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

Theoretical and

Experimental Studies of the

Diketene System: Product

Branching Decomposition

Rate Constants and

Energetics of Isomers

BINH BUI,

_{TI JO TSAY,}

_{M. C. LIN,}

_{C. F. MELIUS}

1_{University of Georgia, Athens, GA 30602-2556} 2_{Emory University, Atlanta, GA 30322-2210}

3_{Lawrence Livermore National Laboratory, Livermore, CA 94551}

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 CO2were 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, k1(s−1)= 1015.74 ± 0.72exp(−49.29 (kcal mol−1) (±1.84)/RT) and

k2 (s−1)= 1014.65 ± 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, cyclobuta-1,3-dione, 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.}
C 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39:

580–590, 2007

Correspondence to: M. C. Lin: e-mail: chemmcl@emory.edu. National Science Council Distinguished Visiting Professor at Chiao-tung University, Hsinchu, Taiwan.

Contract grant sponsor: Basic Energy Sciences, U. S. Department of Energy.

Contract grant number: DE-FG02-97-ER14784. c

2007 Wiley Periodicals, Inc.

INTRODUCTION

The gas phase thermal decomposition of diketene un-der diluted conditions has been known to efficiently produceketene [1].

O

O 2CH2CO

(1) 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−1 [3]. The pyrolysis of diketene can also occur through another reaction path-way to give allene and carbon dioxide [4,5].

O

O CH2CCH2+ CO2 (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-1,3-dione O O 2CH2CO (3) or 2, 4-dimethylene-1,3-dioxetane 2CH2CO O O (4) 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).

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 fragmentaactiva-tion 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-tained a very high activation energy of 61.2 kcal mol−1 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-1,3-dioxetane molecule was energetically less stable

than diketene by 32 kcal mol−1, compared with the value of 42 kcal mol−1 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.

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-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

2 HNCO C N H O HN O _CO 2+ HNCNH (5) was proposed to account for the production of CO2and

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).

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 10−4 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.

The pyrolysis of diketene was studied in the tem-perature range 510–603 K, corresponding to reacting

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 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 at 1012.6, 2163.0, and 2361.7 cm−1, respectively. Figure 1 shows a typical set of spectra for a pyrolyzed (B and C band signal) and unpyrolyzed (A band signal) 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 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 CO2impurities.

Experimental Data

The decomposition of the 0.14%, 0.26/%, and 0.52% diketene–argon mixtures was measured in the

temper-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.

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:

[DK]t = [DK]0exp[−(k1+ k2)t ] (6)

[CH2CO]t = [(2k1[DK]0)/(k1+ k2)]

{1 − exp[−(k1+ k2)t ]} (7)

[CO2]t = [(k2[DK]0)/(k1+ k2)]

{1 − exp[−(k1+ k2)t ]} (8)

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. Evaluaconcentra-tion of Eqs. (7) and (8) can yield the values of k1 and k2, respectively. k1 can be

di-rectly derived from ketene yields or indidi-rectly 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:

k1 (s−1)= 1015.74± 0.72 exp(−49.29(kcal mol−1)

(±1.84)/RT ) (9)

k2 (s−1)= 1014.65± 0.87 exp(−49.01(kcal mol−1)

(±2.22)/RT ) (10) where R= 1.987 × 10−3kcal mol−1K−1.

The values of k1and k2were 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 polymerizareac-tion.

(a) 1.6 1.7 1.8 1.9 2.0 −16 −14 −12 −10 −8 −6 −4 k₂ k₁ ln ki (s − 1 ) 1000/T (K−1 ) (b) 1.6 1.7 1.8 1.9 2.0 −16 −14 −12 −10 −8 −6 −4 Sum of (k₁ + k₂)

k_total by fitting [diketene]

Predicted line ln kto ta l (s − 1 ) 1000/T (K−1 )

Figure 2 The experimentally modeled rate constants: (a)

k1(
) resulted from [ktot(of DK fitting) – k2], k1obtained from direct fitting of [ketene] (), and k2 (•) from fitting [CO₂]; predicted values are shown in solid lines; (b) total rate constants: ktotresulted from [DK] fitting (), and sum of [k1 + k2] (
), respectively obtained from direct fitting of [ketene] and [CO2]; predicted values are shown in solid lines.

Computational

We employed the hybrid density functional method [13], B3LYP, with the 6-311G (d,p) basis set for ge-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-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 Ebasewith

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:

Ebase= E[PMP4/6-311G(d,p)] (11)
E(RCC)= E[RCCSD(T)/6-311G(d,p)] − Ebase (12)
E(+3df2p) = E[MP2/6-311 + G(3df, 2p)] − E[MP2/6-311G(d,p)] (13)
E(HLC, RCC5)= −5.25nβ− 0.19nα (14) E [G2M(RCC5)]= Ebase+
E(RCC) +
E(+3df2p) +
E(HLC, RCC5) + ZPE (15) 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].

RESULTS AND DISCUSSION

Diketene and Its Cyclic Isomers

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-tron diffraction study within 0.01 ˚A, well within the experimental uncertainty of±0.04 ˚A.

Table I Experimental and Predicted Rate Constants, k1and k2, versus Temperature at 800 Torr

Experimental Predicted

Temperature (K) k1 k2 k1 k2

510 7.36E–06 7.81E–07 4.11E–06 3.19E–07

518 8.93E–06 1.07E–06 8.38E–06 6.79E–07

528 1.87E–05 1.28E–06 1.98E–05 1.69E–06

538 4.31E–05 6.87E–06 4.51E–05 4.07E–06

548 1.01E–04 9.17E–06 10.00E–05 9.47E–06

553 1.30E–04 2.01E–05 1.47E–04 1.43E–05

558 2.06E–04 2.44E–05 2.15E–04 2.14E–05

563 2.66E–04 2.41E–05 3.13E–04 3.18E–05

573 6.01E–04 4.87E–05 6.46E–04 6.86E–05

578 1.13E–03 1.05E–04 9.20E–04 9.97E–05

583 1.44E–03 1.86E–04 1.30E–03 1.44E–04

588 3.46E–03 3.62E–04 1.83E–03 2.07E–04

598 1.01E–02 1.03E–03 3.56E–03 4.18E–04

603 8.02E–03 8.26E–04 4.92E–03 5.89E–04

Molecular structures of 1,3-cyclobutanedione (D2h)

and 2,4-dimethylene-1,3-dioxetane (D2h) fit within

0.02 ˚A or less, to those predicted by Seidl and Schaeffer [9] using the DZ+P SCF level of theory. The C O distances are 1.386 ˚A in 2,4-dimethylene-1,3-dioxetane, and the other bond lengths, C C, are 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−1 higher in energy than 1,3-cyclobutanedione.

The other two isomers of diketene are 3,4-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 mol−1energetically higher than 1,3-cyclobutanedione or 4.7 kcal mol−1 above diketene; however, it was not mentioned in any recent experiments or theoreti-cal theoreti-calculations. While 2,4-dimethylene-1,3-dioxetane lies 29.0 kcal mol−1above diketene as compared to the values of 32 and 42 kcal mol−1, respectively, reported by Schaefer and Fu; our BAC-G3B3 value [11] of 29.4 is the closest to the G2M value. 3,4-Dimethylene-1,2-dioxetane is located at 84.0 kcal mol−1 rel-ative to diketene on the potential energy surface (PES).

At each level of theory except for one, diketene iso-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−1more stable than diketene; this was predicted as well in Seidl and Schaeffer’s calculations, i.e., 0.7 kcal mol−1 (CISD) and 0.8 kcal mol−1 (Davidson-corrected CISD) [9]. However, our final G2M and BAC-G3B3 values

indi-cate that 1,3-cyclobutanedione lies above diketene by 1.5 and 2.2 kcal mol−1, respectively.

Mechanism of Diketene Decomposition

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

˚

A accompanied by the rotation of one ketene moiety at −50.8◦ with respect to the other one, and the ex-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.

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 2.105 and 1.806 ˚A, respectively; the TS preserves the

Cssymmetry point group of the reactant. The concerted

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 mol−1, is 3.0 kcal mol−1lower than that of reaction (2) (48.1 kcal mol−1). The BAC-G3B3 method predicts a similar trend as the G2M method, i.e., 45.5 and 47.8 kcal mol−1for 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.

0.00 20.00 40.00 60.00 80.00 0.00 0.03 0.06 0.09 0.12 518 K Time (s) ⴛ 1000 C o nc ent rat io n ( m o l/ c c) ⴛ 10 − 6 0 700 1400 2100 2800 3500 0.00 0.25 0.50 0.75 1.00 573 K C o nc e n tr at io n ( m ol /c c ) ⫻ 10 − 7 Time (s) 0 60 120 180 240 0.00 0.20 0.40 0.60 0.80 603 K C o nc ent rat io n (m ol /c c) x 10 − 7 Time (s)

Figure 3 Concentration versus time plotted for diketene (
), ketene (•), and CO2(), at (a) 518 K (800 Torr), (b) 573 K (800 Torr), and (c) 603 K (800 Torr); modeling values using the experimentally fitted k1 and k2 are expressed in solid lines.

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 CO2through TS5. However, these

path-ways are not possible due to high barriers of the TS3 and TS4 (75.3 and 101.7 kcal mol−1, 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 of the external methylene unit. Also, in principle the dimerization of two ketenes can occur through TS6, 44.9 kcal mol−1, to form 1,3-cyclobutadione, which is located 1.5 kcal mol−1 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 of TS7 (52.1 kcal mol−1) and the low stability of the product (29.0 kcal mol−1above diketene).

Rate Constant Calculations

The rate constants for the unimolecular decomposition of diketene were calculated at temperatures between 510 and 1000 K by using ChemRate [17]. Argon was considered as bath gas according to experimental con-ditions. The exponential-down equation [27,28] with a step size of 
Edown= 350 cm−1 was applied to

model the collisional energy transfer using appropriate Lennard–Jones (L–J) parameters for the Ar-adduct col-lision pairs, i.e. Ar [29] (σ= 3.47 ˚A, ε = 113.5 K) and 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

VL-J= 4εcplx

(σcplx/r)12− (σcplx/r)6



(16) 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 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.]

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-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

Table II Relative Energies of Ketene’s Dimers (kcal mol−1)

Diketene and B3LYP (P)MP4

Its Isomeric ZPE with (SDTQ)/ RCCSD(T)/ MP2/ MP2/ G2M(RCC5) BAC-G3B3

Dimers (Unscaled) ZPE 6-311G(d,p) 6-311G(d,p) 6-311G(d,p) 6-311+G(3df,2p) with ZPE with ZPE

Diketene 45.39 0.00 0.00 0.00 0.00 0.00 0.00 0.00 (2x) Ketene 39.63 10.77 20.96 23.47 22.25 25.92 21.39 22.38 2,4-Dimethylene-1,3-dioxetane 44.70 28.01 33.37 31.53 33.20 31.31 28.95 29.43 3,4-Dimethylene-1,2-dioxetane 44.04 82.44 89.76 87.49 93.28 91.18 84.04 n/a 1,2-Cyclobutadione 44.78 3.99 0.33 1.84 1.65 5.15 4.73 n/a 1,3-Cyclobutadione 44.18 0.65 −0.72 0.01 0.14 2.78 1.45 2.19

conditions of temperatures for the decomposition of diketene, reaction (1) is more favorable than reaction (2) producing allene and CO2as indicated by the low

barrier of TS1 (45.1 kcal mol−1) relatively to that of TS2 (48.1 kcal mol−1). At the high-pressure and tem-perature limit, k2is likely to compete with k1as 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

Reaction Erela Symmetry Moments of Inertia Vibrational Frequenciesb

Species (kcal/mol) Number (10−40g cm2_{) (cm}−1₎

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, 344.76 460i, 92, 206, 346, 421, 484, 494, 626, 671, 711, 865, 954, 1010, 1047, 1090, 1189, 1423, 1449, 1749, 2236, 3047, 3150, 3160, 3258 Ketene 21.4 2 2.94, 81.34, 84.29 447, 563, 596, 991, 1172, 1408, 2234, 3179, 3271 TS2 48.1 1 88.39, 312.51, 395.30 850i, 57, 245, 359, 368, 436, 479, 616, 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, 1423, 1480, 2052, 3117, 3122, 3192, 3192 CO2 2 0.00, 71.53, 71.53 666, 666, 1375, 2436 TS6 44.9 1 126.00, 313.57, 348.21 389i, 109, 207, 322, 437, 482, 548, 599, 653, 710, 805, 966, 998, 1037, 1067, 1165, 1408, 1483, 1841, 2167, 3090, 3147, 3178, 3237 1,3-Cyclobutadione 1.5 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.}

b_{The vibrational frequencies were computed at the B3LYP/6-311G(d,p) level of theory.}

ratio of k1decreases to as low as 0.73, and that of k2

increases to as high as 0.27 at 1000 K.

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

Table IV Relative Energies of Diketene, R eaction Species, a nd Respective Transition Structures (kcal mol − 1) ZPE B 3L YP/ B 3L YP a (P)MP4(SDTQ)/ RCCSD(T)/ MP2/ MP2/ G2M(RCC5) B A C -G3B3 Reaction S pecies (Unscaled) 6 -311G(d,p) with ZPE 6 -311G(d,p) 6-311G(d,p) 6-311G(d,p) 6-311 + G(3df,2p) with ZPE w ith Z PE Dik etene 45.39 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 TS1 42.43 44.92 41.96 44.75 48.75 45.59 44.94 45.15 45.46 K etene (2x) 39.63 16.52 10.77 20.96 23.47 22.25 25.92 21.39 22.38 TS2 42.12 45.06 41.80 50.83 52.59 54.31 53.08 48.09 47.84 CH 2 CCH 2 + CO 2 41.78 − 7.84 − 11.45 − 5.76 − 4.60 − 5.13 − 1.48 − 4.55 − 3.63 TS3 41.10 76.71 72.42 79.69 81.67 78.40 76.30 75.28 74.96 TS4 40.29 106.40 101.31 106.32 107.59 106.71 105.92 101.71 n/a 4-Methyl-ox et-2-one 44.46 7.70 6.78 6.95 7.63 6.59 6.63 6.74 7.15 TS5 42.22 45.43 42.26 49.75 51.22 53.85 52.99 47.20 46.96 CH 3 CCH + CO 2 42.17 − 6.32 − 9.54 − 8.94 − 6.49 − 10.61 − 6.09 − 5.18 − 4.63 TS6 42.40 41.62 38.63 41.72 47.21 42.88 43.58 44.91 44.65 1,3-Cyclob utadione 44.18 1.86 0.65 − 0.72 0.01 0.14 2.78 1.45 2.19 aB3L YP/6-311G(d,p).

the rate constant calculations to fit the experimental values.

Enthalpy of Formation of Ketene

Several existing experimental values for the heat of formation of ketene (
fHo298) are−11.4 ± 0.4 [30],

−12.91 ± 1.20 [31], −11.85 ± 0.21 [32], and −12.8 ± 0.1 kcal mol−1[33]. The first and third values, reported 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– 38]
fHo298of ketene support either one or the other

of the two groups. We derived the new
fHo298 for

ketene at the G2M-level by using the following heat of the reaction (
rHo298= 50.0 kcal mol−1):

CO2+3CH2⇔ CH2CO+3O (17)

The experimental
fHo298 of CO2, and 3O are well

established [39]. There are three recently reported

fHo298values of3CH2, 92.60± 0.50, 92.90 ± 0.14,

and 92.35 ± 1.00 kcal mol−1, by Zabarnick et al. [40], Doltsinis and Knowles [41], and Chase [39], re-spectively; these values result in the following three

fHo298 values of ketene:−11.1, −10.8, and −11.3

kcal mol−1. All three values appear to favor the higher heats of formation of Nuttall et al. [30] and Ruscic et al. [32],−11.4 ± 0.4 and −11.85 ± 0.21 kcal mol−1, respectively.

Enthalpy of Formation of Diketene

and Its Isomers

We employed the predicted
fHo298 value of ketene,

−11.1 kcal mol−1_{, and heat of reaction (1) (298 K)}

to obtain the
fHo298 value of diketene,−45.3 kcal

mol−1, which agrees with the experimental value, −45.47 ± 0.13 kcal mol−1_{[42]. By using the heat of}

re-action between diketene and its isomers together with the predicted
fHo298value of diketene, −45.3 kcal

mol−1, we computed the
fHo298values for

cyclobuta-1,3-dione, cyclobuta-1,2-dione, 2,4-dimethylene-1,3-dioxetane, and 3,4-dimethylene-1,2-2,4-dimethylene-1,3-dioxetane, i.e., −43.6, −40.3, −16.3, and 39.0 kcal mol−1_,

respec-tively. If the experimental
fHo298diketene value of

–45.47 kcal mol−1instead of−45.3 kcal mol−1is used, the corresponding results are only 0.2 kcal mol−1 higher.

CH₂CO (2 x) Diketene TS 2 TS 1 CH₂CCH₂ + CO₂ T S3 TS 5 T SS44 CH₃CCH + CO₂ INT T SS66 1,3-Cyclobutadione 22.4 21.4 0.0 0.0 n/a 101.7 7.1 6.7 −3.6 −4.5 29.4 29.0 45.5 45.1 75.0 75.3 47.8 48.1 47.0 47.2 44.7 44.9 −4.6 −5.2 2.2 1.5 73.6 73.5 T S7 MX BAC-G3B3 G2M(CC5)

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 k1and k2at Different Temperature and Pressure conditions Branching Ratio

Lower-Pressure Limit 760 Torr Infinite Pressure

Temperature k1 k2 k1 k2 k1 k2 510 0.989 0.011 0.928 0.072 0.928 0.072 550 0.988 0.012 0.913 0.087 0.911 0.089 553 0.987 0.013 0.912 0.088 0.909 0.091 580 0.987 0.013 0.902 0.098 0.898 0.102 603 0.986 0.014 0.893 0.107 0.888 0.112 800 0.982 0.018 0.840 0.160 0.804 0.196 1000 0.980 0.020 0.812 0.188 0.734 0.266

CONCLUSION

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 prespres-sures at 100 Torr. The first-order rate constants, k1 (s−1)= 1015.74± 0.72 exp(−49.29

(kcal mol−1) (±1.84)/RT) and k2 (s−1)= 1014.65± 0.87

exp(−49.01 (kcal mol−1) (±2.22)/RT), the bulk of

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
fHo298 values of ketene, diketene,

cyclobuta-1,3-dione, and cyclobuta-1,2-dione computed from the G2M computational scheme were−11.1, −45.3, −43.6, and −40.3 kcal mol−1_{, respectively. Our}

pre-dicted results validate the experimental data and further prove the capability of the G2M level of theory.

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.

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