DFT Study of the Isomerization of Hexyl Species Involved

8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved

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Journal of Ca talysis 181,124–144 (1999)

Art icle ID jcat.1998.2293, availa ble on line at htt p://ww w.idea librar y.com on

DFT Study of the Isomerization of Hexyl Species Involvedin the Acid-Catalyzed Conversion of 2-Methyl-Pentene-2

M. A. Natal-Santiago, R. Alcalá, a nd J. A. D umesic1

D epartment of Chemical E ngineeri ng, Uni versity o f W isconsin, M adison, Wisconsin 53706

R eceived J une 23, 1998; revised O ctob er 1, 1998; a ccepted O ctob er 7, 1998

Quantum-chemical calculations were conducted on the basis of

density-functional theory to study reactions of hexyl species in-

volved in the acid-catalyzed isomerization of 2-methyl-pentene-2.

The production of 4-methyl-pentene-2 and 3-methyl-pentene-2 in-

volves 1,2-migrations of hydrogen atoms and methyl groups whose

activation energies are lower than 30 kJ/mol for gaseous carbe-

nium ions. The activation energy for branching rearrangements of gaseous hexyl cations to form 2,3-dimethyl-butene-2 is 94 kJ/mol.

Transformations of hexyl species were studied in the presence of

gaseous water and an aluminosilicate site to simulate reactions on

acidic oxides. In the presenceof these oxygenated (conjugate) bases,

the cationic center in the carbenium ions bonds with oxygen to form

alkoxonium ions and alkoxy species, respectively. The relative en-

ergies of these species are fairly insensitive to their secondary or ter-

tiary nature. R eactive intermediatesof the same order are stabilized

morethan the corresponding transition statesupon interaction with

an oxygenated base, thus leading to an increase in the activation

energies of isomerization reactions. Transition states have greater

separation of electronic charge than the corresponding alkoxonium

ions and alkoxy species. The transition state for branching rear-

rangement requires the greatest separation of electronic charge in

the aluminosilicate cluster; the transition state for methyl migration

requires the second greatest separation of electronic charge; tran-

sition states for hydride shifts require a smaller separation of elec-

tronic charge; and transition states for the protonation of alkenes

to form alkoxy species require the least separation of electronic

charge in the aluminosilicate cluster. These observations imply the

existence of a correlation between the positive charge localized in

the hydrocarbon fragment of a transition state and the sensitivity

of the corresponding reaction pathway to changes in the acidity

of the catalyst. Lastly, activation energies for alkene isomerization

reactions over aluminosilicates are determined by the energies of transition states with respect to the gaseous reactants plus the acid

site and not by the relative stabilities of the alkoxy intermediates in

the reaction scheme. c 1999 Academic P ress

K ey Words: carbenium; alkoxonium; alkoxy; methyl-pentene;

isomerization; silica–alumina; density-functional theory (dft).

1 To w hom correspondence should be a ddressed.

1. INTRODUCTION

The a cid-cata lyzed conversion of hydrocarbo ns th

cracking, alkylation, and isomerization reactions isportance in the petrochemical industry (1). C ata lys

for these transformations typically consist of ino

liquid acids (e.g., H 2SO 4) or solid oxides such as

phous aluminosilicates and zeolites. Mechanisms focatalyzed conversions of hydrocarbons have tradit

been d escribed in terms of carbenium and /or carb

ions (2–11), which have been observed in homogesuperacidic media (12–14). For example, carbeniu

may be formed by protonation of a lkenes or by pro

cracking of alkanes via carbonium ions. These carb

ions may then lead to surface chain reactions, inv

propagation steps such as isomerization, oligomeriβ-scission, a nd hydride transfer, w hich are eventua

minated by steps such as desorption of a lkenes and

tion of coke.The isomerization of carbenium ions proceeds th

branching and nonbranching rearrangements. Nonb

ing rearrangements involve successive hydrogen an

migration steps, whose activation energies are ty

lower than 30 kJ/mol when the degree of the cat

mains constant (as in tra nsitions between seconda rynium ions) (13, 14). These processes are believed to p

via transition sta tes conta ining three-center, two-e

bonds involving the migrating entity. In contrast,

tion energies of b ranching rearra ngements of speci

ing more than four carbon atoms are typically highe

65 kJ /mol (13, 14), and t hese processes are be lieved ceed via transition states that resemble protonatedpropane rings.

Activity and selectivity patterns for the conversion

drocarbons over solid acid catalysts have been exp

using ana logies with reactions of carbenium ions in

solutions (2–11), where reactivity trends ar e typically

on differences in the stabilities o f primary, seco

and tertiary carbenium ions. However, this tradviewpoint has been shown to be overly simplistic, sin

reactive intermediates on solid catalysts are more s

124


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ISOMERIZATION OF 2-METHYL-PENTENE-2

to (neutral) a lkoxy species than to (charged) carbenium

ions. D espite evidence for the existence o f cyclopentenyl,

indanyl, a nd trityl cat ions on acidic zeolites (15, 16), most

spectroscopic (15, 17–23) and quantum-chemical (20, 24–

34) investigations have shown that the ground states ofprotonated species involve strong interactions with surface

oxygen atoms (the conjugate basic form of the adsorption

site). Therefor e, these species are d escribed more correctly

as alkoxy species covalently bonded to the oxide surface,and their relative stabilities are insensitive to w hether the

hydrocarbon fragment is of a primary, secondary, or ter-

tiary nature. However, these alkoxy species may react viaformat ion of tra nsition states that resemble carbenium ions

by stretching o f the C –O b ond ( 3, 24, 25, 35–44). B eca use of

the ionic character of these transition stat es, a ctivation en-

ergies for reactions of hydro carbons on solid acid cata lysts

are different for primary, secondary, and tertiary species,

thereby suggesting tha t the success of kinetic models ba sed

on reactions of carbenium ions is caused by an o rdering of

the a ctivation energies rather tha n the relative stabilities of

the reaction intermediates (25).R eactions of hydrocarbons that possess multiple path-

ways are useful probes for the characterization of acid cata -

lysts (45–48). Figure 1 show s several pa thw ay s fo r isomer-

ization of hexyl species in the acid-catalyzed conversion of

2-methyl-pentene-2 (2-MP -2). Accord ing t o McVicker a nd

coworkers (45, 46, 48), the conversion of 2-MP -2 can becatalyzed by amorphous aluminosilicates and the relative

rates of isomerizationprocesses depend on the acidity of the

cata lyst: weak a cids cata lyze migration of the double bond

to produce 4-methyl-pentene-2 (4-MP-2) via 1,2-hydride

shifts; stronger acids are req uired to cata lyze methyl migra-tions that lead to 3-methyl-pentene-2 (3-MP-2); and even

stronger acids are needed t o a chieve branching rearrange-ments involved in the productio n of 2,3-dimethyl-butene-2

(2,3-D MB -2).

In the present pa per, we present results from qua ntum-

chemical calculations performed on the basis of density-

functional theory (D FT) to study the isomerization of hexyl

species involved in the acid-cat alyz ed conversion of 2-MP -2

to 4-MP -2, 3-MP -2, a nd 2,3-D MB -2. O ur studies consist ofthree scenarios: isomerization of hexyl cations in the gas

phase, reaction in the presence of gaseous wa ter, and tra ns-

format ions of hexyl species on a B rønsted a cid site chara c-teristic of amorphous aluminosilicates. The use of a water

molecule is intended as a first approximation to simulate

the conjugate ba sic form of a n acid site after protona tion of

an alkene. The use of a neutral (O H )3SiOHAl(OH)3 clus-

ter is intended to simulate more realistically the acid site of

an amorphous aluminosilicate. The three scenarios chosen

for our studies provide a general view of how the rates of

isomerization of hexyl species are aff ected as the a cidity o f

the a cid site becomes progressively wea ker in moving from

H⊕ to H 3O⊕ to a neutral a luminosilicate.

Q uantum-chemical ca lculations ha ve been perf

previously for the isomerization of gaseous butyl (4

and pentyl (52) cat ions; how ever, to o ur knowledge

calculations have not yet been conducted for the isomtion of hexyl species. We w ill show that the a ctivati

ergies for hydride and methyl migrations involving g

carbenium ions are lower tha n 30 kJ/mol. Rea ctions

ing cations of the same d egree proceed through tra

states that contain two -electron, three-center bonds iing the migratory entity, whereas transition states

actions involving cat ions of different degree resembless stable, in our case secondary, cations. Activati

ergies for branching rearrangements in the gas pha

predicted to be near 94 kJ/mol, a nd these reaction

ceed via transition states that resemble protonated

propane rings. In the presence of a water molecu

cationic centers of the various hexyl cations interac

oxygen to form alkoxonium ions whose relative enare less sensitive to their degree, that is, whether th

secondary or tertiary species. The relat ive energies

various hexyl (a lkoxy) species on the aluminosilicaare even less sensitive to their degree. Hydride and m

migrations, a s well a s bra nching rea ctions, fo r t hese

onium ions and alkoxy species require the separat

electronic charge and proceed t hrough transition stwhich the positive charge becomes more localized

hydrocarbon fragment.

2. METHODOLOGY

Q uantum-chemical calculations were performed

ba sis of D FT, using the three-para meter functiona l B(53) along with gaussian-type basis sets (54). This fun

was chosen becauseit has been shown (52) to describe

format ions of hyd rocarbons a s well as M øller–P lessturbation methods (54), while being computationally

efficient. In general, D FT functionals are known to

well for the prediction of thermochemical proper

systems containing light atoms, although they becom

useful for the description of heavy atoms or highly ch

systems (55).

The basis set 6-31G ∗ was used to study reactions lated hexyl catio ns, while t he lar ger ba sis set 6-31+G

used to compare tra nsformations of carbenium ionsgas phase and in the presence of a water molecule.

tions on amorphous aluminosilicates were studied us

Brønsted acid site (OH)3SiOHAl(OH)3. This clust

chosen because it is the smallest one that can be us

liably while maintaining an a cceptable computationaH owever, it should b e recalled that qua ntum-chemic

culations within the cluster approximation are str

dependent on the number surface and bulk atoms

porated in the model, so qua ntitative predictions are

be interpreted absolutely.


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126 NATAL -SANTIAG O, AL CA L Á , AN D D U M E S I C

Simulations involving the aluminosilicate cluster were

conducted using the ba sis set 6-31G ∗ for the hydrocarbon

fragment and the acidic hydrogen, 6-31+G ∗ for the bridg-

ing o xygen, a nd 3-21G ∗ for silicon, a luminum, and the six

terminating hydroxyl groups. D etailed information a boutthe methods used can be found elsewhere (56, 57). The

calculations w ere performed using the software package

G AUSSIAN94® (58) on IB M SP2 and D E C-alpha computers.

Structural parameters w ere determined by optimizing tostationary points on the potential energy surface (PE S) cor-

responding either to the stoichiometry C 6H⊕13, C 6H 13O H

⊕2 ,

or C 6H 13OSiAl(OH)6 using the Berny algorithm and re-dundant internal coordinates (59). Ca rbenium and a lkoxo-

nium ionswere optimized fully, whereas C 6H 13OSiAl(OH)6clusters were optimized partially by constraining the SiO tH ,

A lO tH , O bSiO tH, and O bA lO tH angles to va lues of 129.8◦,

129.9◦, 180.0◦, and 180.0◦, respectively, obtained from an

optimization of the bare acid site, where O t and O b repre-

sent terminal and bridging oxygen atoms, respectively.Tra nsition sta tes were located on the corresponding P E S

to estimate activation energies for the isomerization ofhexyl cations in the ga s phase and interacting with water

FIG. 1. R eact ion scheme fo r isomeriza tion o f 2-meth yl-pentene-2 (2-MP -2) to 4-meth yl-pentene-2 (4-MP -2), 3-meth yl-pentene-2 (3-MP

2,3-dimethyl-butene-2 (2,3-D MB -2) over the a cid H –X. The symbol X is replaced b y a positive charge for t ransforma tions of gaseous carbeni

and aluminosilicate sites. The location of transition

employed a STQ N method, which uses a linear or qu

synchronous transit approach to get closer than an

guess to the quadratic region of the PES, followe

quasi-Newton or eigenvalue-following algorithm tplete the optimiza tion (60). Opt imizatio n criteria co

of maximum a nd ro ot-mean-squared forces of less t

a nd 15 J /mol-pm, respective ly. The clusters resultin

optimizations were classifi ed a s local minima o r trastates on the PES by calculating the Hessian matr

lytically. For local minima, the eigenvalues of the H

matrix were a ll positive, whereas fo r tra nsition stateone eigenvalue wa s negative (54). Vibrationa l freq u

obtained from analyses of force constants were use

ther without scaling to estimate thermochemical p

ties of the clusters at 298 K. Typically, the error asso

with the use of DFT methods for the estimation o

tion energetics is less or equa l to 20 kJ /mol (56, 5

pending on the energy functional, basis sets, and sizemolecular cluster used. To verify t hat the tra nsition

correspond to the chemical reactions of interest, sic reaction coordinate calculations were performe


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mass-weighted internal coordinates to follow the reaction

paths in forw ard and reverse directions from the fi rst-order

saddle points (61–63).

3. RESULTS

3.1. Intermediates in the Isomerization S cheme

The conversion of 2-MP-2 to produce 4-MP-2, 3-MP-2,

and 2,3-D MB -2 can be described a s proceeding throughprotonation of 2-MP-2 to form the tert iary species

2-methyl-pentyl-2 (A), as show n in Fig. 1, which can subse-

quently rea ct through one of three pathw ays. First, speciesA can undergo rearrangement to the secondary species

2-methyl-pentyl-3(B ) through a 1,2-hydrid e migratio n, fol-

lowed by deprotonation to yield the alkene 4-MP-2. Al-

ternatively, species B can undergo consecutive methyl and

hydride migrations to form the tertiary species 3-methyl-

pentyl-3 (D ), whose subsequent deprotonation yields

3-MP -2. Finally, species A can undergo two types of bra nch-

ing rearrangements to produce 2,3-D MB -2. O ne pathw ayconsists of a direct branching rearrangement of species

A to the tertiary species 2,3-dimethyl-butyl (F), w hose

subsequent d eproto nat ion yields 2,3-D MB -2. The second

pathway involves the formation of the secondary species

4-methyl-pentyl-2 (E ) via 1,3-hydrid e shift, follow ed by the

branching rearrangement of this species to species F. Thissecond pathway can also lead to the formation of species

B and, t hus, to the production of 4-MP -2 and eventually to

the forma tion of 3-MP -2 thro ugh a subsequent 1,2-hydrid e

shift.

Optimized structures of the hexyl cations involved in the

gaseousconversion of 2-MP-2are shown in Fig. 2. Structuralpara meters and relat ive energies ar e listed in Tab les 1 and2, respectively. In general, energies for gaseous secondary

catio ns are calculat ed to b e 40–50 kJ /mol higher tha n those

for tertiary cations, in agreement with literatureda ta (13, 14,

64). All hexyl ca tions in our stud y exhibit sp2-hybridization

of the carbon a tom bearing the fo rmal charge, indicating

the presence of an empty p-orbital. All carbenium ions ex-hibit distortions such as elongation of C –H (or C –C) bonds

and reduction of CC H (or CC C) angles resulting from hy-

perconjugative interactions (50). These interactions mini-

mize the energy of the cations by maximizing the overlapbetween the vacant p-orbital at the formal cationic cen-

ter a nd nearb y, occupied orbitals from t he afo rementioned

bond s. To highlight these effect s in Fig. 2, elonga ted C –Hbonds (∼112 pm) are marked by black hydrogen atoms,

wherea s typical C–H bond lengt hs of 109–110 pm are iden-

tified b y shadowed hyd rogen atoms. These elongated bonds

are oriented nearly parallel to the vacant p-orbital. More-

over, secondary cations B, C, and E exhibit additional in-

teractions between their cationic centers and a djacent C–C

bonds, leading to low values for specific CCC angles (thatis, values from 80◦ to 90◦). The incorporation of diffuse

FIG. 2. Struct ures of (A ) 2-meth yl-pentyl-2, (B ) 2-methyl-p

(C ) 3-meth yl-pentyl-2, (D ) 3-meth yl-pentyl-3, (E ) 4-meth yl-penty

(F) 2,3-dimethyl-butyl-2 cations. “Sh ado wed” hydrogen a toms fo

bonds of a typical length within 109to 110 pm, whereas “b lack” h

atoms form elongated C–H bonds of lengths greater than 111 pto hyperconjugative interactions. Structural parameters for the op

cations in this fi gure are listed in Table 1.

functions into the basis set 6-31G ∗ does not affect

icantly the relative energies of the rea ctive interme

however, these a dditional functions accentuate the

of hyperconjugative interactions involving C–C bothe structure of the secondary cations B, C , and E .

In the presence of a water molecule, the carbon

bearing the positive charge in gaseous hexyl cat ion

bridizes to a state betw een sp

2

and sp

3

when it interacthe oxygen atom to form an alkoxonium ion. Opti

structures of the a lkoxonium ions formed from ca ti

B, C, D, and F are shown in Fig. 3, and their structuramet ers and relat ive energies are listed in Tab les 3

respectively. The (attra ctive) energies of interaction,

between water and the gaseous carbenium ions ar

listed in Tab le 4. The ener getic d ifference of ∼45

between secondary and tertiary cations in the gas

is lower b y ∼20 kJ /mol f or the corresponding a lkox

ions, since gaseous seconda ry cations B and C are stamore by interactionswith water than are the tertiary c


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TABLE 1

Structural Parameters Obtained U sing the B asis Set 6-31G∗ for the Optimized R eactants and Products Shown in Fig. 2

A B C D E F

D istances (pm)

C 1C 2 147 (147) 164 (153) — — 153 (153) 147 (147)

C 2C 3 147 (147) 143 (143) 141 (141) 147 (147) 169 (168) —

C 3C 4 153 (153) 146 (146) 171 (152) 147 (147) 141 (141) 153 (153)

C 4C 5 153 (153) 153 (153) 152 (153) 153 (153) 147 (147) 160 (160)C 1C 3 — — 152 (171) 147 (147) —

C 2C 4 — — — — — 146 (146)

C 2C 6 147 (147) 153 (164) 148 (148) 158 (158) 153 (153) 147 (147)

H C 2 — 109 109 109–110 110 —

H C 3 110, 112 109 109 — 109 109–110

H C 4 110 110, 112 109–110 110, 111 109 110

Angles (◦)

C 1C 2C 3 121.0 (121.2) 90.7 (118.6) — — 106.7 (107.7) —

C 2C 3C 4 120.4 (120.4) 128.0 (128.0) 81.3 (122.0) 119.3 (119.3) 88.4 (88.8) —

C 3C 4C 5 111. 5 ( 111. 5) 119. 8 ( 119. 9) 109. 8 ( 114. 2) 119. 7 ( 119. 8) 125. 6 ( 125. 7) 110. 9 ( 111. 0)

C 1C 2C 6 119.3 (119.3) 110.4 (110.4) — — 116.0 (116.0) 118.8(118.8)

C 1C 3C 4 — — 112.4 (113.9) 120.8 (120.9) —

C 2C 3C 1 — — 121.8 (77.8) 119.9 (119.9) — —

C 2C 4C 3 — — — — — 117.9 (117.7)C 2C 4C 5 — — — — — 101.3 (101.8)

C 6C 2C 3 119.5 (119.5) 118.8 (91.3) 125.9 (126.0) 106.5 (106.6) 107.7 (107.0) —

C 6C 2C 4 — — — — — 119.9 (120.0)

C 1C 2C 4 — — — — — 121.2 (121.2)

Note. Values in pa renthesis correspond to the use o f t he ba sis set 6-31+ G ∗ .

A, D, and F. Specifically, the stabilization energy changes

associated with the interaction of wa ter with seconda ry andtertiary hexyl cations to form alkoxonium ions are 72 and

40–53 kJ /mol (Tab le 4), re spectively. Theref ore, t he ener-

gies of alkoxonium ions are less sensitive to their primary,

secondary, or tertiary nature when compared to gaseous

TABLE 2

E nergetics (kJ /mol) P redicted U sing the Basis S et 6-31G∗ for Various Pathways

Involved in the Isomerization of Isolated Hexyl Cations

E a H G

Overall reactions

2-MP -2+H⊕→A −866 (−866) −841 (−841) −846 (−846)

A → B 45 (45) 48 (49) 52 (52)

B →C −5 (4) −3 (5) −2 (4)

C→

D−

44 (−

53)−

47 (−

54)−

50 (−

54)A →E 47 (47) 51 (51) 56 (56)

A → F −5 (−4) −2 (−2) 1 (1)

Tran sition stat es

A →TS1 72 (72) 70 (70) 75 (75)

A →TS2 49 (49) 52 (52) 58 (58)

C →TS3 27 (18) 19 (11) 20 (14)

E →TS4 15 (15) 10 (10) 17 (17)

E →TS5 21 (21) 12 (12) 15 (15)

E →TS6 45 (45) 42 (42) 48 (48)

A →TS7 94 (94) 94 (94) 105 (104)

Note. Values in pa renthesis correspond to the use o f t he ba sis set 6-31+ G ∗.a These values have not been corrected by t he corresponding changes in zero-point energies.

carb enium ions. The dista nce between the cationic ce

the hydrocarbo n and the oxygen atom in wa ter is preto ra nge from 164 to 174 pm. This distance is compar

the typical length of 143 pm for C –O bo nds, suggesti

these two a toms interact covalently. According to Mu

population analyses (Fig. 3), abo ut 60% of the tota l p


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FIG. 3. Alkoxonium ions formed upon interaction of hexyl cations

A, B, C, D, and F with water. Structural parameters for these optimized

cations a re listed in Table 3. The Mulliken charges included in t his figure

are associated w ith the H 2O fragment within each cluster.

charge is localized in the hydrocarbo n fra gment within the

alkoxon ium ions.

The interactions of alkenes with Brønsted acid sites on

the surface of oxides such as aluminosilicates can lead t o for-

mation of π -complexes prior to their protona tion and even-

tual formation of alkoxy species. Optimized structures of

th e π -complex and transition state involved in the protona-tion of 2-MP -2 are show n in Fig. 4. The π -complex fo rmed

upon adsorption of 2,3-D MB -2is also shown in Fig. 4. Struc-

tura l para meters are listed in Tab les 5 and 6, while relat ive

energies are listed in Table 7. A s reported elsewhere f oradsorption of isobutene on silica (27), the fo rmation o f π-

complexes results mainly in perturbation of the C == C bond

by surface hydroxyl groups. The energy of formation asso-ciated with π-complexes is predicted to be −62±4 kJ /mo l

(Table 7), and it is relatively independent o f t he nat ure of

the adsorbed hexene. The Mulliken charge of the hydro-

carbon fra gment of the transition stat e is+0.48e versus the

value of −0.08e for the π-complex, and the a ctivation en-

ergy for protonation, thus, depends on the ability of the

surface to dona te a proton to the ad sorbed alkene. The ac-tivation energy for the protonation of 2-MP-2 to form a

tertia ry a lkoxy species is predicted to b e 71 kJ/mol r

to the π-adsorbed alkene. These results are in agre

with previous ab initio studies performed by K aza ns

coworkers (19, 32, 34) f or the prot onation of ethen

H -zeolites, which led t o a n a ctivat ion energy o f 64 relative to π-adsorbed ethene.

It has been suggested (65–68) that the acid streng

site can be represented theoretically by t he deproto

energy of a representative cluster (and this value is eqthe proton a ffi nity of the conjugate basic form of th

The deprotonation energy is defi ned as the energy re

to remove a proto n from the cluster, and it d ecreasesacid strength of the cluster increases. The deproto

energy of the a luminosilicate cluster used througho

studies is 1420 kJ /mol (Tab le 7), and this va lue is with

range of 1000 to 1600 kJ /mol found by Sauer, Ka z

TABLE 3

Structural Parameters for the Optimized Alkoxonium

Ions Shown in Fig. 3

A –W B –W C –W D –W F–W

D istances (pm)

C 1C 2 151 155 — — 151

C 2C 3 152 152 152 152 —

C 3C 4 155 152 155 152 154

C 4C 5 153 153 153 154 154

C 1C 3 — — 155 151 —

C 2C 4 — — — — 154

C 2C 6 151 154 151 153 152

H C 2 — 110 109 110 —

H C 3 110 109 110 — 109,H C 4 110 110 110 110 110

H O 98 98 98 98 98

C 2O 174 — 164 — 170

C 3O — 164 — 171 —

Angles (◦)

C 1C 2C 3 116.4 108.0 — — —

C 2C 3C 4 112.8 120.7 112.4 113.7 —

C 3C 4C 5 111.0 116. 8 113.8 118.0 110

C 1C 2C 6 115.7 110.5 — — 113

C 1C 3C 4 — — 111.9 116.7 —

C 2C 3C 1 — — 107.7 116.4 —

C 2C 4C 3 — — — — 114

C 2C 4C 5 — — — — 114

C 6C 2C 3 116.6 112.5 119.4 117.8 —C 6C 2C 4 — — — — 116

C 1C 2C 4 — — — — 116

C 1C 2O 100.0 — — — 100

C 3C 2O 100.0 — 104.8 — —

C 4C 2O — — — — 102

C 6C 2O 104.0 — 106.2 — 104

H C 2O — — 97.8 — —

C 1C 3O — — — 100.7 —

C 2C 3O — 104.5 — 101.2 —

C 4C 3O — 106.7 — 105.0 —

H C 3O — 97.7 — — —

H OH 107.8 108.0 108.3 107.6 108


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TABLE 4

Energetics (kJ/mol) Predicted for Various Pathways Involved in the

Isomerization of Alkoxonium Ions Formed upon Interaction of the Hexyl

Cations Shown in Fig. 2 with Water

E a H G E xperimentalb

Overall reactions

H 3O⊕→H 2O +H

⊕ 706 671 675

2-MP -2+H 3O⊕

→A –W −199 −191 −142A –W→B –W 26 29 31

B –W→C –W 4 3 2

C –W→D –W −25 −27 −26

A –W→F–W 9 8 11

Tran sition stat es

A –W→TS1–W 58 43 30 ∼46

A –W→TS2–W 66 58 46 58

C –W→TS3–W 34 18 5 ∼8

A –W→TS7–W 104 92 83 73

Heats of formation (−E w ): I−W→ I +W

A –W 53

B –W 72

C –W 72D –W 44

F–W 40

TS1–W 66

TS2–W 35

TS3–W 56

TS7–W 42

a These values have not been corrected by the corresponding changes in zero-

point energies.b These values correspond t o tra nsformations in liquid, superacidic media a s

report ed in R efs. (13) and (14).

FIG. 4. π-complexes formed upon a dsorption of (a) 2-MP-2 and

(b) 2,3-D MB -2 on a n aluminosilicate site. The transition sta te for t he pro-

tonation of Fig. a is shown in Fig. c. The structural parameters are listed

in Tab les 5 and 6.

and their coworkers (65, 67, 68) for various mo

B rønsted acid sites on aluminosilicates. In compa risdeprotonation energy of the hydronium ion (equal

proton a ffinity of water) is calculated to be 706

(Table 4), reflecting the fa ct tha t t he hydronium i

stronger acid than the neutral aluminosilicate cluste

The protona tion and f urther reactio n of 2-MP -2 ovminosilicates yields a series of alkoxy species, an

optimized structures are shown in Fig. 5. Structu

rameters a nd relative energies are listed in Tables

7. The values of C C C and C CH angles in Table 5 in

that the carbon a tom nearest to the bridging oxygen

hybridized, in contrast to the sp2

hybridization withgaseous carbenium ions. In add ition, the C –O distan

150–155 pm are only slightly longer than the value of

which is typical of single C –O bonds, thus suggesti

these two atoms interact covalently. Therefore, these

species are alkoxy species associated with the alumi

cate cluster. Importantly, the energies of formation

various alkoxy species (−74±14 kJ/mol on averagrelatively independent of their primary, secondary,

tiary nature. Mulliken charges associated with the

carbon f ragments of the a lkoxy species in Fig. 5 rang

+0.25e to +0.30e .


8/21


TABLE 5

Structural Parameters for the Optimized π -Complexes and Hexyl (Alkoxy) Species

on an Aluminosilicate Site as S hown in F igs. 4 and 5

3.2. Transition S tates in the Isomerization Scheme

3.2.1. Pro duction of 4-M P-2 (TS1)

The optimized structure of the transition state (TS1) for

the 1,2-hydride migration involved in the isomerization ofA to B is shown in Fig. 6. E nergetic and structural parame-

ters of TS1 are listed in Tab les 2 and 8. The act ivatio n en-ergies for the forward and reverse reactions are predicted

to be 72 kJ /mol and 27 kJ/mol, respectively. U ncerta inties

in these energies can be caused by ina ccurate accounting of

electron-correlation effects by the D FT method, since the

proper inclusion of electron-correlation energies is crucial

when modelling the behavior of carbenium ions (50–52).

Nevertheless, the results of our calculations are in agree-ment with previous D FT and ab initio studies (52) of sec-

onda ry to tertiary 1,2-hydride shifts in methyl–butyl cations,

which have predicted the activation energy to be be

12 and 32 kJ/mol.

The C–H bond involving the migrating hydrogen

in TS1 is nearly pa rallel to the empty p-orbital in at

which bears the formal charge. This prediction is inment with the suggestion of B rouwer (13, 14) that the

p-orbital in the formal cationic center becomes cowith the sp3-orbital carrying the migrating entity for

shift to achieve maximum stability of the transition

Mulliken population a nalyses indicate that TS1 resem

secondary cation whose positive charge is localized

in atom C 3.

The presence of a water molecule has a significant

on the energetics for the 1,2-hydride migration invothe isomerization of A to B. The optimized structu

this transition state (TS1–W) is shown in Fig. 7, a


9/21


TABLE 6

Structural Parameters for Transition States of 2-MP-2 Protonation and Isomerization

R eactions on an Aluminosilicate Site as S hown in F igs. 4 and 8

energetic a nd structural para meters are listed in Tables 4

and 9, respectively. The activation energies for the forwardand reverse reactions are predicted to b e 58 and 32 kJ/mol,

respectively. These predictions are higher than the valuesof 46 and 8 kJ/mol reported by B rouwer and coworkers

(13, 14) for 1,2-hydride migrations from tertiary to sec-

ondary carbenium ions in superacidic solutions. Calculated

enthalpies of a ctivation are in bett er agreement with these

experimental barriers. Nevertheless, our predictions are

within the error expected from D FT calculation s (56, 57). It

should be noted tha t since TS1 and B ar e seconda ry cations,they are stab ilized by interactions with wa ter more than the

tertiary cat ion A; stab ilization energies are estimate

53, 72, a nd 66 kJ/mol f or intera ctions of A, B, and Tspectively, w ith w at er (Tab le 4). Therefo re, the a ct

energy for the tertiary to secondary 1,2-hydride migin the presence of water is lower than in the gas phase

the activation energy for the secondary to tertiary re

is slightly higher.

The Mulliken charge associated with the hydro

fra gment in TS1–W is increased to 98% of the to ta l

as shown in Fig. 7, and this charge is mainly locali

atom C 3. Therefore, the isomerization process invseparation of electronic charge within the transition


10/21


TABLE 7

E nergetics (kJ /mol) Predicted for Various Pathways Involved

in the Isomerization of Hexyl Species over an Aluminosilicate

Site

E a H E xperiment alb

Overall reactions

H -X→H⊕+X− 1420

2-MP-2→ 4-MP-2 (trans ) 6 5 52-MP-2→ 3-MP -2 (trans ) 3 3 4

2-MP-2→ 2,3-D MB -2 1 0 −1

Intermediates

2-MP -2—H -X (π) −65

A -X −73

B -X −77

C -X −93

D -X −70

F-X −56

2,3-D MB -2—H -X (π) −58

Tran sition sta tes

TS (2-M P -2 p ro t on a tio n) -X 6

TS1-X 41 22–52TS2-X 71 55–68

TS3-X 52

TS7-X 117

No te. Energies of the reactive intermediates a nd transition states

are report ed relative t o 2-MP -2+H-X, where X represents the con-

jugate base of the acid site.a These values ha ve not been corrected by the corresponding

changes in zero-point energies.b Overall heats of reaction are calculated from data in standard

thermodynamic tables. Apparent activation energies correspond to

reactions over amo rphous silica-alumina and ultrastab le Y-zeolite as

reported in R ef. (45).

This view is also supported by the long C 2–O and C 3–Odistances of 324 and 273 pm, respectively, which suggest

that TS1–W consists essentially of a carbenium ion (TS1)

and neutral water.

The optimized structure of TS1 interacting with the alu-

minosilicate cluster (H -X ) is show n in Fig. 8. Structural pa -

ramet ers and rea ctions energetics are listed in Tab les 6 and

7, respectively. The activation energy for the forward re-action (A-X →B -X ) is predicted to be 41 kJ/mol relat ive

to gaseous 2-MP-2 plus the acid site. As in the analogous

case involving alkoxonium ions, the activation of A-X toproduce B -X via 1,2-hydride shift req uires the separat ion

of charge, leading to a transition stat e that resembles a ca r-

benium ion plus the conjugat e ba sic for m of t he oxide clus-

ter: Mulliken charges for the hydrocarbo n fragments withinA-X and B-X are+0.30e a nd +0.26e , whereas thischarge is

increased to +0.51e wit hin TS1-X . The existence of a car be-

nium ion within TS1-X is also evident from the long C 2–O

and C 3–O distances and the predicted rehybridization of

these carbo n ato ms from a sp3 stat e in the alko xy species to

a nea rly sp2 state in the tra nsition state.

3.2.2. Pro duction of 3-M P-2: 1,2-M ethyl Shift ( T S2)

The optimized structure of the transition state (TS

the 1,2-methyl migra tion involved in t he isomerizatio

to C is shown in Fig. 6, and the energetic and structu

rameters are listed in Tables2 and 8. The activation en

for the forward and reverse reactions are both pre

to b e lower tha n 10 kJ/mol. The ma in fea ture o bserthe structure of TS2 is a three-center, two-electron

involving atoms C 2, C 3, and the migrating atom C

C 1–C 2 and C 1–C 3 distances a re nea r 187 and 180 pmthe C 1C 2C 3 and C 2C 3C 1 angles are approximately 6

70◦, respectively. This symmetric position o f t he mig

methyl group is expected on the basis of the smal

getic difference between the stable species involvedreaction. The Mulliken charges associated with ato

through C 6 in TS2 indicate that the positive charge

localized in a specific carbon atom, but that it is deloc

in the C 1C 2C 3-ring.

The presence of a water molecule has a signific

fect on the isomerization of species B to C. The opt


11/21


FIG. 5. H exyl (alkoxy) speciesfo rmed upon adsorption and reaction of 2-MP -2 and its isomers on an aluminosilicate site. The structural par

are listed in Tab le 5.

structure of TS2 interacting with w ater is shown in Fig. 7,

and the corresponding energetic and structural pa rametersare listed in Tab les 4 and 9, respectively. The a ctivatio n en-

ergies for the forward and reverse reactions are predicted

to be 40 and 36 kJ/mol, respectively, a nd these va lues are

higher tha n the experimental va lue of 14 kJ/mol report ed

by B rouw er an d cow orkers (13, 14). The stab ilization ener-gies associated with the formation of alkoxonium ions from

interactions of B and C with wa ter are both near 72 kJ/mol

(Ta ble 4), whe rea s this va lue is 35 kJ/mol fo r TS2. There-

fore, reactive intermediates are stabilized more tha n the

transition stat e upon interaction with w ater, resulting in an

increased activation energy. Mulliken charges (Figs. 3 and7) indicate that nearly all the positive charge is localizedin the hydro carb on fra gment wit hin TS2–W. Moreo ver, the

long C 2–O and C 3–O distances (305 and 322 pm, respec-

tively) also suggest that TS2–W comprises essentia lly a free

carbenium ion (TS2) a nd neutral wa ter.

The optimized structure TS2 interacting with the alumi-

nosilicate cluster is shown is Fig. 8. Structural parameters

and reaction energetics are listed in Tables 6 a nd 7, re-spectively. The activation energy for the forward reaction

(B-X →C-X) is predicted to be 71 kJ/mol relative to

gaseous 2-MP -2 plus the a cid site. As in the ana logous case

involving alkoxonium ions, the activation of B -X to p

C-X via 1,2-methyl shift requires the separation of cleading to a transition state that resembles a carbeniu

plus the conjugate ba sic for m of the oxide cluster: M

charges for the hydrocarbon fragments within B-

C -X are+0.26e a nd +0.27e , whereas thischarge isinc

to +0.54e within TS2-X . The existence of a carb eniwithin TS2-X is also evident fro m the long C 2–O and

distances and t he predicted rehybridization of these

atoms from a sp3 state in the a lkoxy species to a nea

state in the tra nsition state.

3.2.3. Produ ction of 3-M P-2: 1,2-H ydri de Shif t (TS3

The optimized structure of the transition state (T

the 1,2-hydride migration involved in the isomerizaC to D is shown in Fig. 6, and energetic and structu

rameters are listed in Tables2 and 8. The activation e

for the forward and reverse reactions are predicted

27 (18) a nd 71 (71) kJ /mol, respectively, using t he b

6-31G ∗ (6-31+G ∗). TS3 is similar to TS1, since it

bles a secondary cation; Mulliken charges in TS3 s

that the positive charge is localized mainly in C 2. Thformed between the C–H bond containing the mig


12/21


FIG. 6. Tran sition stat es of elementa ry reactio ns (TS1) A ↔ B , (TS2)

B ↔ C, (TS3) C ↔D , (TS4) A↔E, and (TS5) E ↔ B. The structural pa -

ram eters a re listed in Tab le 8.

hydrogen atom and the C 2–C 3 bond is 98◦, showing that

this C–H b ond a ligns with the vacant p-orbital in C 2.The optimized structure of TS3 interacting with water is

shown in Fig. 7, and the corresponding energet ic and struc-

tura l para meters ar e listed in Tab les 4 and 9, respectively.

The activation energies for the forward and reverse con-

version of C to D are 34 and 59 kJ/mol upon interaction

with water, and these values should be compared to the

experimental values of 8 and 46 kJ/mol referred to pre-viously. Calculated enthalpies of activation are in better

agreement with these experimental barriers. Nevertheless,

our predictions are within the error expected from DFT

calculatio ns (56, 57). The a ctivatio n energy for the reversereaction is lower by 12 kJ/mol than the gas-phase va lues,

and this behavior is caused by the stronger interaction with

water of secondary species C and TS3, compared to thetertiary species D. St abilization energies for species C, TS3,

a nd D a re 72, 56, an d 44 kJ /mol, re spectively (Ta ble 4). Fur-

thermore, the isomerization process involves a separa tion

of charge since 99% of the total is localized in the hydro-

carb on fra gment within TS3–W. The lo ng C 2–O and C 3–O

distances (268 and 324 pm, respectively) also suggest that

TS3–W consists essentially of a carbenium ion (TS3) andneutral water.

The optimized structure of TS3 interacting with th

minosilicate site is shown in Fig. 8. Structural pa ram

and reaction energetics a re listed in Tables 6 and

spectively. The activation energy for the forward re(C-X →D -X) is predicted to be 52 kJ/mol relat

gaseous 2-MP -2 plus the bare acid site. As in the

gous case involving alkoxonium ions, the activation

to produce D -X via 1,2-hydride shift req uires the s

tion of charge, leading to a transition state that resea carbenium ion plus the conjugate basic form of t

ide cluster; Mulliken charges for the hyd rocarbon f rawithin C-X a nd D -X a re both+0.26e , whereas thisch

increased to +0.51e wit hin TS3-X . The existence of a

nium ion within TS3-X is also evident from the long

and C 3–O distances and the predicted rehybridizat

these carbo n ato ms from a sp3 state in t he alko xy spe

a nea rly sp2 state in the t ransition stat e.

3.2.4. Pro duction of 2,3-D M B -2 (T S4, TS5, and TS6

The production o f 2,3-D MB -2 can t ake place thtwo pathways. The first pathway consists of conse

1,3-hydride migrations and branching rearrangemenspecies A, to species E, and then to species F. The s

FIG. 7. Transition states o f elementary reactions (TS1–W

↔ B –W, (TS2–W) B –W↔C –W, (TS3–W) C –W↔D –W, and

W) A–W↔ F–W. The structural pa rameters are listed in Table

Mulliken charges included in this figure a re associated w ith the H

ment within each cluster.


13/21


TABLE 8

Structural Parameters Obtained U sing the B asis Set 6-31G∗ for Optimized Transition S tates Shown in Figs. 6 and 9

Note. Values in parenthesis correspond to the use o f t he ba sis set 6-31+G ∗ .

pathwa y consists of a direct bra nching rearrangement from

species A to species F.The optimized structure of the transition state (TS4) for

the 1,3-hydride migration involved in the isomerization of

A to E is shown in Fig. 6, and energetic and structural pa-

rameters a re listed in Tables 2 a nd 8. The a ctivation en-

ergies for the forward and reverse reactions are predicted

to be 62 and 15 kJ/mol, respectively, rega rdless of t he b a-

sis set used. The activation energy for the reverse reaction,

although within the expected error, is slightly lower thanthe va lue of 36 kJ/mol (13) fo r 1,3-hydr ide shifts w ithin t er-

tiary 2,4-dimethyl-pentyl cations. TS4 has a two-electron,

three-center bond involving the migratory entity, but theoverall structure of this edge-protonat ed cyclopropane ring

is somewhat more complex than TS2. The HC 2C 4 angle of

51◦ and the relatively short C 2–C 4 distance of 189 pm sug-gest the formation of a partial bond b etween these two car-

bon atoms. In addition, Mulliken charges associated with

the carbon atoms in TS4 suggest that the positive charge is

delocalized within the H C 2C 4-ring.

Cation E can undergo a 1,2-hydride shift to form sec-

ondary cation B or a branching rearrangement to form

tertiary cation F. The optimized structure of the transitionstate (TS5) for isomerization of species E to B is shown in

Fig. 6, and energetic and structural parameters are li

Tab les 2 and 8. The activa tion energies for the fo rwareverse reactions a re bo th pred icted to be nea r 22 k

and they are ∼10 kJ/mol higher tha n experimenta l

for 1,2-hydrid e shifts in secondary n-butyl catio ns (

The migrating hydrogen atom is positioned symme

between atoms C 3 a nd C 4, which are the atoms b

the forma l positive charge in cations B and E , respe

A two-electron, three-center bond is formed involvmigratory entity, resulting in d elocalization of the p

charge within the HC 3C 4-ring.

The bra nching rearra ngement of species E to F pr

via transition state TS6. The optimized structure ftransition state is shown in Fig. 9, and the energe

structural pa ramet ers are listed in Tab les 2 and 8,

tively. The a ctivation energies for the fo rwa rd a nd rreactions a re predicted to be 45 and 97 kJ/mol, r

tively. These results are in agreement with values o

85 kJ/mol o bta ined fro m previous D FT and ab ini

culations (52) of the activation energy for the sec

to tertiary b ranching rearra ngement of n -pentyl to m

butyl cations.

TS6 resembles a prot ona ted cyclopropane ring. Twa rd reaction requires not only the migration of a hy


14/21


TABLE 9

Structural Parameters for the Optimized Transition

States Shown in Fig. 7

ato m from ato m C2 to C 3, but also the cleavage of t he C 2–C 3bond and formation of the C 2–C 4 bond. The migrating hy-

drogen atom is positioned between atoms C 2 and C 3; the

H –C 2 and H–C 3 distances and the HC 2C 3 angle are 116 pm,

157 pm, and 58◦, respectively. The C 2–C 3 and C 2–C 4 dis-

tances of 183 and 161 pm suggest cleavage of the formerand formation of the latter bond. The positive charge ap-

pears to be localized mainly in atom C 4 according to the

Mulliken cha rges.

3.2.5. Pro duction of 2,3-D M B -2 (T S7)

A second pathway for the production of 2,3-D MB -2 is

through the direct branching rearrangement of species A

to F. This reaction proceeds via tra nsition stat e TS7, whose

structure is shown in Fig. 9 while energetic a nd structural

para meters a re listed in Tab les 2 and 8, respectively. The

activation energies for the forwa rd and reverse reactions

ar e pred icted to be 94 and 99 kJ /mol, r espectively. TS7 re-sembles a protona ted cyclopropane ring, with the migrating

hydrogen ato m positioned between C 3 and C 4. The fo

reaction also requires the cleavage of the C 2–C 3 bon

format ion of the C2–C 4 bo nd. The C 2–C 4 distance of 1

indicatesthe formation of thisbond. The positive cha

pears to be localized in atom C 2 according to the M ucharges.

The optimized structure of the transition state f

direct branching rearrangement in the presence of

(TS7–W) is shown in Fig. 7, and the correspondinggetic and structura l para meters are listed in Tab les 4

The activation energies for the forward and reverse

tions a re 104 and 95 kJ /mol, r espectively, w hich a re than t he experimental value of a pproximately 73kJ /m

ported by B rouwer and coworkers (13, 14). Nevert

our predictions are within the error expected from D F

culations. The activation energy for t he forw ard reac

10 kJ /mol higher tha n tha t predicted in t he gas pha se

the tertiary cat ion A is stabilized by w ater more t ha

In particular, the magnitudes of the energy changeinteraction w ith w ater are 53 and 42 kJ/mol fo r spe

a nd TS7, respectively (Tab le 4).The branching rearrangement of species A to F

presence of a water molecule involves a separat

charge w ithin TS7–W, a s indicated by Mulliken popu

analyses (Figs. 3 and 7). The charge localized in t

drocarbo n f ragment of TS7–W is 98% of the t ota l ccompared to 60% for species A and F in the prese

FIG. 8. Transition stat es for the elementa ry reactions (TS1

↔ B -X, (TS2-X) B -X ↔C-X, and (TS7-X) A-X ↔F-X. The st

para meters are listed in Table 6.


15/21


FIG. 9. Transition stat es of elementa ry reactions (TS6) E ↔ F and

(TS7) A ↔ F. The structura l para meter s are listed in Tab le 8.

water. In a ddition, the C 2–O and C 3–O distances are rela-

tively lo ng (337 and 272 pm, respectively), suggesting t hat

TS7–W consists essentially of a carbenium ion (TS7) andneutral water.

The optimized structure of TS7 interacting with the alu-

minosilicate cluster is shown is Fig. 8. Structural parameters

an d react ion energetics ar e listed in Tab les 6 and 7, respec-tively. The activation energy for the forward (A-X →F-X)

reaction is predicted to be 117 kJ/mol relative to gaseous

2-MP-2 plus the acid site. As in the analogous case involv-ing alkoxonium ions, the activation of A-X to produce F-X

via branching rearrangements requires the separation of

charge, leading to a transition stat e that resembles a carbe-

nium ion plus the conjugate ba sic form o f the o xide cluster;

Mulliken charges for the hydrocarbo n fragment within A-X

and F-X are +0.30e a nd +0.25e , w hereas this charge is in-

creased t o +0.58e within TS7-X . The existence of a carb e-nium ion within TS7-X is also evident from the long C 2–O

and C 3–O distances and the predicted rehybridiza

these carbo n at oms from a sp3 stat e in the a lkoxy spe

a nea rly sp2 state in the tra nsition state.

4. DISCUSSION

The isomerization of gaseous hexyl cations in

branching and nonbranching rearrangements whos

are signifi cantly different. I n particular, nonbranchinrangements consist of relatively fast 1,2-migrations

drogen atoms and methyl groups whose activation en

ar e predicted t o be lower tha n 30 kJ/mol fo r speciessame cationic order, or relative to the less stable

The energetic difference between reactive interm

also pla ys an importa nt ro le: this difference is 40–50

between secondary and tertiary cations. Transition

for rea ctions of cat ions of the same order ha ve the p

charge delocalized within two-electron, three-center

involving the migratory entities, which are symme

positioned between the cationic centersof the reactaproducts. Tran sition states for reactio ns of cat ions of

ent order resemble the less stable, in our case seco

cations. On the other hand, branching rearrange

whose activation energies are predicted to be near

mol, a re more complex reactions involving the sim

ous cleava ge and forma tion of C –C and C –H bonds. tion states for these transformations resemble prot

cyclopropane rings. The complete energy profi le for t

merization of gaseous hexyl cations is shown in Fig.

Activation energies predicted for the isomeriza

gaseous hexyl cations are generally higher than

determined experimentally in superacidic solutioBrouwer and coworkers (13, 14). While uncertainthese energies can be caused by inaccurate accoun

electron-correlation effects by the D FT method (5

these discrepancies could indicate that reaction m

based on gaseousca rbenium ions are not applicable t

ies in condensed media. Better agreement betwee

dicted and experimental activation energies is genera

tained if hexyl cations are allowed to interact with wfor m alkoxonium ions. For example, the proper orde

the rat es of 1,2-methyl versus 1,2-hydrid e shifts is ob

for reaction models based on alkoxonium ions. Thplete energy profi le for reactions of these alkoxoniu

is shown in Fig. 10. Transformations of alkoxoniu

are less dependent on t he degree of the cations sinc

relative energies are less sensitive to the cationic ordactions of alkoxonium ions are determined mainly

required separation of electronic charge upon act

of the reactive intermediates: ∼60% of the total p

charge is localized in the hydrocarbo n fra gments of

onium ions while this charge is increased to more tha

of the total charge within transition states. Therefore

carbenium ions of the same order are stabilized m


16/21


FIG. 10. Energy profile for isomerization of gaseous hexyl cations

(dashed line) and cationsinteractingw ater (solid line) through nonbranch-

ng and branching rearrangements. The energies are reported relative to

hat of alkoxonium ion A–W.

interactions with water than the corresponding transition

states, activation energies are predicted to increase with re-

spect to those for gaseous reactions.The use of a water molecule in our structural models

allows for an understanding of the factors that limit the

transformat ion of hexyl species in the presence of a n oxy-

genated (conjugate) ba se. H owever, the deprotonat ion en-ergy o f hy dro nium ions is too low (706 kJ/mol) compa red

to t hat of a cidic oxides (1000–1600 kJ/mol) to allow for the

generation of a quantitative model of the relevant surface

chemistry. Furthermore, reaction intermediates on oxide

surfaces are expected to b e (neutra l) alkoxy species in con-

trast to (charged) alkoxonium ions. This situation is repre-

sented in the present study by calculations involving neutralaluminosilicate clusters having a deprotonat ion energy o f

1420 kJ/mol. The complete energy profi le fo r rea ctions of

these alkoxy species is shown in Fig. 11.

FIG. 11. E nergy profile for isomerizatio n of hexyl species on an a lu-

minosilicate site. The energiesare reported relative to gaseous2-MP-2plus

he a cid site. Activation energies for the protona tion of π -complexes are

assumed equal to t hat ca lculated f or the proton atio n of 2-MP -2 (Table 7).

The reaction scheme for the isomerization of 2-M

4-MP -2, 3-MP -2, and 2,3-D MB -2 over a luminosilica

be written as

where H -X represents the B rønsted a cid site.

To compare t he results of our calculations with

imental data for isomerization of 2-MP-2 to give 4

over aluminosilicat e cat alysts, it is necessar y to deriveexpression based on the reaction scheme presented

For this purpose, we make the following assumption

(1) a dsorption–desorption processes are q uasi-brated;

( 2) fre e en ergies o f a ct iv at io n fo r p ro t on

deprotonation processes are independent of the nat

the a lkene;

(3) free energies of isomerizatio n steps are indep

of the nature of alkoxy species such that rate coeffi

for the forward a nd reverse reactions are equal in eaca nd

(4) reaction conditions a re such that only 4-M

formed.

O n the ba sis of these assumptions, the overa ll rate

merization () in the limit of zero pressure of 4-MPbe expressed as

4MP2 = f (θ,G) g(G, PA ),

where f a nd g are functions of surface coverage by

species (θ ), G ibbs free energies of gaseous and s

species (G ), and the proton af fi nity of the cata lyst site

Specifically,


17/21


f (θ,G) =K πK pPr

1+ (1+ K p)K π Pr

g(G,PA ) =k AB

1+ 2K p(k AB/k p),

where k A B a nd k p are rate coeffi cientsfor surface isomeriza-

tion (A-X →B -X ) a nd proto nation reactions, respectively;

K p a nd K π are equilibrium constants for surface protona-

tion reactions and for π-ad sorption of 2-MP -2; and P r isthe par tial pressure of 2-MP -2. It should now b e noted tha t,

since

2K pk AB

k p 1,

the effective rate coefficient for the production of 4-MP-2

is approximately given a s

k eff4MP2 ≈ k ABK πK p

=k BT

hK = ABK πK p,

where k A B has been replaced by its estimate from transi-

tion sta te t heory (69). The prod uct K =

A B K πK p is the overall

equilibrium constant for the reaction:

2-MP-2+H -X TS1-X.

Therefore, the rate of double-bond isomerization is deter-

mined by the free energy of the transition state (TS1-X)

with respect to gaseous 2-MP-2 plus the acid site, and itis not controlled by the relative stabilities of π or alkoxy

complexes.The dependence of the rate of double-bond isomeriza-

tion on the a cidity of the cata lyst is incorporated implic-

itly in g through activation energies for surface protona tion

(E p) and isomerization (E AB ) reactions. This dependence

on surface a cidity becomes evident if one a ssumes that

E p = E 0 p − ε p

E AB = E 0 AB − ε AB ,

where E 0p a nd E 0A B a re defi ned with respect to the weak-acid

limit (e.g., amo rphous aluminosilicates) and positive values

of εp a nd εA B correspond to stronger acids, such that

4MP2 = f (θ,G)

k 0 AB exp

ε AB

RT

1+ 2K pk 0 AB

k 0 pexp

ε AB − ε p

RT

.

A s discussed later, we expect εp to be less sensitive than εA Bto changes in the acid strength of the cata lyst; therefore,

εp < εAB , and 4MP2 increases as the catalyst becomes more

acidic.

We no w note tha t M cVicker a nd co-wo rkers (45,

measured t he overa ll activa tion energy t o be 23 kJ /m

the rate of formation of 4-MP-2from 2-MP-2. Accor

the analysis presented above, thisvalue should be comto t he energy of TS1-X relat ive to ga seous 2-MP -2 p

a cid site, wh ich is pred icted to b e 41 kJ /mol (Tab le 7)

experimental a nd predicted values of the o verall act

energy are in agreement, in view of the simplistic na

the aluminosilicate cluster used throughout our studWe consider next the rate of production of 3-MP-

2-MP-2. It can be seen in Fig. 11 that the activation for the conversion of B -X to C -X is predicted to be

than for the conversion of A-X to B -X a nd of C -X t

Therefore, we may assume that

k AB ≈ k CD k BC .

Also, we note that all rate coeffi cients for surface iization reactions are smaller than k p, since the act

energy fo r the protonat ion o f 2-MP -2 is low (6 k

Application of these assumptions leads to the followpression (in the limit of zero pressure of 4-MP -2 and

2):

3MP2 = K pk BC

k p4MP2.

In a manner analogous to that discussed above, o

show that the effective rate coefficient for the prod

of 3-MP-2 is approximately given as

k eff3MP2 ≈ k ABK πK 2 p

k BC

k p

=k BT

h

K = ABK

= BC K πK

2 p

K = p

,

where all rate coefficients have been replaced b

estimates from transition state theory (69). The p

K = ABK

= BC K πK

2 p/K

= p is the overall equilibrium const

the reaction

2-MP-2+ H -X +TSp-X, TS1-X +TS2-

where TSp-X is the transition state fo r the surface prtion of 2-MP-2. Therefore, the rate of production of 3is determined b y t he free energy of transition state

with respect to gaseous 2-MP-2 plus the bare acid s

by the free energy of TS2-X with respect to TSp-X . T

of rea ction is not a ffected by t he relative stab ilities

alkoxy complexes.

The ratio of t he rate of pro duction of 3-MP -2 to th

MP-2 (selectivity, S 3MP2) is approximately given as f

S 3MP2 ≈ K pk BC

k p.


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The dependence of S 3MP2 on the surface acidity becomes

evident if one assumes that

E p = E 0 p − ε p

E BC = E 0 BC − ε BC ,

where E 0p a nd E 0BC are defined with respect to the weak-

acid limit and positive values of εp a nd εB C correspond to

stronger acids, such that

S 3MP2 ≈ K pk 0 BC

k 0 pexp

ε BC − ε p

RT

.

As discussed later, surface protonation reactions are ex-

pected to be less sensitive than isomerization rea ctions to

changes in the acidity of the cata lyst; therefore, εp < εB C ,

a nd S 3MP2 increases as the catalyst becomes more acidic.

This predicted behavior is in agreement with experimental

observations (45, 46, 48).

The activation energies for the forward reactions B-X →C -X→D -X involved in the production of 3-MP -2 are

predicted to be 71 and 52 kJ /mol, respectively, rela tive t o

gaseous 2-MP -2 plus the a cid site. These ba rriers a re com-

parable t o the values of 55 and 23 kJ/mol reported by

McVicker and coworkers (45, 46, 48) for the 1,2-shifts of

methyl groups and hydrogen atoms over amorphous a lu-minosilicates. D iscrepancies between our predictions a nd

experimental values are probably caused by the high de-

protonation energy of the simplistic aluminosilicate cluster

chosen for our studies.

We consider next t he prod uction of 2,3-D MB -2 from 2-MP -2 over a luminosilicate clusters. It can b e seen in Fig. 11

that the activation energy for the reaction A-X →F-X isconsiderably higher than for all other isomerization reac-

tions; therefore, we may assume that

k AB ≈ k CD k BC k AF .

Also, we note that all rate coefficients for surface isomer-

ization reactions are smaller than k p. O n the ba sis of these

assumptions, the following ra te expression is obta ined (in

the limit of zero pressure of products):

23DMB2 =k AF

k AB

1+ K p

k AB

k p

4MP2.

The ratio of the rat e of production of 2,3-D MB -2 to tha t of

4-MP -2 ( selectivity, S 23DMB2) is approximately given a s

S 23DMB2 ≈k AF

k AB

1+ K p

k AB

k p

.

The dependence of S 23DMB2 on the surface a cidity b ecomes

evident if one assumes that

E p = E 0 p − ε p

E AB = E 0 AB − ε AB

E AF = E 0 AF − ε AF ,

where E 0p, E 0A B , and E

0A F are defined with respect

weak-acid limit and positive values of εp, εA B , and εrespond to stronger acids, such that

S 23DMB2

≈k 0 AF

k 0 ABexp

ε AF − ε AB

RT

1+ K p

k 0 AB

k 0 pexp

ε AB − ε

RT

The production of 2,3-D MB -2 is favored over st

acid cata lysts if surface bra nching reactions are mo

sitive than 1,2-hydride shifts and surface protonati

actions to changes in the acidity of the catalyst; tha

εA F > εA B > εp.An alternative approach to the generation of a r

pression for the rate of branching reactions cons

assuming tha t π-adsorption and surface protonatio

cesses are qua si-equilibrated in comparison to the b

ing rearrangement, in view of the high activation e

for t his isomerizat ion step. The surface covera ge by

then given by

θ A− X = K πK pPr θ H – X ,

and the forwa rd rate o f branching is

23DMB2 = k AF θ A− X

= k AF K πK pPr θ H − X

=k BT

hK = AF K πK pPr θ H − X ,

where k A F has been replaced by its estimate from

tion sta te t heory (69). The prod uct K =

AF K πK p is the

equilibrium constant for t he following reaction:

2-MP-2+ H -X TS7-X.

Therefore, we conclude that the rate of branching

rangements and, more generally, the rates of alke

merization reactions are determined by the free en

of transition states with respect to the gaseous reaplus the acid site and not by the relative stabilitie

and alkoxy intermediates in the reaction scheme. I

this reason, and the fact that transition states have

degree o f charge separation, that kinetic models

on carbenium-ion chemistry have been effective f


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description of reactions of hydrocarbo ns on solid acid cata -

lysts.

Finally, we consider whether our calculations can explain

why M cVicker and co-workers have found tha t wea k acids

catalyze 1,2-hydride shifts in 2-MP-2 to produce 4-MP-2;that stronger acids are required to catalyze methyl migra-

tions that lead to 3-MP -2; and that even stronger acids are

needed to achieve branching rearrangements involved in

the production of 2,3-D MB -2. We ha ve seen tha t t he ra teof production of 4-MP-2 is controlled by the free energy

of TS1-X with respect to gaseous 2-MP -2 plus the acid site

H-X, and we defined εA B a s the change in the energy of TS1-X with respect to the acidity of the catalyst. We have also

shown that the rate of production of 3-MP-2 is controlled

by the free energy of TS1-X relative to gaseous 2-MP-2

plus the acid site, and by the free energy of TS2-X relative

to that of TSp-X; εB C a nd εp were defined as the changes

in energy of TS2-X and TS p-X with respect to the acidity

of the cata lyst. Moreover, we ha ve shown that the rate ofproduction of 2,3-D MB -2 is controlled by the free energy

of TS7-X with respect t o ga seous 2-MP -2 plus the acid site,and we defi ned εA F a s the cha nge in t he energy o f TS7-X

with respect t o the a cidity o f t he cata lyst. To explain the

selectivity trends observed by McVicker and co-workers in

terms of acid strength, we need εA F > εB C > εA B > εp. This

trend is, in fact, justified by the Mulliken charges of 0.58e ,0.54e , 0.51e , and 0.48e of the hydrocarbo n fragments in TS7-

X, TS2-X, TS1-X, and TSp-X , respectively. H ence, there is

a correlation between the charge localized in the hydrocar-

bon fragment of a transition state in an alkene isomerization

scheme and the sensitivity of the corresponding reaction

pathw ay to changes in the acidity of the cata lyst. The tran-sition state for branching rearrangement (TS7-X) requiresthe greatest separation of electronic charge in the alumi-

nosilicate cluster, and its energy is most sensitive (through

εA F) to cha nges in the a cidity of t he cluster, tha t is, the ab il-

ity of the cluster to donate a proton. The transition state

for methyl migration (TS2-X) requires the second greatest

separation of electronic charge in the aluminosilicate clus-

ter, and its energy is thus less sensitive (through εB C) tochanges in the acidity o f the cluster. Transition states fo r

hydride shifts (TS1-X and TS3-X) require a smaller sep-

ara tion of electronic charge in t he a luminosilicate cluster,

and their energiesa re even lessd ependent (through εAB ) tochanges in the a cidity o f the ca talyst. La stly, the tra nsition

state fo r the proto nation o f 2-MP -2 (TSp-X) to form alkoxyspecies requires the least separation of electronic charge

in the aluminosilicate cluster, and the energy of this transi-

tion state is expected to be the least sensitive (through εp)

to changes in the acidity of the cluster. These observations

imply that the greater the extent of charge separation in the

transition stat e of certain reaction pathw ay in a n alkene iso-

merization scheme, the more sensitive is the selectivity forthis pathw ay t o changes in the acidity of the cata lyst.

5. CONCLUSIONS

The acid-cata lyzed conver sion of 2-meth yl-penten

MP -2) to 4-meth yl-pentene-2 (4-MP -2), 3-meth yl-pe

2 (3-MP -2), a nd 2,3-dimethyl-butene-2 (2,3-D MBbeen studied o n the b asis of density-functional th eo

production of 4-MP -2 and 3-MP -2 can be described

ceeding first through the protonation of 2-MP-2 t

the tertiary 2-methyl-pentyl-2 species. These specundergo 1,2-hydride migrations and subsequent de

nat ion reactions to yield 4-MP -2. A lterna tively, they

act via consecutive 1,2-shifts of hydro gen atoms and groups to yield 3-MP -2. The prod uction of 2,3-D MB

2-MP-2 can be described through initial protona

2-MP-2 to form tertiary 2-methyl-pentyl-2 species,

can react via two pathways. One pathway involves

hydrid e shift to form seconda ry 4-methyl-pentyl-2 s

which can react further via hydride a nd methyl mig

to yield 4-MP-2 and 3-MP-2, or can undergo brarearra ngement to yield 2,3-D MB -2. The second pa

consists of direct branching rearrangements of tertmethyl-pentyl-2species to form tertia ry 2,3-dimethyl

2 species, a nd t hereby yield 2,3-D MB -2.

The activation energies calculated for reacti

gaseous carbenium ions are not in good agreemen

experimental results for reactions in superacidic solBetter agreement is achieved if the carbenium io

allowed to react with a conjugate base, such as th

gen ato m of wa ter. R eaction intermediates interactin

oxygenated (conjugate) bases such a s wa ter o r an

nosilicate site resemble alkoxonium ions and alkox

plexes, respectively, and hydrocarbon fragments wittra nsition stat es resemble carb enium ions. Tran sitionfor reactions of cations of the same order contai

electron, three-center bonds involving the migrato ry

whereas transition states for reactions of cations of

ent order resemble the less stable cation. In the pr

of water or on an aluminosilicate site, secondary in

diates are stabilized more than tertiary intermediate

all intermediates are generally stabilized to a greater

than transition states. A ccordingly, the activation enassociated with rea ctions involving cations of the sa

der are increased upon interaction with the oxyg

(conjugate) ba se. The relat ive energies of a lkoxoniuand alkoxy species are fairly insensitive to their sec

or tertiary nature. In all cases, isomerization react

alkoxonium ions and alkoxy species require the sep

of charge w ithin the transition state. The rates of a lkemerization reactions are determined by the free ener

transition states with respect t o t he gaseous reactan

the acid site, and not by the relative stabilities of

alkoxy intermediates in the reaction scheme.

Finally, our calculations provide an explanation

McVicker and coworkers found that weak acids ca


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1,2-hydride shifts in 2-MP -2 to produce 4-MP -2; that

stronger acids are required to catalyze methyl migrations

leading to 3-MP-2; and that even stronger acids are needed

to achieve branching rearrangements involved in the pro-

duction of 2,3-D MB -2. Specifically, tra nsition sta tes for theprotonation of alkenes to form alkoxy species require the

least separation of electronic charge in the aluminosili-

cate cluster; transition states for hydride shifts require a

greater separation of electronic charge; the tra nsition statefor methyl migration requires an even greater separat ion of

electronic charge; and the tra nsition state for d irect bra nch-

ing rearrangements requires the greatest separa tion of elec-tronic charge in the aluminosilicate cluster. These obser-

vations imply the existence of a correlation between the

positive charge localized in the hydrocarbon fragment of

a transition state and the sensitivity of the corresponding

reaction pathwa y to changes in the acidity of the cata lyst.

ACKNOWLEDGMENTS

The authors acknowledge the financial support of the Office of BasicEnergy Sciences of the D epartment of Energy and the National C enter

for C lean I ndustrial and Treatment Technologies. We a lso acknow ledge

G EM and AO F fellowships awa rded to M.A .N.S. and a n AOF fellowship

awarded to R.A.

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DFT Study of the Isomerization of Hexyl Species Involved

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Transcript of DFT Study of the Isomerization of Hexyl Species Involved