ab initio determination of the heat of formation of ketenyl

8/8/2019 Ab Initio Determination of the Heat of Formation of Ketenyl

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Ab initio determination of the heat of formation of ketenyl

(HCCO) and ethynyl (CCH) radicals1

Peter G. Szalaya,b, Attila Tajtia and John F. Stantonb

a Department of Theoretical Chemistry, Eotvos Lorand University,

H-1518 Budapest, P.O.Box 32, Hungary

bInstitute for Theoretical Chemistry, Department of Chemistry and Biochemistry,

the University of Texas at Austin, Austin, Texas 78712, USA

September 8, 2004

1Dedicated to Rod Bartlett for the occasion of his 60th birthday


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Abstract

The heats of formation of ketenyl (HCCO) and ethynyl (CCH) radicals have been obtained from high

level ab initio calculations. A set of reactions involving HCCO, CCH and species with well-known

heats of formation has been considered. The reaction enthalpies have been calculated from the total

energy of the species involved. These calculations include a non-relativistic electronic energy from

extrapolated coupled-cluster calculations (up to CCSDTQ), corrections for scalar relativistic and

spin-orbit effect, as well as the diagonal Born-Oppenheimer correction. We also present an accurate

equilibrium geometry for HCCO as well as harmonic and fundamental frequencies for both HCCO

and CCH.


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1 Introduction

Accurate determination of the heat of formation for transient species is a challenging task for both

theory and experiment. Experiments are difficult because of the short lifetime of these species,

while standard theoretical methods are usually less reliable for open-shell systems. Nevertheless,

knowledge of accurate thermochemical quantities for radicals is of great importance in several fields

of chemistry, in particular for atmospheric and combustion chemistry [1].

Ketenyl radical (HCCO) plays an important role in combustion chemistry since it is a key

intermediate in the oxidation of hydrocarbons. In fact,

C2H2 + O HCCO + H

is the most important reaction for removal of acetylene in the combustion cycle [2, 3, 4]. Therefore,

knowledge of its heat of formation is clearly important.

Ethynyl radical (CCH) was also considered to be a possible product in the oxidation of acetylene.

However, this channel is now known to be unimportant even at high temperatures [2]. Still, CCH

is produced in the photofragmentation of acetylene [5, 6]. It also has astrophysical importance: itis found in space in 1974 [7] and is used in surveys of different regions of interstellar medium [8].

Recent advances in electronic structure methods and computer hardware make theoretical de-

termination of thermochemical properties possible with an accuracy which matches or often excels

that of experimental observations [9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. The main focus of this paper

is to obtain accurate heats of formation for HCCO and CCH radicals. In a recent paper we have

reported an accurate equilibrium geometry of CCH using both experimental rotational constants

and high level ab initio calculations [19]. Here, we also present a systematic theoretical study on

the equilibrium geometry of HCCO. Furthermore, since the zero point energy (ZPE) is also needed

in the thermochemical study of this sort, the harmonic and anharmonic force fields have also been

calculated.

In this work, we use a reaction based scheme to estimate the heats of formation (fHo) of

HCCO and CCH. The total energy of the species involved in these reactions have been calculated

using various theoretical methods. The non-relativistic electronic energy is obtained from different

levels of coupled cluster (CC) theory [20, 21, 22, 23] including CCSD (CC with singles and doubles)

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[24], CCSD(T), which includes triple excitation effect approximately [25], and the very advanced

CCSDT [26, 27] and CCSDTQ [28, 29, 30] methods. Hierarchical basis sets are chosen, and the

energies are extrapolated with standard formulas. The scalar relativistic contribution [31, 32] to

the electronic energy is also included along with the spin-orbit interaction for open-shell systems

with degenerate ground states. In addition to the ZPE, the diagonal Born-Oppenheimer correction

(DBOC) [33, 34, 35, 36] has also been applied in the accounting of the nuclear motion contribution

to the ground state energy.

2 Methods

Ab initio calculations in this work were performed with a local version of the ACESII program

package [37] and, for the CCSDTQ calculations, the string-based many-body code of Kallay [38].

The correlation consistent-basis sets cc-pVXZ [39], aug-cc-pVXZ [40] and cc-pCVXZ [41] have been

used with (X=T(3),Q(4),5).

The geometry of HCCO has been optimized at the CCSD(T) level of theory using analytic

gradients of the energy [42, 43]. To test the sensitivity of the results with respect to the choice

of orbitals, both UHF (unrestricted Hartree-Fock) and ROHF (restricted open-shell Hartree Fock)

reference functions have been used. The harmonic vibrational frequencies are calculated at the

CCSD(T) level, again with both UHF and ROHF reference functions. Analytic second derivatives

have been utilized in the UHF calculations [44, 45]. The anharmonic force constants (cubic and

quartic) required to calculate fundamental frequencies using the usual perturbative ansatz [46] have

been obtained by numerical differentiation of the harmonic force constants [47]. Ground state

rotational constants (B0) have also been calculated with the usual formula [46] (see also Ref. [45]).

As will be discussed in detail later, the heat of formation of HCCO and CCH have been obtained

from a series of reactions. The following contributions are included in the total energy of each species

involved in the reactions:

ETot = Eelectronic + EZPE + EREL + EDBOC+ ESO (1)

where Eelectronic is the non-relativistic electronic energy, EZPE is the zero-point energy, EREL is the

scalar relativistic contribution, EDBOC is the diagonal Born-Oppenheimer correction and ESO is the

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stabilization due to spin-orbit interaction.

The electronic energy estimate comes from several sources: the Hartree-Fock (unrestricted for

open-shell species) energy, the valence CCSD, and CCSD(T) correlation contributions have been

calculated with different basis sets and extrapolated with the formulas

EXHF = EHF + a exp(bX), (2)

and

EXcorr = Ecorr +

a

X3(3)

respectively. Here EXHF

and EXcorr

are the Hartree-Fock and the correlation energy, respectively,

calculated with the (aug)-cc-p(C)VXZ basis, and EHF and Ecorr are the extrapolated counterparts.

Eqn. (2) is the exponential relation often used for the HF energy [48], while Eqn. (3) is that suggested

by Helgaker et al. [49, 50]. The extrapolated energy (contribution) will be denoted by a pair of

letters that refer to the X values of the basis sets used in the extrapolation. For example, (TQ)

will denote an extrapolation based on triple-zeta and quadruple-zeta calculations. To account for

imperfections of the CCSD(T) method, an additional triples correction has been applied which is

defined as the difference of CCSDT and CCSD(T) (valence only) energies in the cc-pVTZ basis.

Further correlation effects have been approximated by the difference between CCSDTQ and CCSDT

energies in the cc-pVDZ basis. Since all aforementioned calculations have been performed without

correlating the core electrons, an additional correction is required. This has been calculated by

comparing frozen core and all electron CCSD(T) energies obtained by extrapolating the cc-pCVTZ

and cc-pCVQZ results.

The ZPE is based on anharmonic force fields calculated as described in Ref.[51]. The higherorder force constants have been obtained at the CCSD(T) level using R(O)HF reference function and

different basis sets (see the discussion on vibrational frequencies below). Scalar relativistic effects

have been evaluated by contracting the one-particle density matrix obtained at the CCSD(T)/aug-

cc-pVTZ level with the Darwin and mass-velocity operators [31, 32]. EDBOC has been calculated

at the SCF level with the aug-cc-pVTZ basis using the formalism of Handy et al. [34, 35]. The

ROHF reference function has been used in these calculations. Correction of the ground state energy

due to spin-orbit interaction is based upon a spin-orbit CI procedure implemented in the Columbus

program system [52]: the core electrons have been described by relativistic core potentials (RECP)

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including spin-orbit terms that allow a simple calculation of the spin-orbit interaction integrals.

The CI wave function has been constructed by considering all single and double excitations out

of a valence complete-active-space reference space. To reduce computational time, double-group

symmetry is in Columbus [53]. The special cc-pVDZ type basis developed by Pitzer [54] together

with the corresponding RECPs [55] have been used.

3 Results

3.1 Equilibrium geometry of HCCO

Experimentally, no reliable geometry is available for HCCO. The rotational constants have been

obtained by Endo and Hirota [56]. From this data it was possible to characterize the geometry

as bent. For a quantitative determination of the geometry, however, additional information is

required. Endo and Hirota [56] used the results of an early calculation by Harding [57] but these

calculations have been later proven to be inaccurate [58]. Consequently, the structure proposed by

Endo and Hirota [56] is not reliable, either. Several theoretical studies appeared in the literature

[58, 59, 60, 61, 62, 63], methods up to CCSD(T) and basis sets up to quadruple-zeta quality have

been used [63] for this problem.

In Table 1 the calculated geometry, rotational constants and dipole moments are compared.

The use of different reference functions does not influence the results considerably, thus it seems

that the UHF based CCSD(T) results are not biased by the instability found for example in case

of CCH [19, 64]. There is also a definite convergence of the geometry with the basis set size,

therefore the UHF-CCSD(T) geometry obtained at the cc-pVQZ basis should be considered as the

best estimate for HCCOs equilibrium structure. Note that this geometry is very similar to the

ROHF based CCSD(T) results of Schafer-Bung et al. [63]. The core electrons have been correlated

in our calculations, despite the fact that the basis set is not optimal for treating core correlation

effects. Nevertheless, as has been shown by Bak et. al. [65] all-electron calculations with the cc-

pVQZ basis set provide significantly more accurate geometries than those which use the frozen-core

approximation for first-row atoms.

Since no experimentally determined equilibrium geometry is available, the accuracy of the cal-

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culated geometry can be best checked by comparing the rotational constants to the experimental

values. To that end the calculated equilibrium rotational constants need to be corrected with the

vibration-rotation interaction contribution [46].

The calculated and experimental rotational constants are summarized in Table 2. The reliability

and convergence of the calculated results can be judged by comparing UHF and ROHF based

results in the various basis sets. For the B and C constants, only a very slight dependence is

seen. Especially interesting is that the vibrational-rotational constants are essentially the same for

UHF and ROHF based methods. The agreement of these calculated B0 and C0 constants with

experimental values suggest that the calculated equilibrium geometry must be quite good. Note

that application of the calculated vibrational-rotational corrections to the best geometry of Ref.[63]

(all electron ROHF-CCSD(T)/cc-pCVQZ), gives practically the same rotational constants, again

showing the convergence of the results. More problematic is the A constant, both theoretically and

experimentally, due to the floppy bending mode. In case of HCCO we still see a good agreement;

all the theoretical values are within the error bar of the experimental value. Much larger is the

discrepancy in case of DCCO, although the experimental error bar is considerably smaller here.

We note that considering the results for both isotopomers, the discrepancy of the calculated and

experimental values can not be explained by either an error of the calculated equilibrium value

nor by that of the calculated vibrational-rotational constant. Therefore it appearers possible that

either the experimental A0 of DCCO is too low by 2-3 cm1 , or the HCCO constant is too high

by the same amount. We prefer the first explanation because it is more consistent with the present

theoretical results.

3.2 Vibrational frequencies

Calculating the vibrational frequencies for the ground state of HCCO, one has to keep in mind that

the X 2A state is one component of a Renner-Teller (RT) system [58, 62, 63]. The effect of the

Renner-Teller interaction on the vibrational levels has been investigated in detail by Schafer et al.

[62, 63]. They have calculated the vibronic energy levels of the Renner-Teller system considering

the bending and torsion coordinates. The effect of the CC and CO stretching modes on these levels

have been included approximately. There are two conclusions of these papers which are relevant in

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our discussion [62, 63]. First, the lowest vibronic level is not affected by the RT interaction, i.e. the

zero point energy calculated without considering the other state should be reliable. Second, the RT

interaction lowered both bending frequencies by about 10 cm1 and the anharmonic effect lowered

the CCO by about 25 cm1 .

The calculated vibrational frequencies (both harmonic and fundamental) are listed in Table 3.

The table also includes the corresponding zero point energies (ZPE). Not too much is known from

the experimental vibrational levels. A band assigned to a CCO out-of-phase stretching mode has

been measured by Unfried, Glass and Curl [66], while the CCH bend frequency has been inferred

by Brock et al. [67] by laser induced fluorescence.

Not surprisingly, the CH stretching mode is the most sensitive to the choice of the basis, the

other frequencies decrease by only a few wavenumbers. Much more important are the anharmonic

effects which affect all modes. The out-of-phase CCO stretching frequency decreases by 41 cm1 .

Note that its value is still substantially higher than the experimental value. For the CCH bending

mode, the harmonic values are close to the experimental fundamental, while the anharmonic levels

are about 20 wavenumbers below.

As will be discussed for CCH below, one should pay attention to the reliability of the frequencies

calculated with the UHF-CCSD(T) method. Indeed, the harmonic frequency of the out-of-phase

CCO stretch is about 20 cm1 lower with ROHF references than the UHF. None of the other modes

seem to be influenced. The anharmonic effects calculated by the ROHF or UHF based methods are

very similar, as well, indicating that the UHF-CCSD(T) cubic and quartic constants do not exhibit

the strange behavior found for some other radicals [64]. Further investigations are needed to see

how much the Renner-Teller effect influences the frequency of this mode.In this paper, we are more concerned about the accuracy of the ZPE, since this is used in

the determination of the heat of formation. Therefore, Table 3 lists also the zero point energies

calculated with the different methods. As the table shows, the ZPE is relatively insensitive to

the choice of reference function. To be consistent with CCH, where the UHF-CCSD(T) value

is unreliable [19], the ROHF-CCSD(T) zero point energy will be used in the heat of formation

calculation; this value is expected to have an error smaller than 0.5 kJ mol1. As has been discussed

above, the ZPE is not affected by the RT effect [62] thus these value should be more reliable than

the individual vibrational frequencies.

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The vibrational frequencies of CCH are listed in Table 4. As has been discussed in ref. [19],

the UHF based CCSD(T) method has some problems describing the force field of this molecule.

Indeed, Table 4 shows differences of up to 100 cm1 between the UHF and ROHF based results.

The anharmonic effect is also very important, it lowers the CC stretching frequency by 180-200

cm1 in the ROHF-based calculations. Very good agreement between the experimental values and

best theoretical fundamentals (ROHF-CCSD(T)/cc-pVQZ) can be observed which suggests that

the ZPE values are accurate.

Since the anharmonic ZPE is not available for HCCO at the ROHF-CCSD(T)/cc-pVQZ level,

the value calculated at R(O)HF-CCSD(T)/cc-pVTZ level have been used in the heat of formation

calculations for all species. These ZPE values are (in kJ mol1): CH: 17.0, CO: 13.0, O2: 9.6,

ketene: 82.0.

3.3 Heat of formation

The following reactions have been selected for the calculation of the heat of formation of CCH and

HCCO:

CH + CO HCCO

H2CCO HCCO + H

CCH + O HCCO

2 O + CH + CCH CO + H2CCO

It is widely accepted that the so called isodesmic reactions [68] - where the number and type of

bonds are the same on both sides of the reaction - represent the best choice for the calculationof thermochemical properties. The reason is that, due to the similar bonding environment of

the species, a systematic cancellation of errors due to incompleteness of the methods is achieved.

The reaction above do not satisfy this criteria fully, but the species involved (except HCCO and

CCH, of course) have quite precisely known heats of formation, so the uncertainty of these will not

significantly bias the results. The heats of formation of the species other than HCCO and CCH

have been taken from the Active Thermochemical Table (ATcT) of Ruscic [69, 70]:

fH00 [CH]=593.190.36 kJ mol

1

fH00 [CO] = -113.810.027 kJ mol

1

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fH00 [H2CCO] = -45.38 0.33 kJ mol

1

fH00 [H(

2S)] = 216.0340.0001 kJ mol1

fH00 [O3P)] = 246.844 0.002 kJ mol1

The largest uncertainty is clearly smaller than the error from other sources of the calculation (see

below).

For all species appearing in the above reactions, the different contributions to the total energy

appearing in Eqn. (1) have been calculated as is described in detail in Section 2. The corresponding

contributions to the reaction enthalpy have been calculated separately and are listed in Tables 5 to

8. This partitioning allows an empirical extrapolation of the different terms. These extrapolated

values are given as the best estimate in the tables along with the estimated error. The latter is

also based on the empirical extrapolation. Finally, the last row gives the final estimate for the

reaction enthalpy together with the aggregate error assuming that the uncertainty of the different

contributions are independent.

The final reaction enthalpies and their error bars can be summarized as follows:

rH00 (CH+ CO HCCO)= -302.21.1 kJ mol

1

rH00 (H2CCO HCCO + H)= 438.71.1 kJ mol1

rH00 (CCH+ O HCCO)= -633.11.4 kJ mol

1

rH00 (2O + CH+ CCH CO + H2CCO)= -1809.11.7 kJ mol

1

To calculate the heat of formation of HCCO and CCH, a fitting approach has been used: the

unknown values have been obtained as the optimal solution of an over-determined linear equation

system (formed by the four reactions) in a weighted least-squares (WLS) sense. The weight factors

associated with each reaction were chosen to minimize the overall error of the estimated values. As

the source of inaccuracies, both the estimated error of the calculated reaction enthalpies and the

error bar of the experimental values have been considered. Note that this procedure is basically the

same as solving overdetermined thermochemical networks [71, 72].

This procedure gives fH00 [HCCO]=177.2 kJ mol

1 and fH00 [CCH]=563.3 kJ mol

1. The

uncertainty of these values comes from error in the fit, that of the calculated reaction enthalpies

and the experimental heats of formation. The largest contribution is the estimated uncertainty of

the reaction enthalpies. Since there are four equations for the two unknown heats of formations, itis assumed that the error of the reaction enthalpies partly cancel. Therefore the final conservative

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error estimate is 1.5 kJ mol1 for both values.

Although the primary result of this study is the heat of formation at 0K, to be able to compare

with standard tables, we also provide the the heat of formation corresponding to 298K. The temper-

ature correction (fH0298-fH

00 ) suggested by Ruscic [73] has been chosen: 1.1 kJ mol

1 for HCCO

based on data from ref. [61] and [74] and 4.1 kJ mol1 for CCH based on ref [74]. With these, the

heats of formation at 298 K are: fH0298[HCCO]=178.31.5 kJ mol

1 fH0298[CCH]=567.41.5

kJ mol1.

In Table 9 our calculated values are compared with selected experimental and theoretical values.

Considering first the theoretical results, we can conclude that the values obtained by the G3MP2B3

method [75] seem slightly too low. The same is true for the MR-CI [76] and BAC-MP4 [77] results

for CCH. For HCCO, both W1 [78] and BAC-MP4 [79] estimates agree nicely with the present

results, while in case of CCH our value is in between the G3 [80] and W2 [13] results. Concerning

the experimental numbers, all of the theoretical results show clearly that the value in ref. [81] and

ref. [82] for HCCO and ref. [83] for CCH are in error. All other experimental values are in good

agreement with the calculations, especially if their uncertainties are also considered. It is very

interesting to note that our calculated numbers agree (for both molecules) perfectly with the mean

value obtained by Allison et al. [84, 85] from their negative ion photoelectron experiment.

In judging the reliability of the calculated results, one has to consider that the present theoretical

procedure includes such advanced contributions as correlation beyond CCSD(T), anharmonicity in

ZPE, DBOC which were not included in previous calculations. Since these are non-negligible (their

contribution to the reaction enthalpies can amount several kJ mol1), we are convinced that the

heats of formation of HCCO and CCH (0K value) presented in this paper are to be preferred overprevious computational results.

Acknowledgments

The authors thank Dr. Mihaly Kallay for the CCSDTQ calculations which make up an essential

part of this work. We also thank Branko Ruscic (Argonne National Laboratory) for providing us his

ATcT results prior publication and his valuable comments on the manuscript. Financial support

for this work comes from the Hungarian Research Foundation under OTKA grant T047182 (PGS)

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and the US National Science Foundation and the Robert A. Welch Foundation (JFS). PGS was also

supported by the Fulbright Foundation during a sabbatical at the University of Texas at Austin.

The research presented in this paper is part of a current and future work by a Task Group of

the International Union of Pure and Applied Chemistry (2000-013-2-100) to determine structures,

vibrational frequencies, and thermodynamic functions of free radicals of importance in atmospheric

chemistry.

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Table 1: Equilibrium geometry of ketenyl radical

Methods UHF-CCSD(T) ROHF-CCSD(T) UHF-CCSD(T) UHF-CCSD(T)

Basis cc-pVTZ cc-pVTZ aug-cc-pVTZ cc-pVQZ

rCO (A) 1.1728 1.1741 1.1708 1.1695

rCC (A) 1.2972 1.2963 1.3001 1.2973

rCH (A) 1.0660 1.0659 1.0674 1.0693

CCO (o) 169.4 169.4 169.1 169.4

CCH (o) 134.6 135.1 132.8 134.1

A (cm1 ) 34.99 35.57 32.70 34.19

B (cm1 ) 0.3640 0.3636 0.3645 0.3650

C (cm1 ) 0.3602 0.3600 0.3605 0.3611

(a.u.) 1.585 1.5809 1.591 1.6123

Ea -0.723749 -0.724048 -0.741128 -0.812941

a Total energy + 151. hartree

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Table 2: Calculated and observed rotational constants (cm1 ) of ketenyl radical

Method ROHF-CCSD(T) UHF-CCSD(T) UHF-CCSD(T) experiment[56]

bais cc-pVTZ cc-pVTZ cc-pVQZ

HCCO

Ae 35.57 34.99 34.19

Be 0.3636 0.3640 0.3650

Ce 0.3600 0.3602 0.3611

A0 42.24 41.32 40.55 41.5(1.5)

B0 0.3623 0.3627 0.3638 0.3635

C0 0.3583 0.3587 0.3597 0.3591

DCCO

Ae 22.25 21.85 21.28

Be 0.3309 0.3313 0.3323

Ce 0.3261 0.3263 0.3272

A0 25.50 24.89 24.32 21.75(12)

B0 0.3297 0.3303 0.3312 0.3311

C0 0.3246 0.3249 0.3258 0.3254

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Table 3: Vibrational frequencies (cm

1

) and zero point energy (kJ mol

1

) of ketenyl radical

Methods ROHF-CCSD(T) UHF-CCSD(T) UHF-CCSD(T) exp

Basis cc-pVTZ cc-pVTZ cc-pVQZ

Mode a) b) a) b) a) b)

CH stretch 3372 3239 3371 3233 3352

CCO assym. stretch 2079 2038 2099 2058 2097 2023 [66]

CCO sym. stretch 1245 1238 1249 1248 1246CCO bending 563 569 568 577 567

CCH bending 509 472 511 473 505 494 [86]

torsion 503 528 506 530 500

ZPE (kJ mol1) 49.47 49.24 49.66 49.42 49.48

a) harmonic approximation b) fundamentals

Table 4: Vibrational frequencies (cm1 ) and zero point energy (kJ mol1) of ethynyl radical

Methods UHF-CCSD(T) ROHF-CCSD(T) UHF-CCSD(T) ROHF-CCSD(T) exp

Basis cc-pVTZ cc-pVTZ cc-pVQZ cc-pVQZMode a) b) a) b) a) b) a) b) b)

CH stretch 3485 3351 3479 3332 3458 3332 3452 3319 3298.85 [87]

CC stretch 2071 1956 2029 1829 2069 1961 2027 1845 1840.57 [88]

CCH bending 436 476 359 361 452 476 381 381 371.60 [89]

ZPE (kJ mol1) 38.44 37.93 37.24 36.18 38.46 37.93 37.33 36.37

a)

harmonic approximationb)

fundamentals

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Table 5: Estimation of the reaction enthalpy (kJ mol1) for the reaction CO + CH HCCO

pVXZ pCVXZ aug-pVXZ best error(TQ) (Q5) (TQ) (TQ) estimate estimate

UHF -204.07 -205.60 -204.76 -204.18 -205.7 0.5

[CCSD] -92.69 -91.49 -92.45 -92.70 -91.5 0.5

[CCSD(T)] -17.38 -17.31 -17.41 -17.42 -17.3 0.2

core corr. -5.83 -5.8 0.5

[CCSDT] -0.15a -0.2 0.1

[CCSDTQ] -1.69b -1.7 0.2

ZPE 19.0 0.5

spin-orbit 0.2 0.1

relat. 1.0 0.1

DBOC -0.2

Total -302.2 1.1

a Difference between the CCSDT and CCSD(T) energy, cc-pVTZ basis, frozen core approximation

b Difference between the CCSDQ and CCSDT energy, cc-pVDZ basis, frozen core approximation

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Table 6: Estimation of the reaction enthalpy (kJ mol1) for the reaction H2CCO HCCO + H


UHF 380.50 380.89 380.62 380.45 380.9 0.5

[CCSD] 91.90 91.21 91.92 91.59 91.0 0.5

[CCSD(T)] 0.38 0.30 0.37 0.32 0.3 0.1

core corr. 1.44 1.5 0.5

[CCSDT] -1.53a -1.6 0.5

[CCSDTQ] -0.71b 0.7 0.1

ZPE -32.0 0.5

spin-orbit 0

relat. -0.2 0.1

DBOC 0.5

Total 438.7 1.1



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Table 7: Estimation of the reaction enthalpy (kJ mol1) for the reaction CCH + O HCCO


UHF -396.46 -396.26 -396.78 -396.95 -396.6 1.0

[CCSD] -226.49 -225.93 -226.09 -226.65 -226.0 0.5

[CCSD(T)] -24.08 -24.08 -24.06 -24.11 -24.1 0.1

core corr. -1.44 -1.5 0.5

[CCSDT] 2.32a 2.5 0.5

[CCSDTQ] -1.75b -1.8 0.2

ZPE 12.6 0.5

spin-orbit 0.8 0.2

relat. 0.9 0.1

DBOC 0.1

Total -633.1 1.4



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Table 8: Estimation of the reaction enthalpy (kJ mol1) for the reaction 2 O + CH + HCC

H2CCO + CO

pVXZ pCVXZ aug-pVXZ best error

(TQ) (Q5) (TQ) (TQ) estimate estimate

UHF -1270.40 -1268.79 -1269.80 -1270.85 -1269.1 1

[CCSD] -525.95 -525.68 -525.23 -526.99 -525.7 1

[CCSD(T)] -54.45 -54.44 -54.47 -54.44 -54.5 0.1

core corr. -6.86 -6.9 0.5

[CCSDT] 5.94a

5.9

0.5[CCSDTQ] -3.12b -3.1 0.2

ZPE 41.6 0.5

spin-orbit 1.8 0.2

relat. 1.7 0.1

DBOC -0.8

Total -1809.1 1.7



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Table 9: Comparsion of the experimental and calculated heat of formations (fH0(298K)/kJ mol1)

for HCCO and CCH

fH0(298K)/kJ mol1 Method Reference

HCCO

177.58.8 Negative Ion Photoelectron Spectroscopy [84]

120.6 Electron Impact Mass Spectrometry [81]

175.53 Fast radical beam photofragment spectrosopy [90]

176.63 Fast radical beam photofragment spectrosopy [86]

203.1 Thermochemistry [82]

177.6 ab initio (BAC-MP4) [79]

177.851.9 ab initio (W1) [78]

171.18.2 ab initio (G3MP2B3) [75]

178.31.5 ab initio this work

CCH

5673 Negative Ion Photoelectron spectroscopy [85]

5682 photoion pair formation [91]

568.80.1 Photodissociation [92]

5686 Photodissociation LIF [93]

5148 Thermochemistry [83]

5624 ab initio (MRCI) [76]

550.526.8 ab initio (BAC-MP4) [77]

566.1 ab initio (G3) [80]

569.01.9 ab initio (W2) [13]

563.58.2 ab initio (G3MP2B3) [75]

567.41.5 ab initio this work

ab initio determination of the heat of formation of ketenyl

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