bital) and HOMO (Highest Occu-

pied Molecular Orbital) that are

estimated in the gaussian calculation

(equation 4).

(2)

(3)

(4)

RESULTS

To study the gas phase decomposi-

tion mechanism of t-butyl methyl

ether catalyzed by hydrogen halides

(HX) and the influence of different

halides in the activation mechanism,

four models were built. Then, the ac-

tivation free energies (ΔG‡), activation

enthalpies (ΔH‡), and activation en-

tropies (ΔS‡) were obtained as shown

in Table 1.

InfoANALÍTICA 10(2)

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Table 1. Hydrogen-Halide bond distance (dHX), Halide electonegativity (χ),

and thermodynamic parameters of the gas decomposition of t-butyl methyl

ether catalyzed by hydrogen halides

Model HX dHX χ pKa ΔG‡ ΔH‡ ΔS‡

(Å) (kJ/mol) (kJ/mol) (J/mol.K)

F HF 0.94 3.98 3.1 174.8 98.9 -167.5

Cl HCl 1.31 3.16 -6.0 133.9 68.5 -135.7

Br HBr 1.46 2.96 -9.0 126.9 64.4 -129.0

I HI 1.63 2.66 -9.5 123.6 67.5 -120.9

The experimental activation energies

found for the gas phase decomposi-

tion of t-butyl methyl ether catalyzed

by hydrogen chloride was 134.3

kJ/mol (Stimson & Watson, 1966a),

which is in good agreement with the

activation free energies estimated for

the case of the system catalyzed with

HCl (133.9 kJ/mol). Activation en-

tropy values were all negative, which

was expected as going from the

reagent to the transition state implies

the system becomes more organized.

Results showed that as the halide po-

sition is going down in the periodic

table, the activation free energy and

activation enthalpy decreases, while

entropy increases.

To get insights in all the changes oc-

curring as the decomposition occurs,

IRC calculations were performed on

the four models (Figure 1).

Figure 1. IRC plot of the gas

decomposition of t-butyl methyl ether

by hydrogen halides

The IRC profile of the studied reac-

tions presents a similar shape, an ex-

pected result since they all describe

the same reaction following the same

mechanism. As the mechanism ad-

vances from the reagent to the prod-

ucts, the first event is a shift of the

methyl group in the t-butyl making a

hydrogen atom (H2) points towards

the halide. The proton is then trans-

ferred from the halide to the oxygen

GAS PHASE DECOMPOSITION OF T-BUTYL METHYL ETHER

CATALYZED BY DIFFERENT HYDROGEN HALIDES: A DFT STUDY

Cuesta et al., 65–79

while the C-O bond is cleaved. In the

F model, the C-O bond is cleaved

first than the H-X bond. In the Cl

model, both bonds are cleaved at

roughly the same time. In the Br and

I models, however, the H-X bond is

cleaved before the C-O. The transi-

tion state structure (Figure 2) is achie -

ved as the second proton transfer, the

one that goes from one methyl group

of the t-butyl to the halide, starts. Fi-

nally, the proton is transferred to the

halide and the double bond formed.

The main distances for each model

are shown in Table 2.

a. b. d.c.

Figure 2. Transition state structures of the gas decomposition of t-butyl methyl

ether catalyzed by HF (a), HCl (b), HBr (c), HI (d). e.

Transition state scheme with atom labeling

Table 2. Distance of different atoms at the transition state of the gas

decomposition of t-butyl methyl ether catalyzed by hydrogen halides

Model X1-H2 H2-O3 O3-C4 C4-C5 C5-H6 H6-X1

F 1.451 1.028 2.181 1.432 1.257 1.313

Cl 2.107 0.993 2.483 1.422 1.220 1.833

Br 2.308 0.990 2.535 1.423 1.212 2.009

I 2.527 0.988 2.562 1.427 1.200 2.225

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Julio 2022

To get a better view on the geometri-

cal and electronic changes occurring

as the reaction progresses, the RF

profile was plot for the four halide

systems (Figure 3).

As observed in the IRC, the RF plot is

also similar between the different

models. Although the mechanism oc-

curs in a concerted way, the profiles

obtained present a small change in

the slope around ξ=0.3. Looking at

the changes occurring at this part of

the mechanism, it can be seen it

matches with a first event that is the

proton transfer from the halide to the

oxygen followed by the carbon-oxy-

gen bond cleavage. Then, a minimum

in the RF plot is observed when the

second event starts i.e., the proton

transfer from the t-butyl to the halide,

accompanied by the double bond

formation. To study the geometrical

and electronic contributions, the four

reaction works were estimated (Table

3) where positive work values show

the system is taking up energy, and

negative values means the system is

giving energy (relaxation process).

Figure 3. RF plot of the gas

decomposition of t-butyl methyl ether

by hydrogen halides

Table 3. Reaction works of t-butyl methyl

ether catalyzed by hydrogen halides

Model W1 W2 W3 W4

F 126.50 54.16 -11.49 -76.17

Cl 78.42 59.35 -7.94 -23.10

Br 73.71 51.22 -7.71 -12.41

I 59.00 46.05 -4.33 -11.32

To get more insights in the electronic

events occurring during the gas de-

composition of t-butyl methyl ether

catalyzed by hydrogen halides, the

REF plot was obtained (Figure 4).

Same as observed in the RF plot, the

main event occurs during the second

proton transfer and double bond for-

mation where a negative peak in the

GAS PHASE DECOMPOSITION OF T-BUTYL METHYL ETHER

CATALYZED BY DIFFERENT HYDROGEN HALIDES: A DFT STUDY

Cuesta et al., 65–79

electronic flux of the system can be

observed. Interestingly, a positive

peak is observed as H2is being trans-

ferred to O3and O3-C4bond is being

cleaved. After that maximum, values

start going down up to the second

event where any interaction between

the carbon and the oxygen is lost

while the C5-H6weakens to start the

proton transfer. Finally, all bonds start

strengthening forming C=C double

bond and the H-X bond.

Figure 4. REF plot of the gas

decomposition of t-butyl methyl ether

catalyzed by hydrogen halides

DISCUSSION

The gas phase decomposition of t-

butyl methyl ether catalyzed by hy-

drogen halides is going to produce

isobutene and methanol. The results

found here suggest that, as the halide

is more electronegative, it requires

more energy to transfer its proton to

the oxygen which is detected in an

increased activation energy. To get in-

sights in this proton transfer mecha-

nism, the electronegative values of

the halides, the halide-hydrogen dis-

tance, and the pKa of the halides

were related to the activation param-

eters estimated. A good linear corre-

lation was achieved comparing

thermodynamic parameters with the

studied halides properties (R2values

above 0.8). For the electronegativity,

the highest R2value was obtained for

ΔS‡(0.995) followed by ΔG‡(0.958),

and ΔH‡(0.867). Furthermore, the R2

values found for the correlation be-

tween HX distance vs thermody-

namic parameters were 0.916 for

ΔG‡, 0.804 for ΔH‡, and 0.972 for

ΔS‡. Finally, for the pKa, R2values of

0.991 for ΔG‡, 0.952 for ΔH‡, and

0.984 for ΔS‡were obtained. Interest-

ingly, the highest correlation values

were noticed for the correlation be-

tween thermodynamic parameters

InfoANALÍTICA 10(2)

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and the halides pKa. This parameter

is associated with the halogen-hydro-

gen dissociation energy which is key

in the proton transfer event and di-

rectly influence the activation energy.

High R2values were achieved with

ΔS‡which is related with the loss of

degrees of freedom when going from

the reactant to the transition state,

mainly associate with the rotation

component of the partition function.

ΔH‡present the lowest correlation

values which can be attributed to the

higher activation enthalpy obtained

for the I model compared to the Br

one.

Comparing the transition state of the

different models, the distance from

the halide (X1) to the hydrogen (H2)

at the transition state increases as the

electronegativity of the halide de-

creases ranging from 1.45 Å to 2.53

Å (Table 2). For all models, the proton

of the halide is already forming a

bond with the oxygen except for the

F model where the bond is not fully

formed. While a typical OH bond is

0.96 Å, the Cl, Br, and I models pres-

ent a distance around 0.99 Å, being

0.03 Å longer for the F model. Look-

ing at the carbon-oxygen bond clea -

va ge (O3-C4), the distance is much

smaller in the F model (2.18 Å) than

the other three models where the dis-

tance is around 2.50 Å. Interestingly,

the largest C4-C5distance was found

for the F model followed by the I, Br,

and Cl models. This occurs because

in models Cl, Br, and I, the double

bond formation between C4 and C5

only depends on the H6 transfer,

while in the F model apart from the

proton transfer, the C4-C5 distance is

influenced by O3 that is around 0.2

Å shorter than the other models. For

the distance between the t-butyl car-

bon and the hydrogen (C5-H6), the

distances do not vary much between

the different models being around

1.20 Å. Finally, for the H6-X1dis-

tance, an increase in 0.20 Å was es-

timated from Cl to Br and to I

increasing to 0.50 Å when going from

F to Cl.

During the mechanism, in order to

achieve the transition state structure,

an electronic energy of 54.16 kJ/mol,

59.35 kJ/mol, 51.22 kJ/mol and 46.05

kJ/mol is needed for the F, Cl, Br, and

I models respectively. From that ener -

gy, around 60% is due to the geomet-

rical rearrangement in all models

except the F one, where geometrical

contribution is 10% higher (70%).

GAS PHASE DECOMPOSITION OF T-BUTYL METHYL ETHER

CATALYZED BY DIFFERENT HYDROGEN HALIDES: A DFT STUDY

Cuesta et al., 65–79

Electronic rearrangements are bet -

ween 30.0% in the F model, up to

43.8% in the I model; Br model pre -

sent an electronic contribution of

41.0% and the Cl one 43.1%. Once

the TS is achieved, the system relaxes

up to the products, where geometri-

cal contributions are higher than

electronic ones.

In the REF graph, the peak formed in

the second event is greater, meaning

the second proton transfer is the most

energetic event and, therefore, the

rate limiting step in the reaction, in

accordance with the IRC and RF

plots.

CONCLUSION

Study of the gas phase decomposition

of t-butyl methyl ether catalyzed by

hydrogen halides at the ωB97XD/

LANL2DZ level of theory shows that

although the mechanism is homoge-

neous and unimolecular, the same

can be divided into two main events.

Changing the halide in the reaction

influence the reactivity of the reac-

tion being the reaction catalyzed by

HI the most reactive and the less re-

active the one using HF. The thermo-

dynamic parameters were observed

to have a good correlation with the

electronegativity of the halide and the

distance of the hydrogen-halide

bond. In this sense, the best correla-

tions found were between ΔS‡andX,

and between ΔS‡and H-X (0.995 and

0.972 respectively). The IRC plot

shows a concerted mechanism.

Looking at the RF plot, a small stabi-

lization of the system is noticeable

that matches the first proton transfer.

From the estimated reaction works, it

can be concluded that geometrical

contribution accounts between 57%

to 70% of the energy needed to reach

the transition state structure, while

geometrical contributions only for

about 35%. Finally, the REF profile

agrees with all the above mentioned

where an electronic redistribution is

observed during the two main events

that describe this gas phase decom-

position reaction.

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