-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
1/21
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
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
2/21
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.
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
3/21
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
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
4/21
ISOMERIZATION OF 2-METHYL-PENTENE-2
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
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
5/21
128 NATAL -SANTIAG O, AL CA L Á , AN D D U M E S I C
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
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
6/21
ISOMERIZATION OF 2-METHYL-PENTENE-2
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
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
7/21
130 NATAL -SANTIAG O, AL CA L Á , AN D D U M E S I C
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 .
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
8/21
ISOMERIZATION OF 2-METHYL-PENTENE-2
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
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
9/21
132 NATAL -SANTIAG O, AL CA L Á , AN D D U M E S I C
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
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
10/21
ISOMERIZATION OF 2-METHYL-PENTENE-2
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
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
11/21
134 NATAL -SANTIAG O, AL CA L Á , AN D D U M E S I C
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
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
12/21
ISOMERIZATION OF 2-METHYL-PENTENE-2
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.
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
13/21
136 NATAL -SANTIAG O, AL CA L Á , AN D D U M E S I C
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
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
14/21
ISOMERIZATION OF 2-METHYL-PENTENE-2
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.
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
15/21
138 NATAL -SANTIAG O, AL CA L Á , AN D D U M E S I C
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
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
16/21
ISOMERIZATION OF 2-METHYL-PENTENE-2
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,
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
17/21
140 NATAL -SANTIAG O, AL CA L Á , AN D D U M E S I C
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.
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
18/21
ISOMERIZATION OF 2-METHYL-PENTENE-2
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
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
19/21
142 NATAL -SANTIAG O, AL CA L Á , AN D D U M E S I C
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
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
20/21
ISOMERIZATION OF 2-METHYL-PENTENE-2
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.
REFERENCES
1. Satterfield, C . N., “ Heterogeneous Ca talysis in I ndustrial Pra ctice,”
2nd ed. McG raw–Hill, New York, 1991.
2. Corma, A., Chem. Rev.95, 559 (1995).
3. Van Santen, R. A., and Kramer, G. J., Chem. Rev.95, 637 (1995).
4. Meusinger, J., Vinek, H ., and Lercher, J. A ., J. M olec. C atal. 87, 263
(1994).5. Shertukde, P. V., Marcelin, G., Sill, G . A., and H all, W. K., J. Catal.136,
446 (1992).
6. Moffat, J. B., in “ Theoretical A spects of Heterogeneous C ata lysis”
(B. D avis, Ed.). Van Nostrand–R einhold, New York, 1990.
7. Abb ot, J., a nd Wojciechowski, B. W., J. Catal. 113, 353 (1988).
8. Abb ot, J., a nd Wojciechowski, B. W., J. Catal. 115, 1 (1989).
9. Wojciechowski, B. W., and C orma, A ., “ Ca talytic Cra cking: Ca ta lysis,
Ch emistry, a nd K inetics.” D ekker, New Yo rk, 1986.
10. Co rma, A., Planelles, J., Sánchez-Marı́n, J., and Tomás, F., J. Catal. 93,
30 (1985).
11. Co rma, A., P lanelles, J., and Tomás, F., J. Catal. 94, 445 (1985).
12. G ates, B. C ., “ Ca ta lytic Chemistry.” Wiley, New York, 1992.
13. B rouwer, D. M., and Hogeveen, H., Progr. Phys. Org. Chem. 9, 179
(1972).14. B rouwer,D . M., i n “ Chemistry and Chemical Engineering of Catalytic
Processes” (R . Prins and G . C. A . Schuit, E ds.). Sijthoff &Noordhoff,
Alphen aanden Rijn, The Netherlands, 1980.
15. H aw, J. F., and Xu, T., A dv. Catal.42, 115 (1998).
16. Xu, T., and H aw, J. F., J. A m. C hem. Soc.116, 7753 (1994).
17. H aw, J. F., Nicholas, J. B., X u, T., B eck, L . W., and Ferguson, D. B.,
A cc. Chem. Res. 29, 259 (1996).
18. Stepanov, A. G ., Za maraev, K. I ., and Thomas, J. M., Catal. L ett. 13,
407 (1992).
19. Ka zansky, V. B., A cc. Chem. Res.24, 379 (1991).
20. Malkin, V. G ., C hesnokov, V. V., P aukshtis, E . A ., a nd Zhidomirov,
G. M., J. A m. C hem. Soc.112, 666 (1990).
21. Haw, J. F., Richardson, B. R., Oshiro, I. S., Lazo, N. D., and
J. A., J. A m. C hem. Soc.111, 2052 (1989).
22. Aronson, M. T., G orte, R . J., Farneth, W. E ., and White, D
Chem. Soc. 111, 840 (1989).
23. Zardkoohi, M., Haw, J. F., and Lunsford, J. H., J. A m. C hem.
5278 (1987).
24. B ates, S. P., and van Santen, R., A dv. Catal.42, 1 (1998).
25. Rigby, A. M., Kramer, G. J., and van Santen, R . A., J. Cata
(1997).
26. Frash, M. V., Solkan, V. N., and Ka zansky, V. B., J. Chem. Soc.:
Transactions 93, 515 (1997).27. Natal-Santiago, M. A., de Pa blo, J. J., and D umesic, J. A., Ca
47, 119 (1997).
28. Mota, C . J. A., Esteves, P. M., and de Amorim, M. B., J. Phy
100, 12418 (1996).
29. Evleth, E. M., Ka ssab, E., Jessri, H., Allavena, M., Montero
Sierra, L. R ., J. Phys. Chem. 100, 11368 (1996).
30. Viruela-Mart ı́n, P., Z icovich-Wilson, C. M., and Corma, A.,
Chem. 97, 13713 (1993).
31. Ka zansky, V. B., Sechenya, I. N., and Pa nkov, A. A ., J. M ole
70, 189 (1991).
32. Sechenya, I. N., and Kazansky, V. B., Catal. L ett. 8, 317 (1991
33. Kazanskii, V. B., Bu ll. A cad. Sci. USSR: D iv. Chem. Sci. 39(
(1990).
34. Kazansky, V. B., and Sechenya, I. N., J. Catal. 119, 108 (198935. Ka zansky, V. B., Frash, M. V., and van Sa nten, R. A ., Catal.
61 (1997).
36. B laszkowski, S. R., Nascimento, M. A . C., a nd van Santen
J. Ph ys. C hem. 100, 3463 (1996).
37. Kramer, G. J., and van Santen, R. A., J. A m. C hem. Soc. 1
(1995).
38. B laszkowski, S. R ., Jansen, A. P. J. , Nascimento, M. A .
van Santen, R. A., J. Phys. Chem. 98, 12938 (1994).
39. Kramer, G. J., van Santen, R. A., Emeis, C. A., and Nowak
Nature 363, 529 (1993).
40. Kazansky, V. B., Frash, M. V., and van Santen, R. A., 11th In
Catal.101, 1233 (1996).
41. Collins, S. J. , and O’Malley, P. J. , Ch em. Phys. L ett. 2
(1995).42. Collins, S. J., and O’Malley, P. J., J. Catal. 153, 94 (1995).
43. Ka zansky, V. B., Senchenya, I. N., Frash, M. V., and van Sa
A ., Catal. L ett. 27, 345 (1994).
44. Ka zansky, V. B., Frash, M. V., and van Sa nten, R. A ., Catal.
211 (1994).
45. Kramer, G. M., McVicker, G. B., and Z ieman, J. J., J. Catal
(1985).
46. Kramer, G. M., and McVicker, G. B., A cc. Ch em. Res. 19, 78
47. McVicker, G. B., Kramer, G. M., and Ziemiak, J. J., J. Catal
(1983).
48. Soled, S. L., McVicker, G., Miseo, S., G ates, W., and B aumga
11th Int. Congr. Catal.101, 563 (1996).
49. Carb ó, S., Planelles, J., Ort ı́, E ., Viruela, P., and Tomás, F.
Struc. (Theochem) 150, 33 (1987).
50. Sieber, S., B uzek, P., Schleyer, P. v. R ., Koch, W., and de M . C
J. W., J. A m. C hem. Soc.115, 259 (1993).
51. B oronat, M., Viruela, P., and C orma, A., J. Phys. Chem.
(1996).
52. B oronat, M., Viruela, P., and Corma, A., J. Phys. Chem. 10
(1996).
53. B ecke, A. D., J. Chem. Phys. 98, 5648 (1993).
54. Hehre, W. J., Radom, L., and Schleyer, P. v. R., “Ab Initio M
Orbital Theory.” Wiley, New York, 1986.
55. Davidson, E. R., Int. J. Quant. Chem.69, 241 (1998).
56. Kohn, W., B ecke, A. D., and Pa rr, R . G., J. Phys. Chem. 10
(1996).
57. Z iegler, T., Chem. Rev.91, 651 (1991).
-
8/9/2019 DFT Study of the Isomerization of Hexyl Species Involved
21/21
144 NATAL -SANTIAG O, AL CA L Á , AN D D U M E S I C
58. Frisch, M. J., Trucks, G . W., Schlegel, H . B ., G ill, P. M. W., Jo hnson,
B. G ., R obb, M. A ., Cheeseman, J. R ., Keith, T., Petersson, G . A .,
Montgomery, J. A., R aghavachari, K., A l-Laha m, M. A ., Za krzewski,
V. G., Ortiz, J. V., Foresman, J. B., Cioslowski, J., Stefanov, B. B.,
Nanayakkara, A., Challacombe, M., Peng, C. Y., Ayala, P. Y., Chen,
W., Wong, M. W., Andres, J. L., Replogle, E. S., G omperts, R., Martin,
R. L., Fox, D. J., Binkley, J. S., D efrees, D. J., B aker, J., Stewa rt, J. P.,
Hea d-G ordon, M., G onzalez, C., and Pople, J. A., “ G aussian 94 (Re-
vision C.2).” G aussian, Inc., Pittsburgh, PA, 1995.
59. Peng,C., Ayala, P. Y., Schlegel, H. B., and Frisch, M. J., J. Comp. Chem.
17(1), 49 (1996).60. Peng, C., and Schlegel, H. B., Israel J. Chem.33, 449 (1993).
61. G onzález, C., and Schlegel, H . B., J. Chem. Phys. 90(4), 2154 (1989).
62. G onzález, C., and Schlegel, H . B., J. Phys. Chem. 94, 5523 (19
63. Levine, I. N., “ Qua ntum Chemistry.” Prentice–Hall, Englewo
NJ, 1991.
64. “ G as P hase Ion Chemistry” (M. T. B owers, E d.), Vol. 2. A
P ress, New York, 1979.
65. Sauer, J., U gliengo, P., G arrone, E ., and Saunders, V. R ., Ch
94, 2095 (1994).
66. Kramer, G. J., and van Santen, R. A., J. A m. C hem. Soc. 1
(1993).
67. Sauer, J., Chem. Rev. 89, 199 (1989).
68. Z hidomirov, G . M., and Ka zansky, V. B., A dv. Catal.34, 131 (69. La idler, K. J., “ Ch emical Kinetics,” 3rd ed. H arperC ollins, N
1987.