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j APPLIED CATALYSIS A: GENERAL
ELSEVIER Applied Catalysis A: General 146 (1996) 207-223
Theoretical study of the mechanism of branching rearrangement of
carbenium ions
M. Boronat a p. Viruela b A. Corma a,*
a lnstituto de Tecnolog& Qulmica UPV-CSIC, Universidad
Polit~cnica de Valencia, c~ Camino de Vera s~ n, 46071 Valencia,
Spain
b Departament de Qulmica F&ica, Universitat de Valencia, c~
Dr. Moliner 50, 46100 Burjassot (Valencia), Spain
Abstract
Owing to the practical interest of the acid catalyzed
isomerization reactions of hydrocarbons, the mechanism of the
branching rearrangements of C4H ~- and C5H+1 carbenium ions has
been studied theoretically using ab initio methods which include
electron correlation and extended basis sets. It has been found
that the protonated cyclopropane-type species does not appear as a
common intermediate for these reactions, since it is a transition
state and not a minimum on the potential energy surfaces studied.
In the case of C4H ~- cation, the protonated methyl-cyclopropane
ring is the transition state for the carbon scrambling reaction in
the secondary n-butyl cation, while the isomerization of n-butyl
cation into t-butyl cation occurs via a primary cation. The
activation energies calculated assuming this mechanism are in very
good agreement with those obtained experimentally. For the
branching rearrangement of n-pentyl cation two reaction paths have
been considered. In the first one the secondary n-pentyl cation is
converted through the 1,2-dimethyl- cyclopropane ring into the
secondary 3-methyl-2-butyl cation, which is converted into the
t-pentyl cation by a 1,2-hydrogen shift. In the second one the
secondary n-pentyl cation is directly converted into the t-pentyl
cation through a primary monobranched cation. Comparison of the
calculated activation energies for both mechanisms with the
experimental value indicate that this reaction does not occur via
the primary cation as was the case for n-butyl cation, but occurs
via the protonated 1,2-dimethyl-cyclopropane ring.
Keywords." Carbenium ions; Cracking; Isomerization; Mechanism;
Rearrangement
1. Introduct ion
Catalytic transformations of hydrocarbons such as isomerizat
ion, alkylat ion
and cracking are processes of great importance for the chemistry
of petro leum
* Corresponding author.
0926-860X/96/$15.00 Copyright 1996 Elsevier Science B.V. All
rights reserved. PII SO926-860X(96)O0160-3
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208 M. Boronat et al. / Applied Catalysis A: General 146 (1996)
207-223
[1-3]. The most active and widely used solid acid catalysts for
these reactions are silica-alumina and zeolites either exchanged
with transition metals [4-6] or in their pure acid forms [7-9]. It
is generally accepted that the interaction of hydrocarbons with
solid acids results in the formation of carbenium ions [10,11 ].
Consequently, it has been assumed that the mechanism of
heterogeneous reactions on solid acids is similar to that of
homogeneous reactions in superacid media, although the influence of
the solid acid catalyst on the formation and reactivity of the
carbenium ion is not explicitly considered in this formal
mechanism.
The mechanism of homogeneous isomerization reactions in
superacid media involves three steps: formation of the carbenium
ion either by protonation of an alkene or by hydride transfer from
an alkane, rearrangement of this carbenium ion, and deprotonation
or hydride ion abstraction to give the rearranged hydro- carbon.
The carbenium ion rearrangements involved in the second step may be
classified as branching and non-branching. The classical mechanism
for the non-branching rearrangements, in which the degree of chain
branching remains the same, supposes them to proceed by a
succession of 1,2-hydrogen and alkyl shifts via secondary ions as
intermediates. The branching rearrangements, which are about a
thousand times slower, involve a decrease or an increase in the
degree of chain branching. For this type of rearrangements, a
mechanism with only 1,2-hydrogen and alkyl shifts would necessarily
include primary carbenium ions as intermediates. This is not
consistent neither with the experimental fact that n-butane is not
isomerized at an observable rate by HF/SbF 5 to isobutane under
conditions where n-pentane and n-hexane are rapidly converted into
their branched isomers [12], nor with the finding that the rate of
scrambling or isomerization of n-butane-l-13C to n-butane-2-13C is
comparable to that of isomerization of n-pentane to isopentane
[13]. Consequently, the mechanism proposed by Brouwer [14,15] which
includes a protonated cyclopropane ring as intermediate has been
accepted.
According to this mechanism (see Scheme 1), the positive charge
on C 2 carbon atom attacks the C 4 carbon atom and a protonated
cyclopropane ring is formed. The opening of the cyclic intermediate
at one of the other two sides of
\ I \ / \1 \ / Y --C 1 \+ 1c3\ / q,, ~/c,3,,) /
C2 C 4 ,,/C2 "--~--- C4 ~. R I I "R H +
,.I I.. ..I cl/_ - - --C 1 ci\+ /c3- \c + /
/C2- -C4QR ~ . i I2--C4...R
>cN3 ,,I __~Cl [C2__~4j --C3~+ I / / [ ~'R ~ f2 --C4~. R
Scheme 1.
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M. Boronat et al./ Applied Catalysis A: General 146 (1996)
207-223 209
the ring results in the formation of a secondary monobranched
carbenium ion if R is an alkyl group. If R is an hydrogen atom,
i.e., for C4H ~- cation, the opening of the cyclic intermediate at
side a leads to a n-butyl cation in which a terminal and a
non-terminal carbon atoms have changed positions (C scrambling
reaction), but the opening of the intermediate at side b becomes
more difficult because it would lead to a primary carbenium
ion.
The accepted values for the activation energies for the carbon
scrambling process in the n-butyl cation and for the conversion of
n-butyl into t-butyl cation are 7.5 and 18.0 kcal/mol respectively
[16,17]. The similarity of the last value to the activation energy
for the carbon scrambling in the isopropyl cation, 15.7 kcal/mol
[18], is consistent with the supposition that the branching
isomeriza- tion reaction of n-butyl cation passes through the
high-energy primary isobutyl cation. The low barrier obtained for
the scrambling process, however, suggests that this reaction passes
through a protonated methyl-cyclopropane species, more stable than
the primary isobutyl cation. For the rearrangement of the t-pentyl
cation to the n-pentyl cation an experimental activation energy
value of 18.3 kcal/mol is reported by Brouwer [14,15]. This
reversible rearrangement leads to interchange of the methyl and
methylene carbon atoms and, conse- quently, to scrambling of the
methyl and methylene protons in the observable t-pentyl cation.
From PMR spectroscopic measurements on the t-pentyl cation at high
temperatures Saunders and Rosenfeld have obtained a more precise
value of 18.8 kcal/mol for the activation energy of this proton
scrambling process [19]. The isomerization of the secondary
3-methyl-2-butyl cation into the tertiary 2-methyl-2-butyl or
t-pentyl cation (the last step in Scheme 1) has been found to have
an activation energy value of 2.1 kcal/mol [20].
In order to establish the mechanism of the branching
rearrangements of carbenium ions, we present in this paper a
complete theoretical study of the potential energy surfaces of C4H
~- and C5H/1 cations which include geometry optimization and
characterization of the stationary points at correlated levels.
2. Computational details
All ab initio molecular orbital calculations in this work were
performed on an IBM 9021/500-2VF computer and on IBM RS/6000
workstations of the University of Valencia using the Gaussian 88
[21] and Gaussian 92 [22] computer programs.
The geometry of the stationary points on C4H ~- and C5H/1
potential energy surfaces was first fully optimized by using the
Hartree-Fock procedure and the 6-31G * basis set [23,24] (HF/6-31G*
) which has polarization functions (d-type) on non-hydrogen atoms.
Afterwards, electron correlation was included by means of the
second-order Moeller-Plesset perturbation theory that takes into
account the core electrons. Two types of calculations were carried
out: single point
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210 M. Boronat et al./Applied Catalysis A: General 146 (1996)
207-223
calculations on the HF optimized geometries using the MP2
treatment and the 6-31G * basis set (MP2/6-31G * / /HF /6 -31G * ),
and complete geometry opti- mization of all stationary points at
this correlated theoretical level (MP2/6- 31G * ). The Berny
analytical gradient [25] and the eigenvalue following [26,27]
methods were used for the minima and transition states geometry
optimizations, respectively. All HF/6-31G * and MP2/6-31G *
stationary points were charac- terized by calculating the Hessian
matrix and analyzing the vibrational normal modes. The relative
energies at these two levels were corrected by the zero point
energy (ZPE) obtained from frequency calculations.
3. Results and discussion
3.1. C 4 H9 +
According to Scheme 1, there are four structures involved in the
mechanism of branching rearrangement of C4H ~- cation: the
secondary n-butyl cation, the protonated methyl-cyclopropane ring,
the primary isobutyl cation and the ter- tiary isobutyl cation. The
geometry of these four structures has been completely optimized
without any symmetry restriction.
The tertiary isobutyl cation D is the most stable minimum on C4H
~- potential energy surface both at the HF/6-31G * and MP2/6-31G *
theoretical levels. As can be seen in Fig. 1, the conformation
adopted minimizes the repulsions between the hydrogen atoms and
also between the C -H and C-C bonds.
.479) 1.491
1.447 (1.403),f \2.364 (1.923)
\~ "~1.288 A
1.518(1.S11) 1.494 ) 1.496
B
~1.517) ~1.473(1.459)
C D
Fig. 1. Structures of the C4H ff cation. The HF/6-31G* bond
lengths are given first, followed by the MP2/6-31G* values in
parentheses.
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M. Boronat et al. /Appl ied Catalysis A: General 146 (1996)
207-223 211
The structure of the secondary n-butyl cation has already been
studied at many standard theoretical levels by Schleyer et al.
[28]. They found that both the partially methyl-bridged form A
(shown in Fig. 1) and a trans-hydrogen bridged form (not shown) are
minima on the potential energy surface, structure A being slightly
more stable than the hydrogen-bridged one at every considered
theoreti- cal level. Since apart from being the most stable,
structure A shows a strong positive charge on a secondary carbon
atom, it seems more suitable to induce the cycle formation process
and consequently we have taken it as the starting point for the
carbon scrambling and branching isomerization reactions.
In the present work the geometry of structure A has been
completely optimized at the HF/6-31G* and MP2/631G* levels and, as
was previously reported by Schleyer, both stationary points have
been found to be minima on the potential energy surface. The bond
lengths depicted in Fig. 1 show the changes in geometry due to the
inclusion of electron correlation. The degree of methyl-bridging
becomes more important when electron correlation is included, as
can be observed from the !engthening of the C3-C 4 bond from 1.584
,~ at the HF/6-31G * level to 1.653 A at the MP2/6-31G * level, and
also from the fact that the C2C3C 4 angle is closed from 102.4 at
the HF/6-31G * level to 77.5 at the MP2/6-31G * level.o This
implies an important ShOortening of the C2-C 4 bond length from
2.364 A at the HF/631G * level to 1.923 A at the MP2/631G * level,
while the C 1-C3 bond length remains the same (2.582 and 2.549 ,~).
The calculated energy differences between the secondary A and the
tertiary D butyl cations (or relative energies) summarized in Table
1 are in good agreement with the experimental values of the
enthalpy of rearrangement of n-butyl to t-butyl cation, which are
15-17 [29-31] and 14-15 [32,33] kcal/mol in gas phase and in
solution, respectively.
Three different structures were proposed by Wiberg and Kass [34]
for the protonated methyl-cyclopropane ring: a corner-protonated
species formed by adding a proton to the methine carbon atom, an
edge-protonated species in which the proton is shared by two
neighboring methylene carbon atoms, and a structure formed by
adding a proton to a methylene carbon atom which resulted to be the
open form of the secondary n-butyl cation A. Although at the
Hartree-Fock level the corner-protonated species was found to be
more stable than the edge-protonated one, the inclusion of the
electron correlation reversed
Table 1 Calculated relative energies (kcal/mol) of the
stationary points found on C4H ~- potential energy surface
Method A B C D
HF/6-31G * 13.6 31.5 32.9 0.0 HF/6-31G * +ZPE 14.7 32.8 33.3 0.0
MP2/6-31G * / /HF /6 -31G * 13.9 20.2 34.2 0.0 MP2/6-31G * 11.0
19.9 33.6 0.0 MP2/6-31G * +ZPE 12.9 21.5 34.1 0.0
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212 M. Boronat et al. / Applied Catalysis A: General 146 (1996)
207-223
the relative stability of these two forms. Besides, the
optimized bond lengths reported by Wiberg and Kass for the
corner-protonated species suggest that it could be best described
as a complex between CH3CH ~- cation and CH 2 =CH 2 molecule,
without any chemical meaning in the rearrangements studied. Conse-
quently, we have only considered in this work the edge-protonated
form of the methyl-cyclopropane ring (structure B in Fig. 1).
The HF/6-31G* and MP2/631G* optimized geometries of B depicted
in Fig. 1 are nearly identical, and exhibit a partially distorted C
S symmetry. The C2-C 3 and C2-C 4 bond lengths in the ring and the
C-H bond lengths of the almost symmetrical hydrogen bridge are
equivalent at both theoretical levels. The only noticeable change
that electron correlation introduces in the geometry of B is a
slight shorteningoOf the C3-C 4 bond length from 1.763 A at the
HF/6-31G * level to 1.717 A at the MP2/6-31G * level. Despite this
similarity between the correlated and uncorrelated optimized
geometries of B, the calcu- lated relative energies summarized in
Table 1 are strongly dependent on the theoretical level used. At
the HF/6-31G * level the relative energy of B is 31.5 kcal/mol, and
32.8 kcal/mol with the ZPE correction. The inclusion of the
electron correlation at the MP2/6 -31G* / /HF /6 -31G* level
stabilizes this structure and yields a relative energy value of
20.2 kcal/mol, very similar to the values obtained at the MP2/6-31G
* and MP2/6-31G * + ZPE levels, 19.9 and 21.5 kcal/mol,
respectively.
These energetic changes are not surprising if we take into
account that the inclusion of the electron correlation by the
Moeller-Plesset perturbation treat- ment preferentially stabilizes
the non-classical bridged structures [35]. Since the HF/6-31G*
optimized geometry of B corresponds to a non-classical bridged
structure, the single point calculation at the MP2/6-31G * / /HF /6
-31G * level is able to introduce all the stabilization due to
electron correlation. The MP2/6-31G * geometry optimization cannot
increase the degree of bridging in B and therefore there is no
stabilization with respect to the single point calculation observed
at this level of theory.
What is more surprising is the result obtained from the analysis
of the vibrational normal modes. This analysis indicates that
structure B is a transition state on C4H ~- potential energy
surface both at the HF/6-31G* and MP2/6- 31G* levels of theory. The
negative frequency is clearly associated to the movement of the
bridged hydrogen atom towards one of the methylene carbon atoms to
give the secondary n-butyl cation A. The fact that structure B is
not a minimum but a transition state on the potential energy
surface means that the protonated meth2)l-cyclopropane ring cannot
be a true intermediate of the scrambling and branching
isomerization reactions of n-butyl cation as suggested by Brouwer,
but only a species through which the scrambling reaction
passes.
Finally, the structure of the primary isobutyl cation C has been
calculated. Taking as a starting point the optimized geometry of
the tertiary isobutyl cation D, the distance between one of the
hydrogen atoms attached to C 3 and C2 has
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M. Boronat et al. / Applied Catalysis A: General 146 (1996)
207-223 213
been slowly shortened from 2.037 ,~ to 1.075 A, already
corresponding to a primary cation. In each calculation the C2-H
distance has been fixed and all other parameters have been allowed
to fully optimize. Then, the geometry of the primary cation
obtained has been completely reoptimized using the eigenvector
following transition state search technique. The HF/6-31G * and
MP2/6-31G * optimized geometries of C are very similar, and the
relative energies summa- rized in Table 1 are all of them about 33
or 34 kcal/mol. The force constant calculations indicate that at
both theoretical levels structure C is a transition state with only
one imaginary vibration frequency.
Taking into account all these data and the idea that a
transition state must be connecting two minima on a potential
energy surface, a new mechanism, shown in Scheme 2, is proposed for
the carbon scrambling and branching isomerization reactions of
n-butyl cation. According to this new mechanism the secondary
n-butyl cation is the starting point for the two reactions that,
from the first moment, follow different reaction paths. When the
positive charge on C 2 carbon atom in minimum A attacks C 4 carbon
atom two different processes can take place: (a) a simultaneous
strengthening of the C2-C 4 bond and breaking of the C3-C 4 bond in
A directly leads to transition state C and from this, a shift of
the hydrogen atom from C 2 to C 3 leads to minimum D. The primary
cation is the transition state for the conversion of n-butyl into
t-butyl cation; (b) strengthen- ing of the C2-C 4 bond in A
together with an elongation of a C4-H bond length leads to
transition state B. If the C2-C 3 bond is then broken and the
hydrogen atom of the bridge moves to C 3, the minimum A'
(equivalent to A) is reached and the carbon scrambling reaction has
occurred. The protonated cyclopropane ring is, at least in the case
of C4H ~- cation, not an intermediate but only the transition state
for the carbon scrambling reaction.
Fig. 2 shows the energetic profile for the two reactions studied
and Table 2 summarizes the calculated activation energies together
with experimental data. The activation energy for the carbon
scrambling process, Eal, has been calcu-
\1 \ i --CiN+ i c3 \ /
7 2 74 .
/ L A j i< B A'
X [-\1 I+ -It \1 I/ I -q ~c3- -q\+/c3-- / ~ J ~ 12 L " "7<
i7'\
C D
Scheme 2.
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214 M. Boronat et al. /Applied Catalysis A: General 146 (1996)
207-223
AE (kcal/mol)
35.0 -
30 .0 -
25 .0 -
20 .0 -
15 .0 -
10 .0 -
5 .0 -
0 .0 -
B /--'~\ / / ~ Eal \N
/ \ / r.-J ~ J A' A
I I
I I
i I E~a I
I I
c
k
N
Fig. 2. Energy profile corresponding to the scrambling and
isomerization reactions of the secondary n-butyl cation. The
tertiary ion has been taken as the origin of energies.
lated as the energy difference between the protonated
methyl-cyclopropane ring B and the secondary n-butyl cation A. The
HF/6-31G * and HF/6-31G * + ZPE values, 17.9 and 18.1 kcal/mol
respectively, are too high as compared with the experimental value
of 7.5 kcal/mol. As we have seen before, electron correla- tion
stabilizes structure B and the calculated activation energies at
the MP2/6- 31G * / /HF /6 -31G *, MP2/6-31G * and MP2/6-31G * + ZPE
levels, 6.3, 8.9 and 8.6 kcal/mol respectively, are much closer to
the experimental value. These results indicate that the
Hartree-Fock level is not adequate to study mechanisms in which
non-classical species are involved, and that inclusion of electron
correlation is essential to treat these species correctly. The
activation energies for the direct (n-butyl ~ t-butyl), Ea2, and
reverse (t-butyl ~ n-butyl), Ea3, isomerization reactions have been
calculated as the energy differences between the primary cation C
and structures A and D, respectively. The calculated activation
energies are quite similar at all theoretical levels, between 18.6
and 22.6 kcal/mol for the direct reaction and between 32.9 and 34.2
kcal/mol for the reverse reaction, and in good agreement with the
experimental values.
Table 2 2 + 13Calculated and experimental activation energies
(kcal/mol) for the processes depicted in Fig. 2
Method gal Ea2 Ea3 HF/6-31G * 17.9 19.3 32.9 HF/6-31G* +ZPE 18.1
18.6 33.3 MP2/6-31G * / /HF /6 -31G * 6.3 20.3 34.2 MP2/6-31G * 8.9
22.6 33.6 MP2/6-31G * +ZPE 8.6 21.2 34.1 Exp. 7.5 18.0 32.0
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M. Boronat et al. / Applied Catalysis A: General 146 (1996)
207-223 215
3.2. C5H1~
According to Brouwer's mechanism (see Scheme 1), the following
structures have to be localized and characterized on CsH~- ~
potential energy surface: the secondary n-pentyl cation, the
protonated 1,2-dimethyl-cyclopropane ring, the secondary
3-methyl-2-butyl cation, the tertiary 2-methyl-2-butyl or t-pentyl
cation and the transition state for the hydrogen shift that
converts the secondary branched cation into the tertiary one.
Both at the HF/6-31G * and MP2/6-31G * levels the tertiary
t-pentyl cation I is the most stable minimum on CsH~- ~ potential
energy surface. The optimized bond lengths depicted in Fig. 3
indicate that the t-pentyl cation is not fully classical. A partial
bridging between the C4-C 5 bond and the positive charge on
I .S53
1 .526~'~ 'q
~ 74)
~.519(1.510)
747)
1.462 (I .489)
1.59Z
.836) ~"~0
G H
_ 1.471 ~x "474 (1.464)
I
1.589~ 1"529 (I"516)
J
Fig. 3. Structures of C5H~1 cation. The HF/6-31G* bond lengths
are given first, followed by the MP2/6-31G* values in
parentheses.
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216 M. Boronat et al. /Appl ied Catalysis A: General 146 (1996)
207-223
Table 3 Calculated relative energies (kcal/mol) of the
stationary points found on CsHll + potential energy surface
Method E F G H I J
HF/6-31G * 13.6 29.5 12.9 15.6 0.0 34.2 HF/6-31G * +ZPE 14.2
30.2 13.0 14.5 0.0 34.9 MP2/6-31G * / /HF /6 -31G * 13.6 18.5 11.8
12.0 0.0 35.0 MP2/6-31G * 10.3 17.1 7.2 14.8 0.0 34.5 MP2/6-31G *
+ZPE 11.7 17.8 8.0 14.4 0.0 34.1
C 2 carbon atom can be deduced from the lengthening of the C4-C
5 bond to 1.565 ,~ at the HF/6-31G* level and 1.581 A at the
MP2/6-31G * level, and also from the calculated C2C4C 5 angle
values of 106.3 and 101.5 at the HF/6-31G * and MP2/6-31G * levels,
respectively. The structure of the t-pentyl cation has already been
studied by comparing the ~3C chemical shifts of the C + carbon atom
calculated by IGLO using ab initio geometries with the experimen-
tal values, and our results are in complete agreement with those
previously reported [36].
The secondary n-pentyl cation E has also been found to be a
minimum on the potential energy surface at the HF/6-31G* and
MP2/6-31G* theoretical levels. The optimized bond lengths depicted
in Fig. 3 show the same tendencies that were observed in the
secondary n-butyl cation A. Inclusion of electron correlation at
the MP2/6-31G * level lengthens the C3-C 4 bond from 1.599 to 1.656
~, and closes the C2C3C 4 angle from 102.1 to 78.3 , i.e.,
increases the degree of methyl-bridging. This is reflected in the
important shortenin~ of the Ca-C 4 bond length from 2.366 ,~ at the
HF/6-31G* level to 1.941 A at the MP2/6-31G* level, while the C3-C
5 bond length remains nearly constant (2.545 and 2.587 A at the
HF/6-31G * and MP2/6-31G * levels respectively). These geometric
changes are reflected in the relative energies summarized in Table
3. The HF/6-31G*, HF/6-31G* + ZPE and MP2/6 -31G* / /HF /6 - 31G*
calculated energies, 13.6, 14.2 and 13.6 kcal/mol respectively, are
very similar. The increase in the degree of methyl-bridging
produced by the inclusion of the electron correlation in the
MP2/6-31G * optimization stabilizes structure E and at the
MP2/6-31G* and MP2/6 -31G*+ ZPE levels the calculated relative
energies are 10.3 and 11.7 kcal/mol respectively.
The third minimum found on CsH~] potential energy surface is the
secondary 3-methyl-2-butyl cation, structure G in Fig. 3. At the
HF/6-31G* level the C2-C 3 bond length value of 1.592 A and the
C3C2C 4 angle value of 98.1 are indicative of a partial bridging
between the C 2-C3 bond and the positive charge on C 4 carbon atom,
similar to that previously reported for the t-pentyl cation. At the
MP2/6-31G* level, however, the C2-C 3 bond is lengthened to 1.733
~,, the C3C2C 4 angle is closed to 70.9 and the C3-C 4 bond is
shortened from 2.295 A at the uncorrelated level to 1.836 .A. The
degree of methyl-bridging becomes so important that this structure
could be best described as an unsym-
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M. Boronat et al./Applied Catalysis A: General 146 (1996)
207-223 217
metrical comer-protonated 1,2-dimethyl-cyclopropane ring. The
relative ener- gies summarized in Table 3 reflect the importance of
the geometric changes produced when electron correlation is
included in the calculations. The HF/6- 31G* and HF/6-31G* +ZPE
calculated relative energies, 12.9 and 13.0 kcal/mol respectively,
are about 2 kcal/mol too high in relation to the experimental value
of 11 kcal/mol reported by Collin and Herman [20] for the energy
difference between the secondary 3-methyl-2-butyl and the tertiary
2-methyl-2-butyl cations. The MP2/6-31G*/ /HF/6-31G* calculated
value, 11.8 kcal/mol, is slightly lower than the two uncorrelated
values, probably due to the fact that there is a partial bridging
in the HF/6-31G * optimized geometry of structure G. But the
MP2/6-31G * and MP2/6-31G * + ZPE values are 3.8 and 3 kcal/mol
respectively too low in relation to the experimental value. This
overestabilization of structure G at the best levels of theory used
in this work can be explained if we take into account that the
inclusion of the electron correlation using the Moeller-Plesset
treatment preferentially stabilizes non- classical bridged
structures [35] and, as can be seen in Fig. 3, the degree of
bridging in G is more important than in any of the other
structures.
According to Brouwer's mechanism (Scheme 1), the isomerization
of the linear E to the branched G secondary cations passes through
an edge-protonated cyclopropane ring F. Taking as a starting point
the optimized geometry of the linear cation E, two variables have
been simultaneously controlled in order to obtain structure F: the
C2C3C 4 angle and the C3-H bond length. In each calculation these
two variables have been fixed and all other parameters have been
allowed to fully optimize. The geometry of the cyclic structure
obtained has been completely reoptimized at the HF/6-31G * and
MP2/6-31G * levels using the eigenvalue following transition state
search technique and the two stationary points have been
characterized by force constant calculations. As in the case of C4H
~- cation, they have been found to be transition states, with only
one imaginary vibration frequency associated to the movement of the
bridged hydrogen atom.
The two optimized geometries of structure F depicted in Fig. 3
are ne~ly equivalent, with C-C bond lengths in the ring of 1.450,
1.553 and 1.807 A at the HF/6-31G * level and 1.443, 1.562 and
1.747 A at the MP2/6-31G * level. The effect of alkyl substitution
on the structure of the protonated cyclopropane ring can be clearly
observed in the different symmetry exhibited by the hydrogen bridge
in B (protonated methyl-cyclopropane ring) and F (protonated
1,2-dimethyl-cyclopropane ring). While the two C-H bond lengths in
structure B are equivalent, the hydrogen bridge in F is markedly
unsymmetrical, with C-H bond lengths of 1.176 and 1.478 A at the
HF/6-31G * level and 1.174 and 1.490 ~, at the MP2/6-31G*
level.
The relative energies of structure F reproduce the tendencies
previously observed for structure B. The HF/6-31G* and HF/6-31G * +
ZPE calculated values are high, 29.5 and 30.2 kcal/mol
respectively. The single point calcula-
-
218 M. Boronat et al. / Applied Catalysis A: General 146 (1996)
207-223
tion at the MP2/6-31G*//HF/6-31G* level strongly stabilizes this
cyclic species, yielding a value of 18.5 kcal/mol, while the
MP2/6-31G* and MP2/6-31G* + ZPE calculated values are only slightly
lower, 17.1 and 17.8 kcal/mol respectively.
The last step in Brouwer's mechanism is the hydrogen shift that
converts the secondary branched cation into the tertiary one.
Starting from the optimized geometry of I, the distance between C 2
and the hydrogen atom that is going to migrate has been slowly
shortened from 2.12 A to 1.10 A and the geometry of the obtained
structure has been then completely reoptimized at the HF/6-31G *
and MP2/6-31G* levels using the eigenvector following the
transition state search technique. The two stationary points have
been characterized by force constant calculations and they have
been found to be transition states on their respective potential
energy surfaces, showing only one imaginary vibration frequency. At
the HF/6-31G* level the relative energy of structure H is 15.6
kcal/mol, and 14.5 kcal/mol with the ZPE correction. The single
point calculation at the MP2/6-31G * / /HF/6-31G * level stabilizes
this hydrogen- bridged structure and yields a relative energy value
of 12.0 kcal/mol. However, the value obtained from the MP2/6-31G *
optimization is higher, 14.8 kcal/mol, and 14.4 kcal/mol with the
ZPE correction. The HF/6-31G * and MP2/6-31G * optimized bond
lengths depicted in Fig. 3 explain this energetic values. At the
HF/6-31G * level, the optimized geometry of H corresponds to an
unsymmetri- cally hydrogen-bridged structure with a C-C bond length
of 1.411 A and two
o
C-H bond lengths of 1.189 and 1.582 A. At the MP2/6-31G* level
the optimized C-C bond length value of 1.437 A and the C-H bond
length values of 1.118 and 1.961 A are indicative of a lesser
degree of hydrogen bridging and consequently the structure is
slightly destabilized at this level of theory.
Taking into account all these results, the mechanism depicted in
Scheme 3 is proposed for the branching rearrangement of n-pentyl
cation. According to it, strengthening of the C2-C 4 bond in
minimum E together with weakening of the C3-C 4 bond and migration
of one of the hydrogen atoms attached to C 4 to a bridged position
between C 3 and C a leads to transition state F. From this, braking
of the C 3-C4 bond together with migration of the bridged hydrogen
atom to C 3 leads to minimum G. Then, the hydrogen atom attached to
C 2 migrates to C 4 through transition state H and minimum I is
reached. It is important to note that this calculated mechanism is
not equivalent to that empirically proposed by Brouwer, the main
difference being the nature of the
,,t L \ i \ ] I t , , , / F , , I / lt,.i - -c \ c ( c / [\~1
~'- - / c3 / c, 3 | --c3
E F (3 H I
Scheme 3.
-
M. Boronat et al. / Applied Catalysis A: General 146 (1996)
207-223 219
\1 \ / I / --ctx, +/c3 \ / c5 - -
7 /k
\+ / I t c3
\ I / \ l _ _ _ _ _
/ CI 7 2 C4"~5_._ j ~7 "C5--i\ J I
Scheme 4.
protonated 1,2-dimethyl-cyclopropane ring. Our results indicate
that this cyclic species cannot be an intermediate as affirmed by
Brouwer, because it is a transition state and not a minimum on
CsH~- 1 potential energy surface.
A second mechanism, equivalent to that calculated for the
branching isomer- ization of n-butyl cation, has been considered in
this work. As can be seen in Scheme 4, a simultaneous strengthening
of the C2-C 4 bond and breaking of the C3-C 4 bond in the secondary
n-pentyl cation leads to a primary monobranched cation J and from
this, a shift of an hydrogen atom from C 2 to C 3 leads to the
t-pentyl cation. The structure of the primary cation has also been
calculated. Starting again from the optimized geometry of the
t-pentyl cation I, the distance between C 2 and one of the hydrogen
atoms attached to C 3 has been slowly shortened from 2.12 ,~ to
1.10 A and then, using the eigenvalue following method, its
geometry has been completely reoptimized at the HF/6-31G * and
MP2/6-31G * levels. Characterization of the two stationary points
by force constant calculations indicate that the primary pentyl
cation J is a transition state at both theoretical levels. Since
the HF/6-31G* and MP2/6-31G* optimized geometries of structure .1
depicted in Fig. 3 are very similar and fully classical, the
inclusion of the electron correlation in the calculations produces
no stabiliza- tion of this structure in relation to the t-pentyl
cation and the calculated relative energies of J summarized in
Table 3 are all of them similar, between 34 and 35 kcal/mol.
AE (kca l /mo l )
35.0-
30.0-
25.0-
20.0 -
15.0-
10.0-
5.0-
0.0-
F
l/if I ~\ E Ea4 H
G \ \
J / \
I I
/ I
I /
I I I
I I I
I /
I \\ t I
\ \ \ \ \ \ \
~a6 \ \ \
E
Fig. 4. Energy profile corresponding to the branching
isomerization of the secondary n-pentyl cation. The tertiary ion
has been taken as the origin of energies.
-
220 M. Boronat et al. /Appl ied Catalysis A: General 146 (1996)
207-223
Fig. 4 shows the energetic profile for the branching
isomerization of the n-pentyl cation. The activation energy for the
rearrangement of the t-pentyl cation to the n-pentyl cation, for
which experimental data are available, can be calculated as the
energy difference between the primary transition state J and the
tertiary minimum I if the reaction path depicted in Scheme 4 is
followed. In the mechanism of Scheme 3, the rate determining step
is the conversion of the branched G into the linear E secondary
pentyl cations, and consequently the activation energy for the
global process is the energy difference between transition state F
and minimum I. The calculated activation energies together with
available experimental data are summarized in Table 4. At the
HF/6-31G * and HF/6-31G * + ZPE levels the calculated activation
energies for the two mechanisms are similar, 29.5 and 30.2 kcal/mol
for Ea4 and 34.2 and 34.9 kcal/mol for E,6, and too high as
compared with the experimental value of 18.8 kcal/mol. When
electron correlation is included the energy of the primary cation J
experiments no changes, and the calculated values for Ea6 are again
between 34 and 35 kcal/mol. However, the transition state F is
highly stabilized by inclusion of electron correlation and
consequently the calculated values for Ea4 at the
MP2/6-31G*//HF/6-31G*, MP2/6-31G* and MP2/6-31G* + ZPE levels are
lowered to 18.5, 17.1 and 17.8 kcal/mol respectively. Compari- son
of the calculated activation energies for the two mechanisms
considered with the experimental value of 18.8 kcal/mol indicates
that the branching isomerization of the n-pentyl cation does not
occur through the primary cation, as was the case for the n-butyl
cation, but occurs via the protonated 1,2-di- methyl-cyclopropane
ring, following the reaction path shown in Scheme 3.
As already told, this mechanism consists of two steps: the
conversion of the secondary linear cation E into the secondary
branched cation G discussed above, and the conversion of G into the
tertiary cation I. The activation energy for this process, Ea5 in
Fig. 4 and Table 4, can be calculated as the energy difference
between transition state H and minimum G. The Ea5 calculated values
at the HF/6-31G * and HF/6-31G * + ZPE levels, 2.7 and 1.5 kcal/mol
respectively, compare well with the experimental value of 2.1
kcal/mol. At the MP2/6- 31G */ /HF/6-31G* level the obtained value
is too low, 0.2 kcal/mol, while the MP2/6-31G* optimization yields
a too high barrier for this process, 7.6 kcal/mol, and 6.4 kcal/mol
with the ZPE correction. The reported energy
Table 4 Calculated and experimental activation energies
(kcal/mol) for the processes depicted in Fig. 4
Method Ea4 Ea5 Ea6
HF/6-31G * 29.5 2.7 34.2 HF/6-31G * + ZPE 30.2 1.5 34.9
MP2/6-31G * / /HF /6 -31G * 18.5 0.2 35.0 MP2/6-31G * 17.1 7.6 34.5
MP2/6-31G * +ZPE 17.8 6.4 34.1 Exp. 18.8 2.1 -
-
M. Boronat et al. /Appl ied Catalysis A: General 146 (1996)
207-223 221
difference between the secondary 3-methyl-2-butyl and the
t-pentyl cations, 11 kcal/mol, together with the activation energy
value for the hydrogen shift that converts this secondary branched
cation into the tertiary one yields an energy barrier for the
conversion of the tertiary I into the secondary G cations of 13.1
kcal/mol, which corresponds to the energy difference between
transition state H and minimum I. Exceptuating the HF/6-31G *
result, which is 2.5 kcal/mol too high, the calculated relative
energies of structure H are between 12.0 and 14.8 kcal/mol, i.e.,
they are basically correct. Consequently, the source of the
difference between the calculated and the experimental values of
Ea5 must be in the calculated energy of the secondary branched
cation G. As has been previously discussed, the Moeller-Plesset
perturbation treatment overestabilizes non-classical bridged
structures such as G. The 3 or more kcal/mol of discrepancy between
the calculated and the experimental relative energies of G reported
before added to the 1-2 kcal/mol found for transition state H are
the reason that explains the too high Ea5 values obtained when the
MP2 treatment is used.
4. Conclusions
A theoretical study of the potential energy surfaces of C4H ~-
and C5H~1 cations including geometry optimization and
characterization of the stationary points at correlated levels has
been carried out in order to establish the mechanism of branching
rearrangement of carbenium ions. The results obtained suggest
alternative mechanisms to that empirically proposed by Brouwer for
these reactions, the main difference being the nature of the
protonated cyclo- propane-type species. According to Brouwer's
mechanism, this cyclic type of structure is an intermediate, from
which two different routes lead to two different products. However,
both the protonated methyl-cyclopropane ring and the protonated
1,2-dimethyl-cyclopropane ring have been found to be transition
states and not minima on Call ~- and CsH~- 1 potential energy
surfaces respec- tively, and consequently they cannot be true
intermediates but only species through which the reactions
pass.
The new mechanism proposed for the carbon scrambling and
branching isomerization reactions of the n-butyl cation (Scheme 2)
supposes that, from the first moment, the two reactions follow
different reaction paths. The protonated methyl-cyclopropane ring
is the transition state for the carbon scrambling reaction, and the
isomerization of the linear n-butyl cation into the branched
t-butyl cation occurs through a primary cation. However, the
branching rear- rangement of n-pentyl cation does not occur through
a primary cation as shown in Scheme 4, but it follows the reaction
path depicted in Scheme 3. The secondary n-pentyl cation is
converted through the protonated 1,2-dimethyl- cyclopropane ring
into the secondary 3-methyl-2-butyl cation and then, an
-
222 M. Boronat et al. / Applied Catalysis A: General 146 (1996)
207-223
hydrogen shift converts this branched secondary cation into the
tertiary one. This mechanism can be extrapolated to higher
aliphatic carbenium ions because, as can be observed in Scheme 3,
it does not seem probable that addition of a methyl (or alkyl)
group to the C5 carbon atom introduces any important change in the
relative energy or nature of the different species involved.
From the results obtained at the different levels of calculation
it can also be concluded that the inclusion of the electron
correlation in the geometry optimiza- tions and in the
characterization of the stationary points is essential for the
study of this type of reaction mechanisms, in which non-classical
bridged structures are involved. Thus, the MP2/6-31G* would be the
lowest acceptable level of calculation.
Acknowledgements
The authors thank the Centre de Informhtica and Departament de
Qufmica Ffsica of the University of Valencia for computing
facilities. They thank C.I.C.Y.T. (Project MAT 94-0359) and
Conselleria de Cultura, Educaci6 i Cibncia de la Generalitat
Valenciana for financial support. MB thanks the Conselleria de
Cultura, Educaci6 i Ci~ncia de la Generalitat Valenciana for a
personal grant.
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