Theoretical and experimental studies of the diketene system: Product branching decomposition rate constants and energetics of isomers

Article abstract of DOI:10.1002/kin.20263

The kinetics and mechanism for the thermal decomposition of diketene have been studied in the temperature range 510-603 K using highly diluted mixtures with Ar as a diluent. The concentrations of diketene, ketene, and CO₂ were measured by FTIR spectrometry using calibrated standard mixtures. Two reaction channels were identified. The rate constants for the formation of ketene (k₁) and CO₂ (k₂) have been determined and compared with the values predicted by the Rice-Ramsperger-Kassel-Marcus (RRKM) theory for the branching reaction. The first-order rate constants, k ₁ (s^-1)= 10^15.74±0.72 exp(-49.29 (kcal mol^-1) (±1.84)/RT) and k₂ (s^-1)= 10 ^14.65±0.87 exp(-49.01 (kcal mol^-1) (±2.22)/RT); the bulk of experimental data agree well with predicted results. The heats of formation of ketene, diketene, cyciobuta-1,3dione, and cyclobuta-1,2-dione at 298 K computed from the G2M scheme are -11.1, -45.3, -43,6, and -40,3 kcal mol^-1, respectively.

Full text of DOI:10.1002/kin.20263

Theoretical and
Experimental Studies of the
Diketene System: Product
Branching Decomposition
Rate Constants and
Energetics of Isomers
1
2
2
3
BINH BUI, TI JO TSAY, M. C. LIN, C. F. MELIUS
1
University of Georgia, Athens, GA 30602-2556
Emory University, Atlanta, GA 30322-2210
Lawrence Livermore National Laboratory, Livermore, CA 94551
2
3
Received 18 September 2006; revised 5 March 2007; accepted 6 March 2007
DOI 10.1002/kin.20263
Published online in Wiley InterScience (www.interscience.wiley.com).
ABSTRACT: The kinetics and mechanism for the thermal decomposition of diketene have been
studied in the temperature range 510–603 K using highly diluted mixtures with Ar as a diluent.
The concentrations of diketene, ketene, and CO2 were measured by FTIR spectrometry using
calibrated standard mixtures. Two reaction channels were identified. The rate constants for the
formation of ketene (k1) and CO2 (k2) have been determined and compared with the values
predicted by the Rice–Ramsperger–Kassel–Marcus (RRKM) theory for the branching reaction.
−
1
15.74 ± 0.72
−1
−1
The first-order rate constants, k1 (s ) = 10
exp(−49.29 (kcal mol ) (± 1.84)/RT) and
−
1
14.65 ± 0.87
k2 (s ) = 10
exp(−49.01 (kcal mol ) (± 2.22)/RT); the bulk of experimental data
agree well with predicted results. The heats of formation of ketene, diketene, cyclobuta-1,3-
dione, and cyclobuta-1,2-dione at 298 K computed from the G2M scheme are −11.1, −45.3,
−1
−
43.6, and −40.3 kcal mol , respectively. ꢀC 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39:
5
80–590, 2007
Correspondence to: M. C. Lin: e-mail: chemmcl@emory.edu.
National Science Council Distinguished Visiting Professor at Chiao-
tung University, Hsinchu, Taiwan.
INTRODUCTION
The gas phase thermal decomposition of diketene un-
der diluted conditions has been known to efficiently
produceketene [1].
Contract grant sponsor: Basic Energy Sciences, U. S. Department
of Energy.
Contract grant number: DE-FG02-97-ER14784.
ꢀ
c 2007 Wiley Periodicals, Inc.

THEORETICAL AND EXPERIMENTAL STUDIES OF THE DIKETENE SYSTEM
581
than diketene by 32 kcal mol−1, compared with the
O
2
CH CO
2
O
−1
(
1)
value of 42 kcal mol computed by Fu. Although
these theoretical studies provide us a qualitative idea
of the reaction scheme involved in diketene pyrolysis,
they are quantitatively in discordance.
Experiments with kinetic isotope effect studies were
performed by Chikos to establish that the thermol-
ysis equation (1) is first order [2]. Furthermore, the
activation energy of the concerted reaction has been
determined to be 50 kcal mol [3]. The pyrolysis of
diketene can also occur through another reaction path-
way to give allene and carbon dioxide [4,5].
Diketene as well as its monomer, ketene, is commer-
cially important. Despite the claim made by Rice and
Roberts [6] that reaction (2) could occur, no attempt has
been made to give a theoretical interpretation of this
channel. The aim of our work is, therefore, to experi-
mentally measure the rate constants for the branching
dissociation of diketene by reactions (1) and (2) and
to compare these values with those predicted by the
transition state theory (TST) or the Rice–Ramsperger–
Kassel–Marcus (RRKM) theory for examination of
pressure effect, based on the computational results of
various methods including G2M (modified Gaussian-
−
1
O
CH CCH + CO
O
2
2
2
(2)
Calculations made by Rice and Roberts using the stan-
dard state heats of formation of ketene, allene, and
carbon dioxide suggested that this channel was more
likely to occur thermodynamically than (1) [6]. Sec-
ondary reactions that may occur under high-conversion
conditions include ketene reacting to form cyclobuta-
2) [10] and BAC-G3B3 [11]. By comparing experiment
to theory, we are testing the accuracy of our results and
of the theoretical model.
Our interest in diketene arises in part from the fact
that it is isoelectronic with the dimer of HNCO. In an
earlier study on the thermal reaction of isocyanic acid
between 900 and 1200 K, a new bimolecular process
1,3-dione
2
CH CO
(3)
2
O
O
or 2, 4-dimethylene-1,3-dioxetane
O
O
O
HN C
O
2
CH CO
(4)
2 HNCO
CO2 + HNCNH
2
N
H
(
5)
In principle, these isomers of diketene, cyclobuta-1,3-
dione, and 2,4-dimethylene-1,3-dioxetane may also be
formed by the direct isomerization of diketene and may
subsequently fragment into two ketene molecules, i.e.,
the reverse of (1), (3), and (4).
was proposed to account for the production of CO2 and
nitrogen-containing products, such as HCN and NH3
12]. Employing the same mechanism and similar tran-
sition state geometries as in (5), we can conveniently
explain (1) and (2).
[
Although there have been no comprehensive kinetic
studies on diketene pyrolysis, a few groups have pub-
lished theoretical results that are directly related to our
study and should be mentioned here as a prelude to
our investigation. Jug et al. [7] calculated the activa-
tion energies for the fragmentation of three isomeric
species to form ketene as well as their corresponding
reverse reactions by using the semiempirical SINDO
method. The reverse reaction paths of (3) and (4) were
estimated to have energy barrier of approximately the
same height. Their results also concluded that the iso-
merization of diketene to form cyclobutane-1,3-dione
and 2,4-dimethylene-1,3-dioxetane could not occur
due to energy barrier considerations and the likeli-
hood of fragmentation at higher energies. Fu et al. [8]
studied the dimerization reactions of ketene and ob-
EXPERIMENTAL SECTION
The thermal decomposition of diketene was carried
out in a 270-mL quartz reactor cell heated with a
double-walled cylindrical furnace. A thermocouple
placed in a sealed tube at the center of the cell was
used to measure and maintain the temperature, mon-
itored by an Omega CN-9000 solid-state temperature
controller. Prior to each run, the entire system, i.e. the
cell, the vacuum line, and the FTIR sample cell, was
pumped down to 10 Torr. The chamber enclosing
the sample cell was purged with dry N2 gas in order
to remove water, carbon dioxide, and other impurities
that could potentially mar the spectrum. After the
pyrolysis, the reaction mixture was analyzed with a
Mattson Instrument Polaris FT-IR spectrometer.
−4
−1
tained a very high activation energy of 61.2 kcal mol
by MP2/4-31G for the 2,4-dimethylene-1,3-dioxetane
forming pathway (4). Seidl and Schaefer [9] deter-
mined by CISD+Q/DZ+P that the 2,4-dimethylene-
The pyrolysis of diketene was studied in the tem-
perature range 510–603 K, corresponding to reacting
1,3-dioxetane molecule was energetically less stable
International Journal of Chemical Kinetics DOI 10.1002/kin

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82
BUI ET AL.
times of a few minutes to several hours. Most of the
runs were carried out at a constant pressure of 800 Torr
with high Ar-dilution in order to minimize any reac-
tions occurring on the surface of the reaction cell and to
prevent air leakage into the system. However, several
runs were performed between 100 and 800 Torr with
ature range 510–603 K while maintaining a constant
pressure 800 Torr as alluded to above. The calibration
allowed us to convert the measured reactant and prod-
uct absorbance into concentration versus time profiles
for each of the temperature studied. These profiles were
kinetically modeled by using the following equations
with the initial concentration of diketene, [DK]0:
100-Torr increments in order to test the pressure depen-
dence of the rate constants. Three different concentra-
tions of diketene, highly diluted with ultra pure argon,
were included in our study: 0.14%, 0.26%, and 0.52%.
The products measured and calibrated by FTIR
analysis were diketene, ketene, and carbon dioxide
[
DK]t = [DK]0 exp[−(k1 + k2)t]
(6)
(7)
(8)
[CH CO] = [(2k [DK] )/(k + k )]
2
t
1
0
1
2
−1
{1 − exp[−(k1 + k2)t]}
[CO ] = [(k [DK] )/(k + k )]
at 1012.6, 2163.0, and 2361.7 cm , respectively.
Figure 1 shows a typical set of spectra for a pyrolyzed
2
t
2
0
1
2
(B and C band signal) and unpyrolyzed (A band signal)
{1 − exp[−(k1 + k2)t]}
sample of a diketene mixture. The CO2 and diketene
used in this work were initially obtained from Aldrich
with purities of 99.8% and 98%, respectively. Diketene
was further purified by trap-to-trap distillation from
Consequently, the total rate constants (ktot = k1 + k2)
can in principle be derived from the above equations
through fitting the diketene, ketene, or CO2 concentra-
tion profiles. Evaluation of Eqs. (7) and (8) can yield
the values of k1 and k2, respectively. k1 can be di-
rectly derived from ketene yields or indirectly from
the difference ktot (by [diketene]) −k2 (by [CO2]). The
results from both methods are in reasonable agree-
ment as shown in Fig. 2a. In Fig. 2b, we compare the
values of total rate constant derived from the decay
of diketene with k1 + k2 obtained from the analyses
using ketene and CO2 concentration profiles, respec-
tively. Table I lists the experimental rate constants for
the two channels in the temperature range 510–603 K
for comparison with the computed values (vide infra).
The rate constants were fitted with the standard form
of the Arrhenius equation by weighted least-squares
method to yield the following expressions for k1 and
k2:
273 to 195 K (dry ice temperature). The purified sam-
ple was a clear and colorless liquid. The result of
FTIR analysis revealed no detectable impurities such
as CO2, CH2CO, and CH3COOH. Ketene was prepared
by the pyrolysis of acetic anhydride (Aldrich) at around
773 K. The main product, ketene, was then repeatedly
distilled from 195 to 148 K (n-propanol slush bath) to
eliminate CO2 impurities.
Experimental Data
The decomposition of the 0.14%, 0.26/%, and 0.52%
diketene–argon mixtures was measured in the temper-
k1 (s 1) = 1015.74 ± 0.72 exp(−49.29(kcal mol−1
−
)
(
± 1.84)/RT )
(9)
)
−
1
14.65 ± 0.87
exp(−49.01(kcal mol−1
k2 (s ) = 10
(
± 2.22)/RT )
(10)
−3
−1 −1
K .
where R = 1.987 × 10 kcal mol
The values of k1 and k2 were then inserted in Eqs. (7)
and (8) to remodel the concentration profiles of ketene
and CO2. Figure 3 illustrates examples of concentration
profiles of this system along with the corresponding
modeling results. In general, the agreement between
experimental and computed profiles is good, except
those of ketene at higher temperatures and longer reac-
tion times, probably due to the loss by polymerization.
Figure 1 (A) 319.0 Torr of 0.26% diketene in Ar, unpy-
rolyzed. (B) 0.26% diketene in Ar pyrolyzed at 801.9 Torr
and 573 K for 21 h and 48 min. The final pressure after ex-
pansion was 319.0 Torr. (C) The difference between A and
B.
International Journal of Chemical Kinetics DOI 10.1002/kin

THEORETICAL AND EXPERIMENTAL STUDIES OF THE DIKETENE SYSTEM
583
−
−
−
4
6
8
fied Gaussian-2 (G2M) [10] method to improve the pre-
dicted energies. We applied the G2M(RCC5) scheme
to calculate the base energy (Ebase) at the MP4/6-
311G(d,p) level of theory and improve the Ebase with
an expanded basis set correction (ꢀE(+3df2p)), a re-
stricted couple cluster (ꢀE(RCC)) correction, and the
“higher level correction” (HLC) based on the number
of paired (nα) and unpaired (nβ) valence electrons.
The following is a summary of the G2M scheme:
−
−
−
−
10
12
14
16
k1
k2
Ebase = E[PMP4/6-311G(d,p)]
E(RCC) = E[RCCSD(T)/6-311G(d,p)]
(11)
(12)
ꢀ
1
.6
1.7
1.8
1.9
2.0
−
Ebase
−
1
1
000/T (K )
ꢀE(+3df2p) = E[MP2/6-311 + G(3df, 2p)]
(a)
−
E[MP2/6-311G(d,p)]
E(HLC, RCC5) = −5.25nβ − 0.19nα
E[G2M(RCC5)] = Ebase + ꢀE(RCC)
(13)
−
4
6
8
ꢀ
(14)
−
−
ktotal by fitting [diketene]
Predicted line
+
+
ꢀE(+3df2p)
ꢀE(HLC, RCC5) + ZPE (15)
−
10
Sum of (k + k )
1
2
All calculations were performed using the Gaussian-98
program [16]. Optimized geometries along with bond-
ing information are provided in Fig. 4. Energetic pa-
rameters, ZPE, moments of inertia, and frequencies, to-
gether with high-level relative energies obtained from
the G2M scheme are tabulated and used in our discus-
sion (vide infra). Also, we compare the energetic data
with those obtained by the bond additivity correction
(BAC-G3B3) [11] procedure. Table II includes relative
energies of diketene and its cyclic isomers; Table III
contains relative energies of species resulted from the
diketene reaction; Table IV provides molecular and TS
parameters needed for the standard RRKM calculation
implemented in the ChemRate program [17].
−
12
−
−
14
16
1
.6
1.7
1.8
1.9
2.0
−
1
1
000/T (K
b)
)
(
Figure 2 The experimentally modeled rate constants: (a)
k1 (ꢀ) resulted from [ktot (of DK fitting) – k2], k1 obtained
from direct fitting of [ketene] (ꢁ), and k2 (•) from fitting
[
CO2]; predicted values are shown in solid lines; (b) total
rate constants: ktot resulted from [DK] fitting (ꢂ), and sum
of [k1 + k2] (ꢀ), respectively obtained from direct fitting
of [ketene] and [CO2]; predicted values are shown in solid
lines.
RESULTS AND DISCUSSION
Diketene and Its Cyclic Isomers
Computational
We employed the hybrid density functional method
[
13], B3LYP, with the 6-311G (d,p) basis set for ge-
In Fig. 4, the geometries of diketene and its cyclic
isomers, 1,3-cyclobutadione and 2,4-dimethylene-
1,3-dioxetane, are presented together with two
other geometric isomers, 1,2-cyclobutadione and 3,4-
dimethylene-1,2-dioxetane. The structure of diketene
is compared with available experimental data reported
by Bregman and Bauer [18]. The predicted C C and
C O bond distances agree with those from the elec-
ometric optimization of the reactant, transition struc-
tures (TSs), and products. The intrinsic reaction coordi-
nate (IRC) [14,15] calculations were utilized to confirm
the nature of respective TSs. Thermal and zero-point
vibrational corrections of all species were obtained at
the same level of theory through the calculation of the
harmonic analytic vibrational frequencies.
˚
Higher level single point calculations were also car-
ried out with the optimized geometries using the modi-
tron diffraction study within 0.01 A, well within the
˚
experimental uncertainty of ± 0.04 A.
International Journal of Chemical Kinetics DOI 10.1002/kin

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84
BUI ET AL.
Table I Experimental and Predicted Rate Constants, k1 and k2, versus Temperature at 800 Torr
Experimental
Predicted
Temperature (K)
k1
k2
k1
k2
510
518
528
538
548
553
558
563
573
578
583
588
598
603
7.36E–06
8.93E–06
1.87E–05
4.31E–05
1.01E–04
1.30E–04
2.06E–04
2.66E–04
6.01E–04
1.13E–03
1.44E–03
3.46E–03
1.01E–02
8.02E–03
7.81E–07
1.07E–06
1.28E–06
6.87E–06
9.17E–06
2.01E–05
2.44E–05
2.41E–05
4.87E–05
1.05E–04
1.86E–04
3.62E–04
1.03E–03
8.26E–04
4.11E–06
8.38E–06
1.98E–05
4.51E–05
10.00E–05
1.47E–04
2.15E–04
3.13E–04
6.46E–04
9.20E–04
1.30E–03
1.83E–03
3.56E–03
4.92E–03
3.19E–07
6.79E–07
1.69E–06
4.07E–06
9.47E–06
1.43E–05
2.14E–05
3.18E–05
6.86E–05
9.97E–05
1.44E–04
2.07E–04
4.18E–04
5.89E–04
Molecular structures of 1,3-cyclobutanedione (D2h)
and 2,4-dimethylene-1,3-dioxetane (D2h) fit within
cate that 1,3-cyclobutanedione lies above diketene by
1.5 and 2.2 kcal mol , respectively.
−1
˚
0.02 A or less, to those predicted by Seidl and
Schaeffer [9] using the DZ+P SCF level of theory.
Mechanism of Diketene Decomposition
˚
The C O distances are 1.386 A in 2,4-dimethylene-
1
,3-dioxetane, and the other bond lengths, C C, are
Both reactions (1) and (2) occur through concerted
mechanisms. In (1), the decomposition of diketene to
form two ketene fragments occurs with the elongation
of C(4) O(7) bond in the TS1 from 1.397 to 2.323
˚
1.544 A in 1,3-cyclobutanedione, respectively. Obvi-
ously, the ring strain effect in 1,3-dioxetane may ac-
count for the 27.5 kcal mol higher in energy than
−1
˚
1,3-cyclobutanedione.
A accompanied by the rotation of one ketene moiety
◦
The other two isomers of diketene are 3,4-
at −50.8 with respect to the other one, and the ex-
˚
dimethylene-1,2-dioxetane and 1,2-cyclobutanedione.
They have a higher symmetry order, belonging to
the C2v symmetry point group, than diketene (Cs).
They are not directly derivable from diketene through
isomerization. 1,2-Cyclobutanedione is only 3.3 kcal
tension of the C(1) O(6) bond from 1.508 to 1.697 A.
Vibrational frequency analyses and IRC tests were per-
formed on TS1 to confirm its geometric transformation
and to validate the concerted nature of the transition
structure.
−1
mol energetically higher than 1,3-cyclobutanedione
Diketene decomposition in reaction (2) occurs
through TS2 to form allene and carbon dioxide. The
breaking C(6)−O(7) and C(1)−C(4) bonds in TS2 are
−1
or 4.7 kcal mol above diketene; however, it was
not mentioned in any recent experiments or theoreti-
cal calculations. While 2,4-dimethylene-1,3-dioxetane
˚
2.105 and 1.806 A, respectively; the TS preserves the
−1
lies 29.0 kcal mol above diketene as compared to the
C symmetry point group of the reactant. The concerted
s
−1
values of 32 and 42 kcal mol , respectively, reported
by Schaefer and Fu; our BAC-G3B3 value [11] of 29.4
is the closest to the G2M value. 3,4-Dimethylene-
nature of this reaction path is similar to TS1 and has
been confirmed by an IRC test.
Figure 5 displays the PES of diketene decomposi-
tion computed at the G2M and BAC-G3B3 levels. At
the G2M level of theory, the barrier of (1), 45.1 kcal
−1
1
,2-dioxetane is located at 84.0 kcal mol
ative to diketene on the potential energy surface
PES).
At each level of theory except for one, diketene iso-
rel-
− −1
1
(
mol , is 3.0 kcal mol lower than that of reaction (2)
−1
(48.1 kcal mol ). The BAC-G3B3 method predicts a
similar trend as the G2M method, i.e., 45.5 and 47.8
mer is predicted to be the lowest on the potential energy
surface (Table II). At MP4(SDTQ) level of theory, 1,3-
cyclobutanedione isomer is 0.7 kcal mol more stable
than diketene; this was predicted as well in Seidl and
Schaeffer’s calculations, i.e., 0.7 kcal mol (CISD)
and 0.8 kcal mol (Davidson-corrected CISD) [9].
However, our final G2M and BAC-G3B3 values indi-
−1
kcal mol for TS1 and TS2, respectively. Although in
our rate constant calculation, we employed the values
predicted by the G2M method (whose applicability has
been widely demonstrated in our previous studies [19–
25]), the BAC-G3B3 method should give essentially
the same results.
−1
−1
−1
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THEORETICAL AND EXPERIMENTAL STUDIES OF THE DIKETENE SYSTEM
585
5
18 K
In addition, the PES displays other two high-lying
channels leading to the 4-methyl-oxet-2-one interme-
diate that could be concertedly fragmented into methy-
lacetylene and CO2 through TS5. However, these path-
ways are not possible due to high barriers of the TS3
0.12
0.09
0.06
0.03
0.00
−1
and TS4 (75.3 and 101.7 kcal mol , respectively).
Both TS3 and TS4 describe the hydrogen transfer from
the cyclic methylene moiety to the external methylene
unit. While in TS3, the leaving hydrogen atom is di-
◦
rectly positioned at a dihedral angle of −49.6 with re-
spect to the molecular plane, in TS4 the corresponding
◦
hydrogen atom is located at −0.84 . The TS4 barrier
is higher in energy because its transformation involves
the reconfiguration of the π-electrons in the C C bond,
i.e., elongation from 1.319 to 1.396 A, and the rotation
0.00
20.00
40.00
60.00
80.00
˚
Time (s) ؋ 1000
of the external methylene unit. Also, in principle the
dimerization of two ketenes can occur through TS6,
5
73 K
1
0
0
0
0
.00
.75
.50
.25
.00
−1
4
4.9 kcal mol , to form 1,3-cyclobutadione, which
−1
is located 1.5 kcal mol above diketene. However,
Tenud et al. [26] reported that there was only a small
trace amount of 1,3-cyclobutadione produced from
dimerization of ketenes that leads mainly to diketene.
The reaction of two ketenes to yield 2,4-dimethylene-
1
,3-dioxetane is unlikely because of the high barrier
−1
of TS7 (52.1 kcal mol ) and the low stability of the
product (29.0 kcal mol above diketene).
−1
Rate Constant Calculations
0
700
1400
2100
2800
3500
The rate constants for the unimolecular decomposition
of diketene were calculated at temperatures between
Time (s)
5
10 and 1000 K by using ChemRate [17]. Argon was
6
03 K
considered as bath gas according to experimental con-
ditions. The exponential-down equation [27,28] with
a step size of ꢁꢀEꢂdown = 350 cm was applied to
model the collisional energy transfer using appropriate
Lennard–Jones (L–J) parameters for the Ar-adduct col-
0
.80
.60
.40
.20
.00
−1
0
˚
lision pairs, i.e. Ar [29] (σ = 3.47 A, ε = 113.5 K) and
0
0
0
˚
diketene (σ = 3.95 A, ε = 173.0 K). The L–J param-
eters of diketene were deconvoluted from the DK–He
complex collision parameters (σcplx, εcplx) [27–29] ob-
tained from a direct fit of the computed Lennard–Jones
potential curve of the complex using the equation
ꢀ
ꢁ
= 4εcplx (σcplx/r)12 − (σcplx/r)6
(16)
0
60
120
180
240
V
L-J
Time (s)
where r is the center-of-mass separation between the
two particles. Although the diketene’s Lennard–Jones
parameters are roughly approximated, their effect is
negligible due to the fact that the decomposition reac-
tion of interest was measured primarily at 800 Torr at
Figure 3 Concentration versus time plotted for diketene
ꢀ), ketene (•), and CO2 (ꢃ), at (a) 518 K (800 Torr), (b)
73 K (800 Torr), and (c) 603 K (800 Torr); modeling values
(
5
using the experimentally fitted k1 and k2 are expressed in
solid lines.
International Journal of Chemical Kinetics DOI 10.1002/kin

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86
BUI ET AL.
Figure 4 Optimized [B3LYP/6-311G(d,p)] molecular geometries of all studied species. [Color figure can be viewed in the
online issue, which is available at www.interscience.wiley.com.]
sional frequencies are below 100 cm−1. Predicted rate
constants are fitted to the Arrhenius equation; the cor-
responding expressions are shown in Fig. 2.
Figure 2a displays the rate constants, k1 and
k2 (solid lines), evaluated at 800 Torr. At different
which the rates are pressure independent. Other appro-
priate molecular and thermochemical parameters pre-
dicted by the G2M (Table III) were employed for the
rate constant calculations. Hindered-rotor treatments
were applied to the cases of TS1 and TS2, whose tor-
International Journal of Chemical Kinetics DOI 10.1002/kin

THEORETICAL AND EXPERIMENTAL STUDIES OF THE DIKETENE SYSTEM
587
Table II Relative Energies of Ketene’s Dimers (kcal mol 1)
−
Diketene and
Its Isomeric
Dimers
B3LYP (P)MP4
with (SDTQ)/ RCCSD(T)/
(Unscaled) ZPE 6-311G(d,p) 6-311G(d,p) 6-311G(d,p) 6-311+G(3df,2p) with ZPE
ZPE
MP2/
MP2/
G2M(RCC5) BAC-G3B3
with ZPE
Diketene
45.39
39.63
0.00
10.77
0.00
20.96
0.00
23.47
0.00
22.25
0.00
25.92
0.00
21.39
0.00
22.38
(2x) Ketene
2
,4-Dimethylene-
,3-dioxetane
,4-Dimethylene-
,2-dioxetane
1
44.70
44.04
28.01
33.37
31.53
33.20
31.31
28.95
29.43
3
1
82.44
3.99
0.65
89.76
0.33
−0.72
87.49
1.84
0.01
93.28
1.65
0.14
91.18
5.15
2.78
84.04
4.73
1.45
n/a
n/a
2.19
1
1
,2-Cyclobutadione 44.78
,3-Cyclobutadione 44.18
conditions of temperatures for the decomposition of
diketene, reaction (1) is more favorable than reaction
ratio of k1 decreases to as low as 0.73, and that of k2
increases to as high as 0.27 at 1000 K.
(
2) producing allene and CO2 as indicated by the low
At 800 Torr, the predicted results are compared
with experimental values of k1 and k2 expressed
in Fig. 2a along with the ktot values displayed in
Fig. 2b. The results agree well in the tempera-
ture range 510–603 K. Treatment of the hindered-
rotor in TS1 and TS2 was taken into account in
−1
barrier of TS1 (45.1 kcal mol ) relatively to that of
−1
TS2 (48.1 kcal mol ). At the high-pressure and tem-
perature limit, k2 is likely to compete with k1 as shown
in Table V that displays the branching ratios of channel
1
(k1/ktot) and 2 (k2/ ktot). Nevertheless, the branching
Table III Molecular and Transition-State Parameters Used in the RRKM Calculation
b
Reaction
Species
Erela
(kcal/mol)
Symmetry
Number
Moments of Inertia
Vibrational Frequencies
−
40
2
−1
(10
g cm )
(cm
)
Diketene
0.00
1
68.78, 302.14, 365.57
136, 319, 460, 514, 530, 678, 735, 816,
864, 895, 984, 988, 1019, 1118, 1209,
1265, 1417, 1444, 1766, 1964, 3077,
3128, 3164, 3255
TS1
45.1
1
115.65, 305.78,
460i, 92, 206, 346, 421, 484, 494, 626,
671, 711, 865, 954, 1010, 1047, 1090,
344.76
1
3
189, 1423, 1449, 1749, 2236, 3047,
150, 3160, 3258
Ketene
21.4
48.1
2
1
2.94, 81.34, 84.29
447, 563, 596, 991, 1172, 1408, 2234,
179, 3271
850i, 57, 245, 359, 368, 436, 479, 616,
3
TS2
88.39, 312.51, 395.30
674, 862, 870, 902, 971, 1011, 1077,
1240, 1375, 1446, 1898, 1947, 3095,
3123, 3170, 3241
Allene
4
5.75, 93.83, 93.83
372, 372, 867, 867, 885, 1017, 1017, 1109,
423, 1480, 2052, 3117, 3122, 3192, 3192
1
CO2
TS6
2
1
0.00, 71.53, 71.53
126.00, 313.57,
666, 666, 1375, 2436
389i, 109, 207, 322, 437, 482, 548, 599,
653, 710, 805, 966, 998, 1037, 1067,
44.9
1.5
348.21
1
3
165, 1408, 1483, 1841, 2167, 3090,
147, 3178, 3237
1,3-Cyclobutadione
4
75.92, 321.13, 386.50
72, 374, 402, 425, 475, 537, 626, 717,
871, 917, 923, 1043, 1156, 1160, 1171,
1193, 1380, 1396, 1847, 1930, 3045,
3050, 3096, 3098
a
Energies relative to the reactants are given at the G2M level based on the B3LYP/6-311G(d,p)geometries for the species of the system.
The vibrational frequencies were computed at the B3LYP/6-311G(d,p) level of theory.
b
International Journal of Chemical Kinetics DOI 10.1002/kin

5
88
BUI ET AL.
the rate constant calculations to fit the experimental
values.
Enthalpy of Formation of Ketene
Several existing experimental values for the heat of
o
formation of ketene (ꢀfH 298) are −11.4 ± 0.4 [30],
−
12.91 ± 1.20 [31], −11.85 ± 0.21 [32], and −12.8 ±
−
.1 kcal mol [33]. The first and third values, reported
1
0
by Nuttal et al. [30] and Ruscic et al. [32], agree quite
well within the experimental uncertainty. The fourth
value, most recently reported by Traeger [33] using the
photoionization mass spectrometry method, is close
to the second value derived by Aubry et al. [31]. To
the controversial experimental values that seem to be
divided into two groups of values, many computed [34–
o
3
8] ꢀfH 298 of ketene support either one or the other
o
of the two groups. We derived the new ꢀfH 298 for
ketene at the G2M-level by using the following heat of
o
−1
the reaction (ꢀrH 298 = 50.0 kcal mol ):
3
3
CO2 + CH2 ⇔ CH2CO + O
(17)
o
3
The experimental ꢀfH 298 of CO2, and O are well
established [39]. There are three recently reported
o
3
ꢀ
fH 298 values of CH2, 92.60 ± 0.50, 92.90 ± 0.14,
and 92.35 ± 1.00 kcal mol , by Zabarnick et al.
40], Doltsinis and Knowles [41], and Chase [39], re-
spectively; these values result in the following three
−1
[
o
ꢀ
fH 298 values of ketene: −11.1, −10.8, and −11.3
−1
kcal mol . All three values appear to favor the higher
heats of formation of Nuttall et al. [30] and Ruscic
−1
et al. [32], −11.4 ± 0.4 and −11.85 ± 0.21 kcal mol
,
respectively.
Enthalpy of Formation of Diketene
and Its Isomers
o
We employed the predicted ꢀfH 298 value of ketene,
−
1
−
11.1 kcal mol , and heat of reaction (1) (298 K)
o
to obtain the ꢀfH 298 value of diketene, −45.3 kcal
−1
mol , which agrees with the experimental value,
−1
−
45.47 ± 0.13 kcal mol [42]. By using the heat of re-
action between diketene and its isomers together with
o
the predicted ꢀfH 298 value of diketene, −45.3 kcal
−1
o
mol , we computed the ꢀfH 298 values for cyclobuta-
1,3-dione, cyclobuta-1,2-dione, 2,4-dimethylene-1,3-
dioxetane, and 3,4-dimethylene-1,2-dioxetane, i.e.,
−
1
−
43.6, −40.3, −16.3, and 39.0 kcal mol , respec-
o
tively. If the experimental ꢀfH 298 diketene value of
−1
−1
–
45.47 kcal mol instead of −45.3 kcal mol is used,
−1
the corresponding results are only 0.2 kcal mol
higher.
International Journal of Chemical Kinetics DOI 10.1002/kin

THEORETICAL AND EXPERIMENTAL STUDIES OF THE DIKETENE SYSTEM
589
BAC-G3B3
G2M(CC5)
n/a
1
01.7
TS4
7
7
5.0
5.3
7
3.6
3.5
7
TS3
TS7
4
7.8
4
4
7.0
7.2
4
5.5
5.1
4
4.7
4.9
48.1
4
4
TS2
TS5
TS1
TS6
2
9.4
9.0
2
2
2
2.4
1.4
MX
CH CO
2
7
6
.1
.7
(
2x)
2.2
0
.0
.0
1.5
−3.6
4.5
INT
0
−4.6
−
1,3-Cyclobutadione
−5.2
Diketene
CH CCH + CO2
2
2
CH CCH + CO
3 2
Figure 5 Potential energy surface (kcal mol 1) of diketene decomposition; G2M’s and BAC-G3B3’s values are in boldface
−
and normal. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]
Table V Predicted Branching Ratio of k1 and k2 at Different Temperature and Pressure conditions
Branching Ratio
Lower-Pressure Limit
760 Torr
Infinite Pressure
Temperature
k1
k2
k1
k2
k1
k2
510
550
553
580
603
800
1000
0.989
0.988
0.987
0.987
0.986
0.982
0.980
0.011
0.012
0.013
0.013
0.014
0.018
0.020
0.928
0.913
0.912
0.902
0.893
0.840
0.812
0.072
0.087
0.088
0.098
0.107
0.160
0.188
0.928
0.911
0.909
0.898
0.888
0.804
0.734
0.072
0.089
0.091
0.102
0.112
0.196
0.266
CONCLUSION
the data agrees well with those predicted at 800 Torr
Ar by the quantum mechanical and statistical calcula-
tions. The fact that reaction (1) is favored is consistent
with the predicted lower barrier for ketene production.
The ꢀfH 298 values of ketene, diketene, cyclobuta-
1,3-dione, and cyclobuta-1,2-dione computed from
The thermal decomposition of diketene has been stud-
ied experimentally in the temperature range 510–603 K
by means of FTIR product analysis. The experiments
were performed at 800 Torr using highly diluted Ar
mixtures. The reaction was observed to be weakly pres-
sure dependent at pressures at 100 Torr. The first-order
o
the G2M computational scheme were −11.1, −45.3,
−1
−43.6, and −40.3 kcal mol , respectively. Our pre-
dicted results validate the experimental data and
further prove the capability of the G2M level of
theory.
−
1
15.74 ± 0.72
−1
rate constants, k1 (s ) = 10
exp(−49.29
−
1
14.65 ± 0.87
(
kcal mol ) (± 1.84)/RT) and k2 (s ) = 10
−
1
exp(−49.01 (kcal mol ) (± 2.22)/RT), the bulk of
International Journal of Chemical Kinetics DOI 10.1002/kin

5
90
BUI ET AL.
M. C. Lin acknowledges the support from the National Sci-
ence Council of Taiwan for a Distinguished Visiting Pro-
fessorship at National Chiao Tung University in Hsichu,
Taiwan.
19. Choi, Y. M.; Park, J.; Wang, L.; Lin, M. C.
ChemPhysChem 2004, 5, 1231–1234.
20. Choi, Y. M.; Park, J.; Lin, M. C. ChemPhysChem 2004,
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1. Xu, Z. F.; Park, J.; Lin, M. C. J Chem Phys 2004, 120,
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