Ab initio determination of the heat of formation of ketenyl
(HCCO) and ethynyl (CCH) radicals1
Péter G. Szalaya,b , Attila Tajtia and John F. Stantonb
a
Department of Theoretical Chemistry, Eötvös Loránd University,
H-1518 Budapest, P.O.Box 32, Hungary
b
Institute for Theoretical Chemistry, Department of Chemistry and Biochemistry,
the University of Texas at Austin, Austin, Texas 78712, USA
September 8, 2004
1 Dedicated
to Rod Bartlett for the occasion of his 60th birthday
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.
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,
C2 H2 + 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: it
is 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 determination 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 (∆f H o ) 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)
1
[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 Kállay [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:
ET ot = Eelectronic + EZP E + EREL + EDBOC + ESO
(1)
where Eelectronic is the non-relativistic electronic energy, EZP E is the zero-point energy, EREL is the
scalar relativistic contribution, EDBOC is the diagonal Born-Oppenheimer correction and ESO is the
2
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
X
∞
EHF
= EHF
+ a exp(−bX),
(2)
and
X
∞
∆Ecorr
= ∆Ecorr
+
a
X3
(3)
X
X
respectively. Here EHF
and ∆Ecorr
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 higher
order 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)/augcc-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)
3
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 RECP’s [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 HCCO’s equilibrium structure. Note that this geometry is very similar to the
ROHF based CCSD(T) results of Schäfer-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 ccpVQZ 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-
4
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 cm−1 , 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 X̃ 2 A00 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 Schäfer 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
5
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 cm−1 and the anharmonic effect lowered
the CCO by about 25 cm−1 .
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 cm−1 .
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 cm−1 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 mol−1 . 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.
6
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 cm−1 between the UHF and ROHF based results.
The anharmonic effect is also very important, it lowers the CC stretching frequency by 180-200
cm−1 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 mol−1 ): 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
H2 CCO → HCCO + H
CCH + O → HCCO
2 O + CH + CCH → CO + H2 CCO
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 calculation
of 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]:
∆f H00 [CH]=593.19±0.36 kJ mol−1
∆f H00 [CO] = -113.81±0.027 kJ mol−1
7
∆f H00 [H2 CCO] = -45.38 ±0.33 kJ mol−1
∆f H00 [H(2 S)] = 216.034±0.0001 kJ mol−1
∆f H00 [O3 P )] = 246.844 ± 0.002 kJ mol−1
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:
-302.2±1.1 kJ mol−1
∆r H00 (CH + CO → HCCO)=
438.7±1.1 kJ mol−1
∆r H00 (H2 CCO → HCCO + H)=
-633.1±1.4 kJ mol−1
∆r H00 (CCH + O → HCCO)=
∆r H00 (2O + CH + CCH → CO + H2 CCO)= -1809.1±1.7 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 ∆f H00 [HCCO]=177.2 kJ mol−1 and ∆f H00 [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, it
is assumed that the error of the reaction enthalpies partly cancel. Therefore the final conservative
8
error estimate is ± 1.5 kJ mol−1 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 temper0
ature correction (∆f H298
-∆f H00 ) 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 mol−1 for CCH based on ref [74]. With these, the
0
0
heats of formation at 298 K are: ∆f H298
[HCCO]=178.3±1.5 kJ mol−1 ∆f H298
[CCH]=567.4±1.5
kJ mol−1 .
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 mol−1 ), we are convinced that the
heats of formation of HCCO and CCH (0K value) presented in this paper are to be preferred over
previous computational results.
Acknowledgments
The authors thank Dr. Mihály Kállay 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)
9
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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15
Table 1: Equilibrium geometry of ketenyl radical
Methods
UHF-CCSD(T)
ROHF-CCSD(T)
UHF-CCSD(T)
UHF-CCSD(T)
cc-pVTZ
cc-pVTZ
aug-cc-pVTZ
cc-pVQZ
rCO (Å)
1.1728
1.1741
1.1708
1.1695
rCC (Å)
1.2972
1.2963
1.3001
1.2973
rCH (Å)
1.0660
1.0659
1.0674
1.0693
Basis
6
CCO (o )
169.4
169.4
169.1
169.4
6
CCH (o )
134.6
135.1
132.8
134.1
A (cm−1 )
34.99
35.57
32.70
34.19
B (cm−1 )
0.3640
0.3636
0.3645
0.3650
C (cm−1 )
0.3602
0.3600
0.3605
0.3611
µ (a.u.)
1.585
1.5809
1.591
1.6123
-0.723749
-0.724048
-0.741128
-0.812941
Ea
a
Total energy + 151. hartree
16
Table 2: Calculated and observed rotational constants (cm−1 ) of ketenyl radical
Method ROHF-CCSD(T)
UHF-CCSD(T)
UHF-CCSD(T)
cc-pVTZ
cc-pVTZ
cc-pVQZ
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
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
bais
experiment[56]
HCCO
DCCO
17
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)
cc-pVTZ
cc-pVTZ
cc-pVQZ
Basis
ω a)
ν b)
ω a)
ν b)
ω a)
CH stretch
3372
3239
3371
3233
3352
CCO assym. stretch
2079
2038
2099
2058
2097
CCO sym. stretch
1245
1238
1249
1248
1246
CCO bending
563
569
568
577
567
CCH bending
509
472
511
473
505
torsion
503
528
506
530
500
49.47
49.24
49.66
49.42
49.48
Mode
ZPE (kJ mol−1 )
a)
harmonic approximation
b)
exp
ν b)
2023 [66]
494 [86]
fundamentals
Table 4: Vibrational frequencies (cm−1 ) and zero point energy (kJ mol−1 ) of ethynyl radical
Methods
Basis
UHF-CCSD(T)
ROHF-CCSD(T) UHF-CCSD(T)
cc-pVTZ
cc-pVTZ
ROHF-CCSD(T)
cc-pVQZ
exp
cc-pVQZ
ω a)
ν b)
ω a)
ν b)
ω a)
ν b)
ω a)
ν b)
ν 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]
38.44
37.93
37.24
36.18
38.46
37.93
37.33
36.37
Mode
ZPE (kJ mol−1 )
a)
harmonic approximation
b)
fundamentals
18
Table 5: Estimation of the reaction enthalpy (kJ mol−1 ) for the reaction CO + CH → HCCO
pVXZ
(TQ)
(Q5)
pCVXZ
aug-pVXZ
best
error
(TQ)
(TQ)
estimate
estimate
UHF
-204.07 -205.60
-204.76
-204.18
-205.7
± 0.5
δ[CCSD]
-92.69
-91.49
-92.45
-92.70
-91.5
± 0.5
δ[CCSD(T)]
-17.38
-17.31
-17.41
-17.42
-17.3
± 0.2
-5.8
± 0.5
core corr.
-5.83
δ[CCSDT]
-0.15a
-0.2
± 0.1
δ[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
19
Table 6: Estimation of the reaction enthalpy (kJ mol−1 ) for the reaction H2 CCO → HCCO + H
pVXZ
(TQ)
(Q5)
pCVXZ
aug-pVXZ
(TQ)
(TQ)
best
error
estimate estimate
UHF
380.50 380.89
380.62
380.45
380.9
± 0.5
δ[CCSD]
91.90
91.21
91.92
91.59
91.0
± 0.5
δ[CCSD(T)]
0.38
0.30
0.37
0.32
0.3
± 0.1
1.5
± 0.5
core corr.
1.44
δ[CCSDT]
-1.53a
-1.6
± 0.5
δ[CCSDTQ]
-0.71b
0.7
± 0.1
-32.0
± 0.5
ZPE
spin-orbit
0
relat.
-0.2
DBOC
0.5
Total
438.7
± 0.1
± 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
20
Table 7: Estimation of the reaction enthalpy (kJ mol−1 ) for the reaction CCH + O → HCCO
pVXZ
(TQ)
(Q5)
pCVXZ
aug-pVXZ
best
error
(TQ)
(TQ)
estimate
estimate
UHF
-396.46 -396.26
-396.78
-396.95
-396.6
± 1.0
δ[CCSD]
-226.49 -225.93
-226.09
-226.65
-226.0
± 0.5
δ[CCSD(T)]
-24.08
-24.06
-24.11
-24.1
± 0.1
-1.5
± 0.5
core corr.
-24.08
-1.44
δ[CCSDT]
2.32a
2.5
± 0.5
δ[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
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
21
Table 8: Estimation of the reaction enthalpy (kJ mol−1 ) for the reaction 2 O + CH + HCC →
H2 CCO + CO
pVXZ
(TQ)
(Q5)
pCVXZ
aug-pVXZ
best
error
(TQ)
(TQ)
estimate
estimate
UHF
-1270.40 -1268.79 -1269.80
-1270.85
-1269.1
±1
δ[CCSD]
-525.95
-525.68
-525.23
-526.99
-525.7
±1
δ[CCSD(T)]
-54.45
-54.44
-54.47
-54.44
-54.5
± 0.1
-6.9
± 0.5
core corr.
-6.86
δ[CCSDT]
5.94a
5.9
± 0.5
δ[CCSDTQ]
-3.12b
-3.1
± 0.2
41.6
± 0.5
spin-orbit
1.8
± 0.2
relat.
1.7
± 0.1
DBOC
-0.8
Total
-1809.1
ZPE
± 1.7
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
22
Table 9: Comparsion of the experimental and calculated heat of formations (∆f H 0 (298K)/kJ mol−1 )
for HCCO and CCH
∆f H 0 (298K)/kJ mol−1
Method
Reference
HCCO
177.5±8.8
Negative Ion Photoelectron Spectroscopy
[84]
120.6
Electron Impact Mass Spectrometry
[81]
175.5±3
Fast radical beam photofragment spectrosopy
[90]
176.6±3
Fast radical beam photofragment spectrosopy
[86]
203.1
Thermochemistry
[82]
177.6
ab initio (BAC-MP4)
[79]
177.85±1.9
ab initio (W1)
[78]
171.1±8.2
ab initio (G3MP2B3)
[75]
178.3±1.5
ab initio
this work
CCH
567±3
Negative Ion Photoelectron spectroscopy
[85]
568±2
photoion pair formation
[91]
568.8±0.1
Photodissociation
[92]
568±6
Photodissociation LIF
[93]
514±8
Thermochemistry
[83]
562±4
ab initio (MRCI)
[76]
550.5±26.8
ab initio (BAC-MP4)
[77]
566.1
ab initio (G3)
[80]
569.0±1.9
ab initio (W2)
[13]
563.5±8.2
ab initio (G3MP2B3)
[75]
567.4±1.5
ab initio
this work
23