Experimental and theoretical studies of the elimination kinetics of 3-hydroxy-3-methyl-2-butanone in the gas phase

Article abstract of DOI:10.1002/poc.913

The kinetics of the gas-phase elimination of 3-hydroxy-3-methyl-2-butanone was investigated in a static system, seasoned with allyl bromide, and in the presence of the free chain radical inhibitor toluene. The working temperature and pressure range were 439.6-4-89.3°C and 81-201.5 Torr (1 Torr = 133.3 Pa), respectively. The reaction was found to be homogeneous, unimolecular and to follow a first-order rate law. The products of elimination are acetone and acetaldehyde. The temperature dependence of the rate coefficients is expressed by the following equation: log[k₁(s^-1)] = (13.05 ± 0.53) - (229.7 ±5.3) kJ mol^-1 (2.303RT)^-1. Theoretical estimations of the mechanism of this elimination suggest a molecular mechanism of a concerted non-synchronous four-membered cyclic transition-state process. An analysis of bond order and natural bond orbital charges suggests that the bond polarization of C(OH) - C(=O) -, in the sense of C(OH) ^δ+...C(=O)^δ-, is rate limiting in the elimination reaction. The rate coefficients obtained experimentally are in reasonably good agreement with the theoretical calculations. The mechanism of 3-hydroxy-3-methyl-2-butanone elimination is described. Copyright

Full text of DOI:10.1002/poc.913

JOURNAL OF PHYSICAL ORGANIC CHEMISTRY
J. Phys. Org. Chem. 2005; 18: 595–601
Published online 11 February 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/poc.913
Experimental and theoretical studies of the elimination
kinetics of 3-hydroxy-3-methyl-2-butanone in the
gas phase
Mariana Graterol,1 Alexandra Rotinov,2 Tania Cordova1 and Gabriel Chuchani2*
1
´
´
´
Laboratorio de Fisico-Quımica Organica, Escuela de Quımica, Facultad de Ciencias, Universidad Central de Venezuela, Apartado 1020-A,
Caracas, Venezuela
2
´
´
Centro de Quımica, Instituto Venezolano de Investigaciones Cientıficas (IVIC), Apartado 21827, Caracas 1020-A, Venezuela
Received 28 June 2004; revised 11 January 2005; accepted 17 January 2005
ABSTRACT: The kinetics of the gas-phase elimination of 3-hydroxy-3-methyl-2-butanone was investigated in a
static system, seasoned with allyl bromide, and in the presence of the free chain radical inhibitor toluene. The working
temperature and pressure range were 439.6–489.3 ꢀC and 81–201.5 Torr (1 Torr ¼ 133.3 Pa), respectively. The
reaction was found to be homogeneous, unimolecular and to follow a first-order rate law. The products of elimination
are acetone and acetaldehyde. The temperature dependence of the rate coefficients is expressed by the following
equation: log [k1(sꢁ1)] ¼ (13.05 ꢂ 0.53) ꢁ (229.7 ꢂ 5.3) kJ molꢁ1 (2.303RT)ꢁ1. Theoretical estimations of the me-
chanism of this elimination suggest a molecular mechanism of a concerted non-synchronous four-membered cyclic
transition-state process. An analysis of bond order and natural bond orbital charges suggests that the bond polarization
ꢀþ
of C(OH)—C( O)—, in the sense of C(OH) ꢃ ꢃ ꢃC( O)ꢀꢁ, is rate limiting in the elimination reaction. The rate
—
—
—
—
coefficients obtained experimentally are in reasonably good agreement with the theoretical calculations. The
mechanism of 3-hydroxy-3-methyl-2-butanone elimination is described. Copyright # 2005 John Wiley & Sons, Ltd.
KEYWORDS: kinetics; elimination; pyrolysis; RHF/6–31G*; MP2/6–31G*; DFT B3LYP/6–31G*; 3-hydroxy-3-methyl-
2-butanone
INTRODUCTION
It would be obvious that if the hydroxy substituent of
hydroxy ketones is at the ꢁ-position with respect to the
—
O bond, a different mechanistic pathway in the
—
The gas-phase elimination kinetics of primary, secondary
and tertiary 2-hydroxy ketones have been examined and
reported [reaction (1)].1,2 The kinetic data for these retro-
Aldol type of decomposition give increased rates from
primary to tertiary carbon bearing the hydroxyl substi-
tuent. In other words, methyl substitution at the hydroxyl
carbon caused a significant increase in rates, which
means that bond breaking from primary to tertiary—
C
elimination process may occur. Therefore, the present
work was aimed at examining the kinetics of elimination
of primary, secondary and tertiary 1-hydroxy ketones in
the gas phase, together with theoretical studies for a
reasonable mechanistic interpretation. The theoretical
calculations aimed to procure the kinetic parameters
and the characterization of the potential energy surface
(PES) as a means to understand the nature of the
molecular mechanism of this reaction. Consequently,
the kinetics for the gas-phase elimination reaction of 3-
hydroxy-3-methyl-2-butanone into acetone and acetalde-
hyde was studied using ab initio RHF, MP2 and DFT/
B3LYP methods with 6–31G, 6–31G* and 6–31G**
basis sets as implemented in Gaussian 98W.3 Calcula-
tions with MP2/6–31G** were carried out specifying 6–
31G** for the hydrogen being transferred in the reaction;
for all other atoms 6–31G* was used. The Berny analy-
tical gradient optimization routines were used for opti-
mization. The nature of stationary points was established
by calculating and diagonalizing the force constant ma-
trix to determine the number of imaginary frequencies.
Intrinsic reaction coordinate (IRC) calculations were
C(OH)—, in the sense of R2C(OH)ꢀþꢃ ꢃ ꢃCH2COCH3
ꢀꢁ
bond polarization, is a determining factor [reaction (1)].
ð1Þ
´
*Correspondence to: G. Chuchani, Centro de Quımica, Instituto
Venezolano de Investigaciones Cientıficas (IVIC), Apartado 21827,
´
Caracas 1020-A, Venezuela.
E-mail: chuchani@quimica.ivic.ve
Copyright # 2005 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2005; 18: 595–601

596
M. GRATEROL ET AL.
Table 1. Temperature and pressure data for pyrolysis
reaction for 3-hydroxy-3-methyl-2-butanone
performed to verify transition-state structures. The tran-
sition-state structures were characterized by means of a
normal-mode analysis.
Temperature ( ꢀC) P0 (Torr) Pf (Torr)
Pf/P0 Average
The unique imaginary frequency associated with the
transition vector (TV) was characterized. Frequency cal-
culations provided thermodynamic quantities such as
zero point vibrational energy (ZPVE), temperature cor-
rections and absolute entropies, and consequently the rate
coefficient can be estimated assuming that the transmis-
sion coefficient is equal to 1. Temperature corrections and
absolute entropies were obtained assuming ideal gas
behavior, from the harmonic frequencies and moments
of inertia by standard methods4 at average temperature
and pressure values within the experimental range
(737.15 K and 0.197 atm). Scaling factors for frequencies
and zero point energies for the HF, DFT/B3LYP and MP2
methods used were taken from the literature.5
439.6
450.2
460.2
468.2
104.5
129
139
217
2.08
2.28
2.18
2.20
2.19
294.5
279.5
275
125
Table 2. Stoichiometry of the elimination reaction for 3-
hydroxy-3-methyl-2-butanone at 460.5 ꢀC
Parameter
Value
13
Time (min)
6
10
17
24
Reaction (%) (pressure) 16.90 30.15 36.75 45.25 53.85
Acetone (%) (GC) 17.80 31.08 35.72 44.38 51.81
The first-order rate coefficient k(T) was calculated
using the TST6 and assuming that the transmission
coefficient is equal to 1, as expressed in the following
relation:
where P0 is the initial pressure. The average experimental
Pf/P0 values at four temperatures and after 10 half-lives is
2.19 (Table 1). The observed Pf/P0 > 2 was found to be
due to a small degree of decomposition of the acetone
product. Additional verification of stoichiometry (2) was
made by comparing, up to 55% decomposition, the
pressure measurements with the results of quantitative
analyses of the product acetone (Table 2).
The effect of the addition of different proportions of
toluene inhibitor is shown in Table 3. The pyrolysis
experiments on hydroxybutanone were always carried
out in seasoned vessels and in the presence of at least
twice the amount of toluene in order to prevent any
possible radical chain reaction. No induction period
was observed and the rates were reproducible with a
relative standard deviation not greater than 5% at a given
temperature.
kðTÞ ¼ ðKT=hÞexpðꢁꢀGz=RTÞ
where ꢀGz is the Gibbs free energy change between the
reactant and the transition state and K and h are the
Boltzmann and Planck constants, respectively.
ꢀGz was calculated using the following relations:
ꢀGz ¼ ꢀHz ꢁ TꢀSz
and
ꢀHz ¼ Vz þ ꢀZPVE þ ꢀEðTÞ þ PV
where Vz is the potential energy barrier and ꢀZPVE and
ꢀE(T) are the differences in ZPVE and temperature
corrections between the transition state (TS) and the
reactant, respectively.
To examine the effect of the surface on the rate of
elimination, several runs in the presence of at least a
twofold amount of toluene inhibitor were carried out in a
vessel with a surface-to-volume ratio of six times greater
than that of the normal vessel. The rate of elimination of
the hydroxybutanone was unaffected in a packed and an
unpacked seasoned Pyrex vessel, whereas a significant
heterogeneous effect was observed in the clean packed
and unpacked Pyrex vessels (Table 4).
RESULTS AND DISCUSSION
Attempts to examine the gas-phase elimination kinetics
of hydroxyacetone (acetol, HOCH2COCH3) and 3-hy-
droxy-2-butanone [acetoin, CH3CH(OH)COCH3] were
difficult owing to the hydroscopic nature of the former
(92.4% purity), and crystallization to a dimer of the latter
(95.2% purity). For kinetic determinations it is essential
to have organic substrates above 97.5% purity.
The pyrolysis products of 3-hydroxy-3-methyl-2-buta-
none described in reaction (2), a twofold increase in the
final pressure, Pf, is required, i.e. Pf ¼ 2P0:
Table 3. Effect of the inhibitor toluene on rates for 3-
hydroxy-3-methyl-2-butanone at 469.0 ꢀCa
Ps (Torr)
Pi (Torr)
Pi/Ps
104 k1 (sꢁ1
)
114
—
90.5
113
155
282
280
—
0.5
1.1
1.3
2.3
3.4
9.43
8.97
8.43
7.84
7.25
7.43
168.5
106
123
121.5
81
a
Ps ¼ pressure of the substrate; Pi ¼ pressure of the inhibitor. Vessel
ð2Þ
seasoned with allyl bromide.
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GAS-PHASE ELIMINATION KINETICS OF 3-HYDROXY-3-METHYL-2-BUTANONE
597
Table 4. Homogeneity of the reaction for 3-hydroxy-3-
methyl-2-butanone at 460.5 ꢀC
S/V (cmꢁ1 a 104 k1 (sꢁ1 b
)
)
104 k1 (sꢁ1 c
)
1
6
10.12
18.75
5.01
5.06
a S ¼ surface area (cm2); V ¼ volume (cm3).
b Clean Pyrex vessel.
c Vessel seasoned with allyl bromide.
Table 5. Variation of rate coefficients with initial pressure
for 3-hydroxy-3-methyl-2-butanone at 468.2 ꢀCa,b
Parameter
Value
P0 (Torr)
81
7.46
121.5
7.25
131
7.28
154.5 201.5
7.02 7.42
104 k1 (sꢁ1
)
a Vessel seasoned with allyl bromide.
b In the presence of the inhibitor toluene.
Figure 1. Transition-state structures found by RHF/6–31G*
and B3LYP are virtually identical. Product formation involves
the transfer of hydrogen from C-6 to C-1, to give acetalde-
hyde and the enol form of acetone. Activation parameters
for RHF deviate from the experimental values (Table 7);
B3LYP values are better than RHF but still show some
departure from experimental
Table 6. Temperature dependence of the rate coefficients
for 3-hydroxy-3-methyl-2-butanone
Parameter
Value
Temperature
( ꢀC)
439.6 450.2 460.5 468.2 479.0 489.3
104 k1 (sꢁ1
)
1.59
3.03
5.01 7.38 12.32 20.60
implemented in Gaussian 98W. Calculations at the aver-
age experimental temperature and pressure were carried
out for both substrate conformers C-1 and C-2. Starting
from these two conformers of 3-hydroxy-3-methyl-2-
butanone, two possible four-membered ring transition
states, TS-1 and TS-2, were obtained from MP2/6–
31G* calculations (Fig. 2).
Rate equation: log[k1 (sꢁ1)] ¼ (13.05 ꢂ 0.53) ꢁ (229.7 ꢂ 5.3)kJ molꢁ1
(2.303 RT)ꢁ1; r ¼ 0.9996.
The first-order rate coefficients of this substrate de-
scribed from k1 ¼ (2.303/t)logP0/(2P0 ꢁ Pt) were inde-
pendent to initial pressures (Table 5). A plot of
log(2P0 ꢁ Pt) against time t gave a good straight line up
to 55% reaction. The variation of the first-order rate
coefficient with temperature and the corresponding
Arrhenius equation are described in Table 6, which gives
rate coefficients at the 90% confidence level obtained
from a least-squares procedure.
According to the results in Table 6, and to describe
the most probable mechanism for the elimination of
3-hydroxy-3-methyl-2-butanone in the gas phase, a the-
oretical study was carried out.
THEORETICAL RESULTS
The substrate 3-hydroxy-3-methyl-2-butanone exists
mainly in two conformations; C-1 and C-2 (Fig. 1). In
conformer C-1, the hydroxyl group is anti to the carbonyl
whereas in conformer C-2 these groups are eclipsed and
an additional stabilization of 11.17 kJ molꢁ1 (MP2/
6–31G*, 737.15 K and 0.197 atm) is obtained owing to
an intramolecular hydrogen bond (Fig. 1).
Figure 2. Conformations of the reactant 3-hydroxy-3-
methyl-2-butanone C-1 and C-2 and their corresponding
transition-state structures, TS-1 and TS-2, from MP2/6–
31G* calculations. Activation parameters for TS-2 are best
when compared with experimental values (Table 7). This TS
structure is late in the sense of C-1—C-2 bond breaking
Transition-state geometries were obtained using quad-
ratic synchronous transit protocols QST2 and QST3 as
Copyright # 2005 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2005; 18: 595–601

598
M. GRATEROL ET AL.
Table 7. Activation parameters calculated at the RHF, B3LYP and MP2 levels of theory for the thermal decomposition of 3-
methyl-3-hydroxy-2-butanone at 737.15 K and 0.917 atm
Level
ꢀHz (kJ molꢁ1
)
Ea (kJ molꢁ1
)
ꢀGz (kJ molꢁ1
)
ꢀSz (J molꢁ1 Kꢁ1
)
Log [A (sꢁ1)]
k1 (sꢁ1
)
ꢁ12
ꢁ5
ꢁ13
ꢁ4
ꢁ4
ꢁ4
RHF/6–31G*
341.8
242.8
353.0
226.4
228.6
223.6
347.9
248.9
359.1
232.5
234.8
229.7
349.7
250.7
360.9
234.3
236.6
231.5
ꢁ10.72
ꢁ10.72
ꢁ10.72
ꢁ10.72
ꢁ10.76
ꢁ10.77
13.06
13.06
13.06
13.06
13.07
13.05
2.55 Â 10
2.64 Â 10
4.07 Â 10
7.62 Â 10
2.69 Â 10
5.89 Â 10
B3LYP/6–31G*
MP2/6–31G*TS-1
MP2/6–31G*TS-2
MP2/6–31G**/TS-2
Experimental
Even though theoretical calculations of transition-state
structures have been a useful tool for reasonable mechan-
istic interpretations of organic reactions, the results have
usually been limited to enthalpy of activation, and con-
sequently to energy of activation. Frequently the entro-
pies of activation are far from experimental. It is our
experience in gas-phase reactions that the difference in
Using
ꢀGztheo ¼ ꢀHztheo ꢁ TꢀSztheo
ꢀSztheo was obtained. From ꢀSztheo and Eatheo, logA and
the rate coefficients can be calculated.
Transition states from RHF and B3LYP/6–31G* are
very similar in structure (Fig. 1), being very late with
regard to C-1—C-2 bond breaking. Polarization of the
C-1—C-2 bond in both TS structures occurs in the sense
values between experimental energy of activation (Eaexp
)
and the free energy of activation (ꢀGzexp) gives an idea of
the magnitude of the entropy of activation.
C(OH)ꢀþꢃ ꢃ ꢃC( O)ꢀꢁ, that is, C-2 becomes more posi-
—
—
In view of the above considerations, entropy values
were estimated according to Chuchani–Cordova,7 con-
sidering a factor Cexp. This factor is intended to rationa-
lize the limitations of the theoretical methods since they
do not consider the collisional entropy. Therefore,
tive and C-1 less positive in charge. The TS is a twisted
four-membered ring structure including atoms C-1, C-2,
C-6 and H-7. There is a hydrogen transfer from C-6 (one
of the methyl groups in C2) to C-1, whereas C-2—C-6
˚
has double bond character in the transition state (1.407 A,
Table 8), leading to the formation of acetaldehyde and the
enol form of acetone. Activation parameters for RHF/6–
31G* (Table 7) are too high compared with the experi-
mental values, whereas the B3LYP/6–31G* values are
better but still show some departure from the experi-
mental data.
ꢀHzexp ffi ꢀHztheo
and consequently
Eaexp ffi Eatheo
MP2 results vary depending on the conformation of the
substrate. For conformer C-1 transition state TS-1 was
found and for conformation C-2 TS-2 (Fig. 2). Activation
parameters for TS-2 are in good agreement with the
experimental values, whereas for TS-1 they are too
high (Table 7). This result suggest that TS-2 is the most
likely transition-state structure for this reaction. The
structure of the transition state TS-2 is a twisted four-
membered ring, compressing atoms C-1, C-2, O-3 and H-
4, where a hydrogen atom is being transferred from the
hydroxyl group to C-1 to give acetaldehyde and acetone.
TS-2 is late in the sense of C-1—C-2 bond breaking and
there is some double bond character in the C-2—C-6
bond in the transition state (Table 9). NBO charges reveal
a strong polarization for the C-1—C-2 bond in the sense
We expect that
ꢀGzexp ffi ꢀGztheo
and therefore
ꢀGzexp ꢁ Eaexp ¼ Cexp
hence we obtain
ꢀGztheo ¼ Eatheo þ Cexp
where the superscripts exp and theo refer to experimental
and theoretical values, respectively, and the parameter
Cexp is given by
C(OH)ꢀþꢃ ꢃ ꢃC( O)ꢀꢁ, as found in the previous calcula-
—
—
tions (RHF and B3LYP described above).
Electronic structure calculation results suggest that the
thermal decomposition of 3-methyl-3-hydroxy-2-buta-
none may occur through TS-2 (MP2/6–31G* from con-
formation C-2), leading to acetaldehyde and acetone. An
alternative pathway is possible through TS-1 (B3LYP/6–
31G*) to give acetaldehyde and the enol form of acetone.
Cexp ¼ nRT ꢁ TꢀSzexp ðn ¼ 1 unimolecular reactionÞ
Cexp includes the contribution of colisional entropy,
which has not been considered in frequency calculations
(isolated molecules).
Copyright # 2005 John Wiley & Sons, Ltd.
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GAS-PHASE ELIMINATION KINETICS OF 3-HYDROXY-3-METHYL-2-BUTANONE
599
Table 8. Structural parameters for reactant and transition states for RHF/6–31G* and B3LYP/6–31G* calculationsa
Structure
C-1—C-2
C-2—O-3
O-3—H-4
C-1—O-5
H-7—C-1
C-2—C-6
Reactant RHF
TS RHF
Reactant B3LYP
TS B3LYP
1.550
3.200
1.544
3.157
1.410
1.280
1.410
1.310
0.940
1.012
0.970
1.070
1.210
1.200
1.220
1.210
2.710
1.690
2.730
1.600
1.536
1.407
1.544
1.413
C-2—O-3—H-4
C-1—C-2—O-3
C-2—C-1—O-5
O-3—C-2—C-1—O-5
TS RHF
TS B3LYP
107.14
104.89
61.58
61.250
104.59
129.973
95.11
76.260
a
˚
Atom distances are in A and dihedral angles in degrees.
Mu¨lliken atomic charges for reactant and transition states from RHF/6–31G* and B3LYP/6–31G* levels of theory
Structure
C-1
C-2
O-3
H-4
O-5
H-7
C-6
Reactant RHF
TS RHF
Reactant B3LYP
TS B3LYP
0.516
0.115
0.438
0.120
0.238
0.533
0.250
0.422
ꢁ0.773
ꢁ0.664
ꢁ0.658
ꢁ0.555
0.473
0.488
0.407
0.383
ꢁ0.551
ꢁ0.520
ꢁ0.460
ꢁ0.372
0.178
0.216
0.157
0.147
ꢁ0.488
ꢁ0.680
ꢁ0.453
ꢁ0.537
Table 9. Structural parameters for reactant conformations C-1 and C-2 and transition states TS-1 and TS-2
Structures
C-1—C-2
C-2—O-3
O-3—H-4
C-1—O-5
C-1—H-4
C-2—C-6
C-1
TS-1
C-2
TS-2
Products
1.545
2.911
1.550
3.020
3.320
1.430
1.330
1.410
1.300
1.220
0.960
0.990
0.940
1.030
2.379
1.210
1.220
1.210
1.210
1.220
4.300
1.082
2.229
1.100
1.100
1.530
1.430
1.530
1.430
1.510
C-2—O-3—H-4
C-1—C-2—O-3
C-2—C-1—O-5
O-3—C-2—C-1—O-5
TS-1
TS-2
102.11
104.89
77.090
61.250
67.834
129.973
ꢁ178.922
76.260
a
˚
Atom distances are in A and dihedral angles in degrees (MP2/6–31G*).
Atomic charges from NBO analysis for C-2, TS-2 and products (MP2/6–31G* level of theory)
Structure
C-1
C-2
O-3
H-4
O-5
C-6
C-2
TS-2
Products
0.626
0.157
0.454
0.226
0.715
0.661
ꢁ0.790
ꢁ0.702
ꢁ0.655
0.493
0.477
0.200
ꢁ0.614
ꢁ0.640
ꢁ0.627
ꢁ0.486
ꢁ0.654
ꢁ0.592
Both transition-state structures are twisted four-mem-
bered rings. This is in accord to the experimental pre-
exponential factor A as suggested by Benson and
O’Neal.8 This means that the experimental logA ¼ 13.05
13.05 suggests a four-membered cyclic transition state
rather than a radical process. The latter type of decom-
position commonly gives logA ¼ 8–10.
and 0.09% for MP2/6–31G**. The first-order rate coeffi-
cient for TS-2 is of the same order of magnitude as the
experimental value (29% error). Values for TS-1 are far
from the experimental data, therefore TS-2 is the most
reasonable transition state for the reaction path of the
gas-phase elimination reaction of 3-hydroxy-3-methyl-2-
butanone.
Rate coefficients and Arrhenius pre-exponential factors
were determined and compared with experimental va-
lues. The results show very good agreement for TS-2 for
MP2/6–31G* and MP2/6–31G** calculations (Table 7),
within 1.25, 1.22, 1.21 and 0.46% error for ꢀHz, Ea, ꢀGz
and ꢀSz, respectively, MP2/6–31G* and 2.23, 2.22, 2.20
Bond order analysis
To investigate further the nature of the TS along the
reaction pathway, bond order calculations were
Copyright # 2005 John Wiley & Sons, Ltd.
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600
M. GRATEROL ET AL.
performed9–11 using the TS-2 structure. Wiberg bond
indexes12 were computed using the natural bond orbital
(NBO) program13 as implemented in Gaussian 98W.
Bond-breaking and -making process involved in the
reaction mechanism can be monitored by means of the
synchronicity (Sy) concept proposed by Moyano et al.,14
defined by the expression
resulting in a polarized TS. The partial charge on the
hydrogen being transferred is positive in the TS. The TS
can be described as late in the sense of C-1—C-2 bond
breaking but early in the sense of hydrogen transfer. The
polarization of the transition state in which C-1—C-2 is
almost broken supports a polar molecular mechanism
instead of a free radical pathway. These estimations are in
accord with the experimental values since this reaction is
not affected by radical inhibitors (Table 3).
ꢀ
ꢁꢂ
n
X
Sy ¼ 1 ꢁ
jꢀBi ꢁ ꢀBavj=ꢀBav
2n ꢁ 2
i¼1
CONCLUSIONS
where n is the number of bonds directly involved in the
reaction and the relative variation of the bond index is
obtained from
Theoretical calculations suggest that the reaction pro-
ceeds by a concerted non-synchronous mechanism,
through a twisted four-membered transition-state struc-
ture. Calculations gave the best results at the MP2/6–
31G* and MP2/6–31G** levels of theory. The activation
parameters are in agreement with experimental values for
the MP2/6–31G* and MP2/6–31G** levels of theory and
the first-order reaction rate coefficient is of the same
order of magnitude. The suggested transition state, TS-2,
is late in the sense of C-1—C-2 bond breaking. Structural
parameters, natural charges and NBO analysis of the
proposed TS suggest that the polarization of the C-1—
C-2 bond in the sense COꢀꢁꢃ ꢃ ꢃCꢁ(OH)ꢀþ is the deter-
mining factor in the decomposition process. The syn-
chronicity parameter Sy ¼ 0.65 is in accord with a
molecular concerted polar non-synchronic mechanism.
It was demonstrated experimentally that this reaction is
molecular in nature, therefore restricted wavefunctions
were used for all calculations (RHF, RB3LYP, RMP2).
Consequently, calculation problems may arise in this
approach if radicals are involved. This was not observed.
Moreover, it is known that MP2 tends to stabilize radi-
cals. Even though the best results for activation para-
meters were obtained with MP2, an alternative
mechanism suggested from B3LYP results cannot be
ignored.
ꢃ
ꢄꢃ
ꢅ
ꢀBi ¼ BTi S ꢁ BRi Š BPi ꢁ BRi
where the superscripts R, TS and P represent reactant,
transition state and product, respectively.
The evolution in bond change is calculated as
%Ev ¼ ꢀBi  100
The average value is calculated from
ꢂ
n
X
ꢀBav ¼ 1
n
ꢀBi
i¼1
Bonds indexes were calculated for those bonds suffer-
ing major modifications during the reaction, i.e. C-1—C-
2 (B12), C-2—O-3 (B23), O-3—H-4 (B34) and H-4—C-
1(B41). The results are given in Table 10. The greatest
progress in the reaction coordinate is the breaking of the
C-1—C-2 bond.
The synchronicity parameter Sy ¼ 0.65 reveals a con-
certed non-completely synchronic mechanism, where the
polarization of the C-1—C-2 bond plays an important
role. This is supported by the changes in charges at the C-
1 and C-2 atoms as the reaction progress from the
reactant to the transition state as described above. Transi-
tion state TS-2 gives the observed products showing more
progress in the C-1—C-2 bond breaking than in the
transfer of the hydrogen from the hydroxyl to C-1,
EXPERIMENTAL
3-Hydroxy-3-methyl-2-butanone. This substrate (Aldrich)
of 98.1% purity as determined by GLC (dinonyl phtha-
late–5% Chromosorb G AW DMCS, 80–100 mesh). The
product acetone (Merck ) was quantitatively analyzed in
the same column. The verification of the identities of
substrate and products was carried out by GC–MS
(Saturn 2000, Varian) using a DB-5MS capillary column
(30 Â 0.25 mm i.d., 0.25 mm film thickness).
Table 10. NBO analysis for MP2/6–31G* calculationsa
C-1—C-2
C-2—O-3 O-3—H-4 H-4—C-1
0.671 0.496 0.005
0.927 0.293 0.178
38.6 40.9 22.0
BiR
0.964
ꢁ0.051
105.1
BTi S
%Ev
dBav
Sy
Kinetic studies. The kinetic experiments were carried out
in a static reaction system reported previously15–17 with
an Omega DP41-TC/DP41-RTD high-temperature perfor-
mance digital temperature indicator. The reaction vessels
were seasoned at all times with allyl bromide and the
0.517
0.655
a
Wiberg bond indexes (Bi), % evolution through the reaction coordinate
(%Ev), average bond index variation (dBav) and synchronicity parameter
(Sy) for reaction mechanism (2) are shown.
Copyright # 2005 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2005; 18: 595–601

GAS-PHASE ELIMINATION KINETICS OF 3-HYDROXY-3-METHYL-2-BUTANONE
601
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Petersson GA, Ayala PY, Cui Q, Morokuma K, Malick DK,
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Johnson B, Chen W, Wong MW, Andres JL, Gonzalez C, Head-
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Gaussian: Pittsburgh, PA, 1998.
process of decomposition was carried out in the presence
of the free radical inhibitor toluene. The rate coefficients
were determined by quantitative chromatographic analy-
sis of the product acetone. The temperature was con-
trolled by a Shinko DC-PS resistance thermometer
controller and an Omega Model SSR280A55 solid-state
relay maintained within ꢂ 0.2 ꢀC and measured with a
calibrated platinum–platinum–13% rhodium thermocou-
ple. No temperature gradient was detected along the
reaction vessel. The substrate was injected (0.05–0.1 ml)
directly into the reaction vessel with a syringe through a
silicone-rubber septum.
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Copyright # 2005 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2005; 18: 595–601