11institutetext: Grupo de Astrofísica Molecular, Instituto de Física
Fundamental (IFF-CSIC), C/ Serrano 121, 28006 Madrid, Spain. 11email:
<EMAIL_ADDRESS>22institutetext: Univ. Lille, CNRS, UMR 8523 - PhLAM -
Physique des Lasers Atomes et Molécules, 59000 Lille, France 33institutetext:
Department of Applied Chemistry, Science Building II, National Chiao Tung
University, 1001 Ta-Hsueh Rd., Hsinchu 30010, Taiwan 44institutetext: CNRS,
IPAG, Univ. Grenoble Alpes, F-38000 Grenoble, France 55institutetext:
Observatorio Astronómico Nacional (IGN), C/ Alfonso XII, 3, 28014, Madrid,
Spain. 66institutetext: Centro de Desarrollos Tecnológicos, Observatorio de
Yebes (IGN), 19141 Yebes, Guadalajara, Spain.

# Discovery of the acetyl cation, CH3CO+, in space and in the laboratory
††thanks: Based on observations carried out with the Yebes 40m telescope
(projects 19A003, 20A014, and 20D15) and the Institut de Radioastronomie
Millimétrique (IRAM) 30m telescope. The 40m radiotelescope at Yebes
Observatory is operated by the Spanish Geographic Institute (IGN, Ministerio
de Transportes, Movilidad y Agenda Urbana). IRAM is supported by INSU/CNRS
(France), MPG (Germany), and IGN (Spain).

J. Cernicharo 11 C. Cabezas 11 S. Bailleux 22 L. Margulès 22 R. Motiyenko 22
L. Zou 22 Y. Endo 33 C. Bermúdez 11 M. Agúndez 11 N. Marcelino 11 B. Lefloch
44 B. Tercero 5566 and P. de Vicente 55

(Received; accepted)

Using the Yebes 40m and IRAM 30m radiotelescopes, we detected two series of
harmonically related lines in space that can be fitted to a symmetric rotor.
The lines have been seen towards the cold dense cores TMC-1, L483, L1527, and
L1544. High level of theory _ab initio_ calculations indicate that the best
possible candidate is the acetyl cation, CH3CO+, which is the most stable
product resulting from the protonation of ketene. We have produced this
species in the laboratory and observed its rotational transitions $J_{u}$ = 10
up to $J_{u}$ = 27. Hence, we report the discovery of CH3CO+ in space based on
our observations, theoretical calculations, and laboratory experiments. The
derived rotational and distortion constants allow us to predict the spectrum
of CH3CO+ with high accuracy up to 500 GHz. We derive an abundance ratio
$N$(H2CCO)/$N$(CH3CO+)$\sim$44\. The high abundance of the protonated form of
H2CCO is due to the high proton affinity of the neutral species. The other
isomer, H2CCOH+, is found to be 178.9 kJ mol-1 above CH3CO+. The observed
intensity ratio between the $K$=0 and $K$=1 lines, $\sim$2.2, strongly
suggests that the $A$ and $E$ symmetry states have suffered interconversion
processes due to collisions with H and/or H2, or during their formation
through the reaction of H${}_{3}^{+}$ with H2CCO.

###### Key Words.:

Astrochemistry — ISM: molecules — ISM: individual (TMC-1) — line:
identification — molecular data

##  1 Introduction

The cold dark core TMC-1 presents an interesting chemistry. It produces a
significant number of the molecules detected in space, in particular long
neutral carbon-chain radicals and their anions (see e.g. Cernicharo et al.
2020a; Marcelino et al.  2020a, and references therein) as well as
cyanopolyynes (see Cernicharo et al.  2020b and Xue et al. 2020, and
references therein). The presence in this object of O-bearing carbon chains,
such as C2O (Ohishi et al. 1991), C3O (Matthews et al. 1984), HC5O (McGuire et
al. 2017), HC7O (Cordiner et al. 2017), HCCO, and HC3O+ (Cernicharo et al.
2020c), is a surprising result that has not yet been fully accounted for by
chemical models.

The abundance of polyatomic cations in cold interstellar clouds is relatively
low because they react fast with electrons. Interestingly, all polyatomic
cations detected in cold clouds are protonated forms of stable and abundant
molecules. Chemical models and observations suggest a trend in which the
protonated-to-neutral abundance ratio [MH+]/[M] increases with the proton
affinity of M (Agúndez et al. 2015; Cernicharo et al.  2020c, d; Marcelino et
al.  2020a).

It has been suggested that some O-bearing cations are sufficiently long-lived
to be abundant (Petrie et al. 1993). We have recently reported the discovery
of the cation HC3O+ in TMC-1 (Cernicharo et al.  2020c). In this letter, we
report the detection of two series of lines that are harmonically related
towards the cold dark core TMC-1. These lines can be fitted as the $K$=0 and
$K$=1 lines of a symmetric rotor. From the astronomical data and the derived
rotational constants, together with high-level _ab initio_ calculations, we
suggest CH3CO+ as the best possible carrier. We have performed microwave
laboratory experiments that fully support this hypothesis: We detected 79
rotational transitions near the predicted frequencies from the astronomical
constants. Hence, we report the discovery in space and in the laboratory of
CH3CO+ (acetyl cation), which is the most stable isomer resulting from the
protonation of ketene (H2CCO). The presence of CH3CO+ can be expected on the
basis of the high abundance of H2CCO in TMC-1 and its large proton affinity
(825.3 kJ mol-1; Traeger et al.  1982). An anomalous abundance ratio of 2.2 is
found between the $A$ and $E$ symmetry species of CH3CO+. We discuss these
results in the context of state-of-the-art chemical models and in terms of the
interconversion of $E$-CH3CO+ into $A$-CH3CO+ through the formation process of
the molecule or by collisions with H and/or H2.

##  2 Observations

New receivers, built as part of the Nanocosmos
project111https://nanocosmos.iff.csic.es/ and installed at the Yebes 40m radio
telescope, were used for the observations of TMC-1. The Q-band receiver
consists of two high electron mobility transistor (HEMT) cold amplifiers that
cover the 31.0-50.3 GHz band with horizontal and vertical polarizations.
Receiver temperatures vary from 22 K at 32 GHz to 42 K at 50 GHz. The
spectrometers are $2\times 8\times 2.5$ GHz fast Fourier transform
spectrometers (FFTs) with a spectral resolution of 38.1 kHz, providing the
whole coverage of the Q-band in both polarizations. The main beam efficiency
varies from 0.6 at 32 GHz to 0.43 at 50 GHz (Tercero et al. 2020).

The observations that led to the line survey in the Q-band towards TMC-1
($\alpha_{J2000}=4^{\rm h}41^{\rm m}41.9^{\rm s}$ and
$\delta_{J2000}=+25^{\circ}41^{\prime}27.0^{\prime\prime}$) were performed in
several sessions, between November 2019 and February 2020. The observing
procedure was frequency switching with a frequency throw of 10 MHz. The
nominal spectral resolution of 38.1 kHz was used for the final spectra. In
these runs, two different frequency coverages were observed, 31.08-49.52 GHz
and 31.98-50.42 GHz. This permits the user to check that no spurious ghosts
are produced in the down-conversion chain, in which the signal coming from the
receiver is down-converted to 1-19.5 GHz and then split into eight bands with
a coverage of 2.5 GHz, each of which are analysed by the FFTs. Additional data
were taken in October 2020 to improve the line survey at some frequencies and
to further check the consistency of all observed spectral features. These
observations were also performed in frequency switching but with a throw of 8
MHz. The sensitivity varies along the Q-band between 0.5 and 2.5 mK, which is
a considerable improvement compared to previous line surveys in the 31-50 GHz
frequency range (Kaifu et al. 2004).

Figure 1: Observed lines of CH3CO+ towards TMC-1. The abscissa corresponds to
rest frequencies (in MHz) assuming a local standard of rest velocity of 5.83
km s-1 (Cernicharo et al.  2020a, b). Frequencies and intensities for the
observed lines are given in Table 1. The ordinate is the antenna temperature
(in mK). Spectral resolution is 38.1 kHz below 50 GHz and 48.8 kHz above. The
blue labels correspond to the series of lines we assign to the $A$ species of
CH3CO+, while the red ones correspond to those of the $E$ species.

The IRAM 30m data come from a line survey performed towards TMC-1 and B1, and
the observations have been described by Marcelino et al. (2007) and Cernicharo
et al.  (2012). The observations of L1527 and L1544 were obtained as part of
the IRAM 30m Large Program ASAI and were described by Lefloch et al.  (2018).
The intensity scale and antenna temperature ($T_{A}^{*}$) for the two
telescopes used in this work were calibrated using two absorbers at different
temperatures as well as the atmospheric transmission model ATM (Cernicharo
1985; Pardo et al. 2001). Calibration uncertainties were adopted to be 10 %.
All data were analysed using the GILDAS
package222http://www.iram.fr/IRAMFR/GILDAS.

Table 1: Observed line parameters for CH3CO+ in TMC-1.

Ju | $K$ | $\nu_{obs}^{a}$ | $\Delta\nu_{oc}^{b}$ |  T${}_{A}^{*}$c |  $\Delta$vd |  $\int$T${}_{A}^{*}$dv e
---|---|---|---|---|---|---
|  | (MHz) | (kHz) | (mK) |  (km s-1) |  (mK km s-1)
2 | 0 | 36537.765 | -3.5 |  39.0$\pm$0.6 |  0.63$\pm$0.01 |  26.1$\pm$0.6
2 | 1 | 36537.014 | -0.6 |  11.8$\pm$0.6 |  0.60$\pm$0.03 |  7.5$\pm$0.6
4 | 0 | 73074.769 | 2.7 |  71.0$\pm$3.5 |  0.47$\pm$0.03 |  35.7$\pm$2.0
4 | 1 | 73073.252 | -6.6 |  25.0$\pm$3.5 |  0.65$\pm$0.11 |  17.2$\pm$2.0
5 | 0 | 91342.732 | -3.5 |  37.5$\pm$3.0 |  0.46$\pm$0.04 |  18.2$\pm$1.0
5 | 1 | 91340.865 | 14.2 |  11.9$\pm$3.0 |  0.49$\pm$0.11 |  6.3$\pm$1.0
6 | 0 | 109610.225 | 2.1 |  12.8$\pm$2.8 |  0.45$\pm$0.09 |  6.1$\pm$1.0
6 | 1 | 109607.954 | -7.3 |  6.6$\pm$2.8 |  0.60$\pm$0.10 |  4.2$\pm$1.0
333

##  3 Results and discussion

The assignment of the observed features in our line surveys was done using the
CDMS and JPL catalogues (Müller et al. 2005; Pickett 1998) and the MADEX code
(Cernicharo  2012). Most of the weak lines found in our survey of TMC-1 can be
assigned to known species and their isotopologues. Nevertheless, many features
remain unidentified. Frequencies for the unknown lines were derived by
assuming a local standard of rest velocity of 5.83 km s-1, a value that was
derived from the observed transitions of HC5N and its isotopologues in our
line survey (Cernicharo et al.  2020a, b). Our new data towards TMC-1 allowed
us to detect C3N- and C5N- (Cernicharo et al.  2020a), as well as new species
such as the isocyano isomer of HC5N, HC4NC (Cernicharo et al.  2020b), the
cation HC3O+ (Cernicharo et al.  2020c), the cation HC3S+ (Cernicharo et al.
2020d), and the cation HC5NH+ (Marcelino et al.  2020a), in addition to
several tens of already known molecules and their isotopologues.

Within the unidentified features in our surveys in the 3 mm band and the
Q-band, we found two series of four lines with a harmonic relation of 2:4:5:6
(see Fig. 1). Taking into account the line density in TMC-1, the possibility
that the observed pattern is fortuitous is very small. The observed lines are
shown in Fig. 1, and the derived line parameters are given in Table 1. In
fact, the $J$=5-4 line at 91342 MHz has intrigued us since 2017 when we
detected it in TMC-1, L483, L1527, and L1544. We interpreted the $K$=0,1 lines
and the U line at $\sim$91344 (see Fig. 3) as the hyperfine structure of a
$J$=1-0 or $J$=2-1 transition of a molecule containing a nucleus with a spin
of 1. Using the old receivers of the Yebes 40 m telescope, and assuming that
the three lines around 91342 MHz could correspond to $J$=2-1, we searched for
lines at 45671 MHz without success. Only when the new receivers covering the
whole Q-band were available at the telescope, and we detected the doublet at
36537 MHz (see Fig. 1), did we realized that two of the lines around 91342 MHz
correspond to a $J$=5-4 transition in harmonic relation 2:5 with the 36537 MHz
doublet. Moreover, the U line at 91344 MHz is produced by another carrier as
it is detected in B1, while the other lines are not. Once we relaxed the
initial idea that these features were the hyperfine structure of a low-$J$
transition, other features were found in the 3 mm domain ($J$=4-3 and $J$=6-5,
as well as $J$=7-6 in L1527).

The two series of lines can be fitted to two linear rotors with rotational
constants $B$ = 9134.4738 $\pm$ 0.0006 MHz and $B$ = 9134.2860 $\pm$ 0.0020
MHz. The distortion constant is exactly the same for both series, $D$ = 4.00
$\pm$ 0.02 kHz. The observed spectra is reminiscent of the $K$=0 and $K$=1
components of the rotational transitions of a symmetric rotor. In fact, the
eight observed lines in TMC-1 can be fitted with a single rotational constant
and two distortion constants if we assume that the carrier is the same for
both series and that it has a $C_{3v}$ symmetry (i.e. that it is a symmetric
rotor). Using the standard Hamiltonian for this kind of molecular rotor (Gordy
& Cook 1984), we derived the rotational and distortion constants provided in
Table 2.

Table 2: Derived spectroscopic parameters (in MHz) for CH3CO+.

Constant |  Spacea |  Laboratoryb |  Mergedc
---|---|---|---
$B$ | 9134.47424(82) | 9134.47083(27) | 9134.47211(20)
$D_{J}$ |  4.014(12) 10-3 |  3.99198(25) 10-3 |  3.99307(21) 10-3
$D_{JK}$ |  1.8847(53)10-1 |  1.87616(41) 10-1 |  1.87736(46) 10-1
$H_{JK}$ |  |  8.66(33) 10-7 |  9.56(37) 10-7
$H_{KJ}$ |  |  6.58(59) 10-6 |  7.19(74) 10-6
$rms$(kHz)d | 6.9 | 34.3 | 33.2
$J_{min}/J_{max}$ | 1/7 | 10/27 | 1/27
$K_{min}/K_{max}$ | 0/1 | 0/6 | 0/6
$N_{lines}^{e}$ | 10 | 79 | 89
$\nu_{max}$(GHz) | 127.87 | 492.95 | 492.95
444

From the derived rotational constant, 9134 MHz, the molecule should contain at
least three atoms between C, N, and O. We analysed the possible candidates
that could have a rotational constant similar to the observed one. Detailed ab
initio calculations for the possible linear and asymmetric carriers are given
in Appendix B. Concerning symmetric rotors, it is amazing to realize that all
CH3X, with X=CN, NC, and CCH, have rotational constants close to our
rotational and distortion constants. For example, CH3CN has a rotational
constant of 9198.9 MHz (Müller et al. 2009), which is really very close to our
result. The other possible candidates, CH3CNH+ ($B$=8590.5 MHz; Amano et al.
2006) and CH3NCH+ (see, Table 4), are too heavy. Hence, the best symmetric
rotor candidate seems to be a species similar to CH3CN. The acetyl radical,
CH3CO, has been observed in the laboratory by Hirota et al.  (2006), but it is
asymmetric and its lines show a very complex hyperfine structure. However,
CH3CO+ is a symmetric rotor (Mosley et al.,  2014) and the lowest energy
isomer of H3C2O+. Its possible precursor, if formed through protonation, is
ketene, which is one of the most abundant O-bearing species in TMC-1 (see
Cernicharo et al.  2020c).

Table 3: Scaled theoretical values for the spectroscopic parameters of CH3CO+,
CH2COH+, and CH3NCH+ together with the experimental values obtained in this
work (all in MHz).

Parameter |  Exp.aa$a$Observed frequencies (in MHz) adopting a vLSR of 5.83 km s-1 for TMC-1. The uncertainty is 10 kHz for all the lines.Fit to the lines of CH3CO+ observed in TMC-1. In this fit, the $J$=7-6 and $K$=0,1 lines observed in L1527 (with frequencies of 127877.133$\pm$0.025 and 127874.494$\pm$0.050 MHz, respectively) have been included (see Fig. 3 and Appendix A). |  CH3CO+ |  CH2COH+ |  CH3NCH+
---|---|---|---|---
$B$ | 9134.4742(8) | 9129.6 |  9309.5bb$b$Observed minus calculated frequencies (in kHz) resulting from a fit to the observed frequencies. The $J$=7-6 $K$=0,1 lines observed in L1527 have been included in the fit (see text).Fit to the lines of CH3CO+ observed in the laboratory. | 9105.5
$D_{J}\times$10-3 | 4.014(13) | 3.9 | 2.8 | 4.0
$D_{JK}\times$10-3 | 188.47(50) | 184.6 | 378.7 | 171.7
555

###  3.1 Quantum chemical calculations and assignment to CH3CO+

Precise geometries and spectroscopic molecular parameters for the species
mentioned above were computed using high-level _ab initio_ calculations. The
first screening for all plausible candidates (see Appendix B) was done at the
CCSD/cc-pVTZ level of theory (Cížek 1969; Dunning 1989). These results are
shown in Table 4. In a second stage, the most promising candidates, namely
CH3CO+, CH2COH+, and CH3NCH+, were calculated at the CCSD(T)-F12b/aug-cc-pVQZ
levels of theory (Raghavachari et al. 1989; Adler et al. 2007; Knizia et al.
2009). To obtain more precise values for the rotational parameters of these
three species, we calibrated our calculations using experimental to
theoretical scaling ratios for analogue molecular species. This method has
been proved to be suitable to accurately reproduce the molecular geometry of
other identified molecules (Cernicharo et al.  2019; Marcelino et al.  2020a;
Cernicharo et al.  2020c). In our present case, we used CH3CN, CH2CNH, and
CH3NC, which are isoelectronic species of CH3CO+, CH2COH+, and CH3NCH+,
respectively, for this purpose. Table 5 shows the results of these
calculations, which are summarized in Table 3. As can be seen, the employed
level of theory reproduces the rotational parameters for CH3CN, CH2CNH, and
CH3NC very well, with relative discrepancies around 0.08% and 0.04% for $B$ in
the cases of CH3CN and CH3NC, respectively. After correcting the calculated
parameters for CH3CO+, CH2COH+, and CH3NCH+ using the derived scaling ratios
for CH3CN, CH2CNH, and CH3NC, respectively, we obtained a $B$ constant of
9129.62 MHz for CH3CO${}^{+},$ which shows the best agreement with that
derived from the TMC-1 lines. The centrifugal distortion values, obtained in
the same manner but at the MP2/aug-cc-pVQZ level of theory for CH3CO+ and
CH3NCH+, are both compatible with those obtained from the fit of the lines.
The agreement between the experimental constants and those calculated for
CH2COH+ is substantially worse. The calculated dipole moments for CH3CO+ and
CH3NCH+ are 3.5 D and 2.0 D, respectively, while the $\mu_{a}$ and $\mu_{b}$
values for CH2COH+ are 0.8 and 1.7 D, respectively.

In addition to the geometry optimizations, we calculated the energy associated
with the plausible formation of CH3CO+, starting from ketene and three proton
donors; H${}_{3}^{+}$, H3O+, and HCO+. All these calculations were carried out
at the CCSD/cc-pVTZ level of theory. We found a total energy change in the
protonation of ketene to form CH3CO+ of $-$421.8, $-$130.9, and $-$244.8 kJ
mol-1 when ketene reacts with H${}_{3}^{+}$, H3O+, and HCO+, respectively.
More details can be found in Appendix C.

Figure 2:  $J$=22$\rightarrow$21, $K$=0–3 transitions obtained by chirped-
pulsed excitation. The record corresponds to the average of 67 million spectra
acquired in $\sim$20 min.

###  3.2 Laboratory detection of CH3CO+

We conducted an experiment to detect the CH3CO+ cation in the laboratory using
rotational spectroscopy below 500 GHz. The experimental setup was similar to
the one used to detect NS+ (Cernicharo et al.  2018). The cation was produced
in a liquid-nitrogen-cooled Pyrex absorption cell by glow-discharging a
mixture of CH4, CO (1:1), and Ar. A solenoid coil wound on the cell can
generate an axial magnetic field (up to 300 G) to magnetically extend the
negative glow, the region known to produce the highest concentrations of
cations (compared to the positive column discharge; De Lucia et al.  1983). We
also tried acetone and acetaldehyde as precursors (Mosley et al.,  2014), but
without success.

To optimize the experimental setup, we first observed the $J$=2$\leftarrow$1
transition of HCO+ at 178375.056 MHz, which was produced in the same gas
mixture. We then searched for the $J$=10$\leftarrow$9, $K$=0-2 series of lines
of CH3CO+ between 182.658 and 182.675 GHz based on the rotational constants
derived from the lines observed in TMC-1. Weak spectra were observed within
500 kHz. The best experimental conditions were found to be P(CH4)=P(CO)=1.5
mTorr, P(Ar)=5.5 mTorr (gas mixture cooled using liquid nitrogen but pressures
measured at room temperature), an electric discharge of 3.5 kV/10 mA, and an
axial magnetic field of 200 G. These lines disappeared when one of the
precursors was suppressed, or when the axial magnetic field was cut off. The
latter phenomenon confirmed almost unambiguously that they were due to a
cation. Subsequent measurements of higher-$J$ transitions fully support the
astrophysical assignment of the observed lines to CH3CO+.

In total, 79 lines were observed in the laboratory with quantum numbers in the
ranges $J$=10-27 and $K\leq$6 (see Table LABEL:freq_labo). Transitions
occurring below 330 GHz were measured by standard frequency modulation
absorption spectroscopy, resulting in second-derivative lineshapes. These
lines ($K\leq$3) were found unshifted from the first prediction. Those from
400 to 500 GHz were measured by emission spectroscopy (Zou et al.  2020),
giving Voigt-profile lineshapes. Compared to the prediction, some deviations
were observed up to 1 MHz for $K$=6; these measurements led us to determine
the $H_{JK}$ and $H_{KJ}$ centrifugal distortion terms. For maximum
sensitivity, these lines were measured using the single frequency excitation
method with 5-20 million acquisitions (which took 1 to 5 min.). Additionally,
a 120 MHz wide chirped excitation spectrum, measured with 67 million
acquisitions, is given in Fig. 2 for illustration and comparison purposes. The
uncertainty of the laboratory frequency measurements are estimated to be 50
kHz. Given the mass of the cation, and that the negative glow is a nearly
electric field-free region, the reported laboratory frequencies are expected
to be unshifted by the Doppler effect. The separate and merged least-squares
analysis of all (astronomical and laboratory) measured transitions are
provided in Table 2. The measured frequencies and the observed minus
calculated values are given in Table LABEL:freq_labo. Frequency predictions
are given in Table 7.

###  3.3 Chemistry of CH3CO+

From the observed line intensities of CH3CO+, we derived a rotational
temperature of $\sim$5 K and a total column density of
(3.2$\pm$0.3)$\times$1011 cm-2 (see Appendix D). The column densities for the
$A$ and $E$ species are (2.2$\pm$0.2)$\times$1011 cm-2 and
(9.7$\pm$0.9)$\times$1010 cm-2, respectively. Adopting the column density for
ketene derived by Cernicharo et al.  (2020c), we obtained a H2CCO/CH3CO+ ratio
of 44. Assuming the H2 column density derived by Cernicharo & Guélin (1987),
the abundance of CH3CO+ is 3.2$\times$10-11.

The chemistry of protonated molecules in cold dense clouds has been discussed
by Agúndez et al. (2015). Chemical model calculations similar to those that
they presented predict that the abundance of protonated ketene is controlled
by the typical routes operating for protonated molecules. That is, CH3CO+ is
mostly formed by proton transfer to H2CCO from HCO+, H3+, and H3O+, while it
is destroyed through dissociative recombination with electrons. The radiative
association between CH${}_{3}^{+}$ and CO is also an important route to
CH3CO+. The abundance ratio H2CCO/CH3CO+ predicted by the model is in the
range 250-450 and depends on whether the UMIST RATE12 (McElroy et al. 2013) or
KIDA kida.uva.2014 (Wakelam et al. 2015) chemical networks are used. As occurs
for most protonated molecules observed in cold dense clouds, the abundance of
the protonated form with respect to the neutral is underestimated by the
chemical model. In this case, there is a factor of 5-10 difference between the
model and observations. Incorrect estimates for the rate constants of the
dominant reactions of the formation and destruction of CH3CO+ may be behind
this disagreement. Alternatively, the chemical network may miss some important
formation route to CH3CO+, although it is difficult to identify reactions
producing this ion from abundant reagents. For example, plausible reactions of
CH${}_{n}^{+}$ ions with CO, H2CO, or CH3OH tend to form products other than
CH3CO+ (Adams & Smith 1978). In this context, it is worth noting that not all
species resulting from the protonation of abundant molecules in TMC-1 are
detected. For example, CH3CNH+ is not detected in TMC-1 despite the CH3CN
proton affinity of 787.4$\pm$5.9 kJ mol-1 (Williams et al.  2001). The
3$\sigma$ upper limit to the column density of CH3CNH+ is $2.5\times 10^{11}$
cm-2. The column density of CH3CN is $(3.2\pm 0.2)\times 10^{12}$ cm-2 (see
Appendix A); hence, the abundance ratio between the neutral and its protonated
form is $\geq$13\. The low dipole moment of CH3CNH+ compared to that of CH3CN
(1.01 D versus 3.93 D) limits the chances of detecting this species.

###  3.4 $A$-CH3CO+/$E$-CH3CO+ abundance ratio

The column densities derived for the $A$ and $E$ species of CH3CO+ are not
identical, as would be expected for a symmetric top. The $A$/$E$ abundance
ratio for this molecule is 2.27. However, all symmetric molecules of CH3X
detected in TMC-1 have an abundance ratio between their $A$ and $E$ species
that is close to unity (see Appendix D and Fig. 6). In a symmetric top, the
two symmetry states $A$ and $E$ are not connected radiatively nor through
inelastic collisions with H2. Unlike the rest of the CH3X molecules detected
in TMC-1, CH3CO+ is a cation, and its reactive collisions with H2 or H could
produce a proton interchange if there is no barrier to the reaction. The
lowest energy level of the $E$ symmetry state is the $J$=1, $K$=1, which is
7.8 K above the ground $J$=0, $K$=0 level of the $A$ state. Hence, the
reaction of interchange of a proton

$E$-CH3CO+ \+ H2/H $\rightarrow$ $A$-CH3CO+ \+ H2/H + 7.8 K

is exothermic, although it is unknown if there is a barrier; this is something
that has to be established via detailed theoretical calculations. At thermal
equilibrium, and for a kinetic temperature of 10 K, the $A$/$E$ abundance
ratio could be $e^{0.78}$=2.18, which is very close to the observed value of
2.27. For neutral molecules with two or more symmetric hydrogens, the proton
interchange could be mainly produced through collisions with H+, H3+, HCO+,
and H3O+, which are much less abundant than H2 and H. In Appendix D, we
discuss the $A/E$ abundance ratio of all neutral symmetric rotors that have
been detected so far in TMC-1, including CH3NC, which has previously only been
observed in two cold dense clouds: L1544 (Jiménez-Serra et al. 2016) and L483
(Agúndez et al. 2019). For all these species, the $A$/$E$ abundance ratio is
close to unity.

Alternatively, we could also consider the possibility that the collisional
rates of the acetyl cation with H2 or He are higher for the $A$ species than
for the $E$ species. As the acetyl cation is isoelectronic to CH3CN, we could
use the collisional rates of the latter species (Khalifa et al.  2020) to
estimate possible differences in the excitation temperature of the $K$=0 and
$K$=1 lines. We explored a density range of $(4-10)\times 10^{4}$ cm-3 and a
kinetic temperature range of 5-10 K. No significant differences were found in
the predicted brightness temperature between these lines. Of course, if the
effect is due to inelastic collisions, then methyl cyanide (CH3CN) would also
show a similar behaviour. Nevertheless, although both species are
isoelectronic, the fact that CH3CO+ is positively charged could result in very
different collisional rates with H2 compared to CH3CN.

We could also consider that the $A/E$ abundance ratio is affected by the
formation process of the molecule. As shown in Sect. 3.1, the reaction of
ketene with H3+ is the most favourable for protonation from the
thermodynamical point of view. Both species, ketene and H3+, could also have
their ortho/para ratio affected by the low temperature of dense dark clouds,
which will introduce a non-trivial spin statistic into the formation process
of CH3CO+. Additional calculations are needed to evaluate the role of
collisional excitation and of spin interchange in order to understand the
anomalous behaviour exhibited by the $A$ and $E$ symmetry species of CH3CO+.

###### Acknowledgements.

The Spanish authors thank Ministerio de Ciencia e Innovación for funding
support through project AYA2016-75066-C2-1-P, PID2019-106235GB-I00 and
PID2019-107115GB-C21 / AEI / 10.13039/501100011033. We also thank ERC for
funding through grant ERC-2013-Syg-610256-NANOCOSMOS. MA and CB thanks
Ministerio de Ciencia e Innovación for grants RyC-2014-16277 and
FJCI-2016-27983, respectively. Y. Endo thanks Ministry of Science and
Technology of Taiwan through grant MOST108-2113-M-009-25. We would like to
thank Evelyne Roueff and Octavio Roncero for useful comments and suggestions.

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##  Appendix A CH3CO+ in other sources

The acetyl cation, CH3CO+, has also been detected towards L483, L1544, and
L1527 (see Fig. 3). However, it is not observed towards Sgr B2 (PRIMOS 666
Access to the entire PRIMOS data set, specifics on the observing strategy, and
overall frequency coverage information is available at http://www.cv.nrao.edu/
aremijan/PRIMOS/ line survey; Neill et al.  2012), towards Orion-KL (Tercero
et al.  2010, 2011), or in our line survey of B1 (Marcelino et al. 2007, 2009,
2010; Cernicharo  2012). In the PRIMOS data on SgrB2, a very tentative
detection of the $J$=1-0 $K$=0 line could be claimed at a velocity of 80 km
s-1. However, only an upper limit can be obtained for the $J$=2-1 transition
as this line is heavily blended with a strong line of acetone. It seems,
hence, that CH3CO+ is typical of cold interstellar clouds.

Figure 3: Observations of the $J$=5-4 transition of CH3CO+ towards L483,
L1544, L1527, and B1 (top panels); the bottom panel shows the $J$=7-6 line
towards L1527. The abscissa corresponds to the rest frequency (in MHz) and the
ordinate is the antenna temperature (in mK). The spectral resolution is 48.8
kHz for all sources except L1527, for which it is 198 kHz. The vertical dashed
blue lines indicate the position of the $K=0$ and $K=1$ lines (detected in all
sources except B1), and the cyan line corresponds to the U feature at 91344
MHz (detected in all sources except L1527). The rest velocities of L1527 and
L1544 were taken as vLSR= 5.9 km/s and 7.2 km/s, respectively, based on Sakai
et al.  (2009) and Vastel et al.  (2015), respectively.

##  Appendix B Potential carriers of the series of lines

All known diatomic species in cold dark clouds have overly large rotational
constants compared with those derived from the lines in TMC-1. For example, a
molecule containing one S (CS, NS, SO) will have a rotational constant that is
too high by more than 12 GHz. Adding one or two H atoms to these combinations
of sulphur produces radicals (with overly high rotational constants, such as
HCS) or asymmetric rotors such as H2CS, which is too heavy (Müller et al.
2019). A molecule with two S atoms is, of course, too heavy (for example,
$B$(S2)=8831 MHz; Pickett 1979), and we do not expect to have Si- or P-bearing
polyatomic species in this cloud. The first step in finding candidates is to
exclude the possibility of having a slightly asymmetric species. In that case,
we could expect to have lines corresponding to $K$=$\pm$1 at roughly
$\pm$($B$-$C$) from the $K$=0 lines. We searched in the Q-band survey
($J$=2-1) for such a pattern. No lines up to one-fourth of the intensity of
the $K$=0 line are observed. Moreover, taking into account that there is no
evidence for a radical as a possible carrier, the species resulting from the
addition of one hydrogen to the closed-shell asymmetric species HNCO, HCOOH,
and H2CCC have to be excluded. However, their protonated species are also, at
least in principle, closed-shell species. Hence, possible candidates are
H2CCCH+, CH3CCH2+, HCNOH+, HNCOH+, HCOOH2+, and CH3OO+, all of which, with the
exception of the last one, are protonated forms of known neutral and abundant
species in TMC-1. Nevertheless, the resulting molecular structures will be
highly asymmetric for most of them, or they are too light or too heavy, as are
the cases for H2CCCH+ and CH3CCH2+, respectively. HNCOH+ is a linear species
characterized in the laboratory with a rotational constant of 9955 MHz
(Latanzi et al.  2012) and is not detected in our data. Other exotic species,
such as NH2CHOH+, CH2ONH2+, and CH3NOH+, which could result from the
protonation of interesting molecules (NH2CHO for example), are discarded for
their molecular asymmetry and because the neutral species have not been
observed in TMC-1. Ab initio calculations have been performed for the most
promising candidates (see Table 4), and their isomers and the results are
discussed in Sect. 3.1.

Table 4: Rotational constants and electric dipole moments of potential
candidates.

Species(a)(a)footnotemark: $(a)$ |  $\Delta E$/kJ/mol (b)(b)footnotemark: $(b)$ |  $A$, $B$, $C$/MHz |  $D_{J}$, $D_{JK}$/kHz |  $\mu_{a}$, $\mu_{b}$, $\mu_{c}$/D
---|---|---|---|---
|  | 154355.3 | 3.9 | 2.5
0.0 | 9107.2 | 178.7 | 0.0
H3CCO+ |  | 9107.2 |  | 0.0
|  | 201325.3 | 2.7 | 1.6
178.0 | 9411.2 | 341.6 | 0.1
H2COH+ |  | 9222.3 |  | 0.0
|  | 155571.2 | 3.8 | 1.9
0.0 | 9090.7 | 160.6 | 0.0
H3CNCH+ |  | 9090.7 |  | 0.0
|  | 285625.5 | 2.6 | 0.5
0.0 | 9673.5 | 457.3 | 0.0
H2CCCH+ |  | 9356.6 |  | 0.0
|  | 280905.8 | 3.5 | 5.0
0.0 | 10338.2 | 492.0 | 0.0
H2CCN+ |  | 9971.2 |  | 0.0
|  | 277331.4 | 4.00 | 3.7
5.9 | 11582.1 | 685.4 | 0.0
H2CNC+ |  | 11117.8 |  | 0.0
|  | 595150.6 | 2.7 | 1.5
102.5 | 10359.3 | 1285.8 | 1.9
HNCCH+ |  | 10182.1 |  | 0.0
|  | 328396.0 | 3.6 | 4.6
176.4 | 10180.7 | 593.3 | 0.0
H2NCC+ |  | 9874.5 |  | 0.0
|  |  |  |
196.2 | 11120.9 | 2.9 | 0.0
HCNCH+ |  |  |  |
|  | 324210.9 | 2.9 | 3.8
0.0 | 10295.5 | 380.4 | 0.0
H2NCO+ |  | 9978.6 |  | 0.0
|  | 723374.4 | 2.8 | 1.3
70.4 | 10034.0 | 1255.3 | 1.7
HNCOH+ |  | 9896.7 |  | 0.0
|  | 625942.1 | 3.8 | 2.4
285.4 | 10400.0 | 1859.1 | 1.6
HCNOH+ |  | 10230.0 |  | 0.0
|  | 268002.3 | 3.6 | 2.9
333.8 | 11140.1 | 461.1 | 0.0
H2CNO+ |  | 10695.5 |  | 0.0
|  | 259994.7 | 4.6 | 2.3
613.2 | 11321.2 | 484.7 | 0.0
H2CON+ |  | 10848.8 |  | 0.0
777 .

Table 5: Scaled theoretical values for the spectroscopic parameters of CH3CO+,
CH2COH+, and CH3NCH+ (all in MHz).

| CH3CN | CH3CO+
---|---|---
Parameter | Calc.aa$a$This work.Calculations at the CCSD/cc-pVTZ level of theory. | Exp.bb$b$($B$+$C$)/2The energy taken as reference is the lowest energy species within the same isomer family | Calc.aa$a$Rotational constants calculated at the CCSD(T)-F12b/aug-cc-pVQZ level of theory, and centrifugal distortion constants calculated at the MP2/aug-cc-pVQZ level of theory. | Scaledcc$c$Antenna temperature (in mK).Fit to the the lines of CH3CO+ observed in space and in the laboratory. | Exp.dd$d$Linewidth at half intensity (in km s-1).The standard deviation of the fit (in kHz).
($A$-$B$)$\times 10$-3 | 150.4 | 148.900074(65) | 145.0 | 143.5 | -
$B$ | 9191.5 | 9198.899134(11) | 9122.3 | 9129.6 | 9134.4742(8)
$D_{J}\times$103 | 3.6 | 3.807528(9) | 3.7 | 3.9 | 4.014(13)
$D_{JK}\times$103 | 174.0 | 177.40796(28) | 181.0 | 184.6 | 188.47(50)
| CH2CNH | CH2COH+
Parameter | Calc.aa$a$Rotational constants calculated at the CCSD(T)-F12b/aug-cc-pVQZ level of theory, and centrifugal distortion constants calculated at the MP2/aug-cc-pVQZ level of theory. | Exp.ee$e$Integrated line intensity (in mK km s-1).Number of lines included in the fit. | Calc.aa$a$Rotational constants calculated at the CCSD(T)-F12b/aug-cc-pVQZ level of theory, and centrifugal distortion constants calculated at the MP2/aug-cc-pVQZ level of theory. | Scaledff$f$Scaled by the ratio Exp/Calc. of the corresponding parameter for CH2CNH species | Exp.dd$d$This work.
$A$ | 198393.1 | 201443.685(75) | 198278.8 | 201327.7 | -
$B$ | 9666.3 | 9663.168(2) | 9411.8 | 9408.7 | -
$C$ | 9488.0 | 9470.127(2) | 9227.6 | 9210.2 | 9134.4742(8)
$D_{J}\times$103 | 2.9 | 2.980(2) | 2.7 | 2.8 | 4.014(13)
$D_{JK}\times$103 | 244.4 | 232.8(3) | 397.7 | 378.7 | 188.47(50)
| CH3NC | CH3NCH+
Parameter | Calc.aa$a$Rotational constants calculated at the CCSD(T)-F12b/aug-cc-pVQZ level of theory, and centrifugal distortion constants calculated at the MP2/aug-cc-pVQZ level of theory. | Exp.gg$g$Plíva et al. (1995). | Calc.aa$a$Rotational constants calculated at the CCSD(T)-F12b/aug-cc-pVQZ level of theory, and centrifugal distortion constants calculated at the MP2/aug-cc-pVQZ level of theory. | Scaledhh$h$Scaled by the ratio Exp/Calc. of the corresponding parameter for CH3NC species | Exp.dd$d$This work.
($A$-$B$)$\times 10$-3 | 169.0 | 167.36100(23) | 164.5 | 162.9 | -
$B$ | 10049.0 | 10052.88568(25) | 9102.0 | 9105.5 | 9134.4742(8)
$D_{J}\times$103 | 4.4 | 4.69212(18) | 3.8 | 4.0 | 4.014(13)
$D_{JK}\times$103 | 222.9 | 227.5116(83) | 168.2 | 171.7 | 188.47(50)
888 $b$$b$footnotetext: Müller et al. (2009). $c$$c$footnotetext: Scaled by
the ratio Exp/Calc. of the corresponding parameter for CH3CN species.
$e$$e$footnotetext: Rodler et al. (1984). . .

##  Appendix C Additional quantum chemical calculations for CH3CO+

The potential energy surface (PES) for the protonation of ketene has been
explored at the CCSD/cc-pVTZ level of theory. In the calculations, we
considered three possible proton donors: H${}_{3}^{+}$, H3O+, and HCO+, as
well as the formation of the two isomers of protonated ketene, CH3CO+ and
CH2COH+. Figure 4 depicts the PES along the reaction coordinate for the
protonation of ketene and the relative energies for all the stationary points
when ketene reacts with H${}_{3}^{+}$, H3O+, or HCO+. For each reaction, the
two reactants, ketene and the proton donor, that separated from each other
were assumed to be the energy zero. The protonation of ketene in the CH2 in
the three cases is exothermic, and it proceeds without any transition state
(TS) to form CH3CO+. This formation is more favourable in the case of
H${}_{3}^{+}$. On the other hand, the formation of CH2COH+ is exothermic in
the cases of H${}_{3}^{+}$ and HCO+, but endothermic in the case of H3O+. The
less stable isomer, CH2COH+, can interconvert through a hydrogen migration to
CH3CO+, which has a TS barrier height of 210.1 kJ/mol. As shown in Figure 4,
the TS for this interconversion lies over the energy of the reactants in the
protonation of ketene with H3O+ and HCO+. In contrast, this TS lies below the
energy of the reactants when ketene reacts with H${}_{3}^{+}$.

Figure 4:  Energy diagram for the protonation of ketene. Total energies
relative to those of the separated reactants, ketene and the proton donor X,
are given in the enclosed table in kJ mol-1. C* is the TS energy for the
interconversion between CH2COH+ and CH3CO+ isomers. Y** is the energy
difference between the reactants and the interconversion TS; a negative value
indicates that the TS is submerged below the reactant energy, and a positive
value implies that the TS lies above the reactant energy.

##  Appendix D CH3X species in TMC-1

As noted above, the intensity of the $J$=2-1 $K$=1 line in TMC-1 is well below
the expected value if the rotational temperature for the $A$ and $E$ species
is the same. In order to check this point, we show in Fig. 5 the rotational
diagrams for the $A$ and $E$ species of CH3CO+ using the observed line
parameters given in Table 1. The observed intensities have been corrected for
beam dilution and the beam efficiencies of the Yebes 40m and IRAM 30m
telescopes. We assumed a uniform source of radius 40′′ (Fossé et al. 2001).
The derived rotational temperatures, T${}_{rot}(A)$=4.4$\pm$0.4 K and
T${}_{rot}(E)$=5.0$\pm$0.5 K, are consistent with a common excitation through
collisions with H2. The derived column densities are
N($A$-CH3CO+)=(2.2$\pm$0.2)$\times$1011 cm-2 and
N($E$-CH3CO+)=(9.7$\pm$0.9)$\times$1010 cm-2. Hence, as discussed in Sect.
3.4, the $A/E$ abundance ratio for CH3CO+ has been modified through collisions
with H+, H3+, HCO+, and H3O+. This is a similar effect to that found in cold
molecular clouds for molecules having ortho and para symmetry species.

In order to check this peculiar result, we analysed all symmetric rotors
having transitions within our line survey: CH3CCH, CH3C4H, CH3CN, and CH3NC.
The cation CH3CNH+ has not been detected in TMC-1 (see Sect. 3.3). The
symmetric top CH3C3N is discussed in Marcelino et al.  (2020b). Figure 6 shows
the $J$=2-1 transition for CH3CN, CH3CCH, CH3NC, and CH3CO+ (for this species,
see also Fig. 1). The $K$=0 and $K$=1 lines of CH3CN exhibit the typical
hyperfine structure introduced by the quadruple moment of the N nucleus. For
all these additional molecules, we assumed a rotational temperature of 10 K
and a source radius of 40′′ (Fossé et al. 2001), and we produced a synthetic
spectrum that is compared to the observations. We found that the $A/E$
abundance ratio is $\simeq$1 for all species but CH3CO+. Adopting a lower
rotational temperature has little effect on the derived $A/E$ abundance ratio
for these symmetric rotors.

Figure 5:  Rotational diagrams for the $A$ (black line) and $E$ (red line)
symmetry species of CH3CO+ in TMC-1.  Figure 6:  Observed lines in the
transition $J$=2-1 $K$=0,1 of different symmetric rotors in TMC-1. The colour
lines represent the expected line profiles for the $A$ species (red) and $E$
species (blue). The abundance ratio between them in the model is indicated in
each panel.

##  Appendix E Observed and calculated frequencies of CH3CO+

The frequencies observed in space and in the laboratory were merged to obtain
the recommended rotational and distortion constants. A total of 89 rotational
transitions, ten in space (see Table 1) and 79 in the laboratory (see Table
LABEL:freq_labo), were fitted to the standard Hamiltonian of a symmetric rotor
(Gordy & Cook 1984). For the lines observed in TMC-1 and other dark clouds,
only $B$, $D_{J}$, and $D_{JK}$ can be obtained as only rotational transitions
with $K$=0 and 1 have been observed. The results are given in Table 2. For the
79 lines observed in the laboratory, the constants $H_{JK}$ and HKJ were
included in the fit, and the results are given in Table 2. Finally, the merged
fit to the astronomical and laboratory lines produces the recommended set of
rotational constants given in the last column of Table 2. The observed and
calculated frequencies, together with the observed minus calculated values for
the merged fit, are given in Table LABEL:freq_labo.

We used the rotational and distortion constants that resulted from the merged
fit to the astronomical and laboratory lines (see Table 2) to produce
frequency predictions, frequency uncertainties, line strengths, upper energy
levels, and Einstein coefficients for all transitions involving levels with
energies below 2000 K. They are given in Table 7. The whole table is
electronically available at the CDS. It should be noted that this table
contains the transitions for the $A$ and $E$ species, and that the $E$ lowest
energy level, $J_{K}$=$1_{1}$, is 7.8 K above the $0_{0}$ level of the $A$
species.

Table 6: Observed and calculated frequencies (in MHz) for CH3CO+.  Ju | K | Freq. Obser. | (Unc) | Freq. Calc. | (Unc) | Obs-Calc
---|---|---|---|---|---|---
2 | 0 | 36537.765 | 0.010 | 36537.761 | 0.001 | 0.004
2 | 1 | 36537.014 | 0.010 | 36537.010 | 0.001 | 0.004
4 | 0 | 73074.769 | 0.010 | 73074.755 | 0.002 | 0.014
4 | 1 | 73073.252 | 0.010 | 73073.253 | 0.002 | -0.001
5 | 0 | 91342.732 | 0.010 | 91342.725 | 0.003 | 0.007
5 | 1 | 91340.865 | 0.010 | 91340.848 | 0.003 | 0.017
6 | 0 | 109610.225 | 0.010 | 109610.215 | 0.003 | 0.010
6 | 1 | 109607.954 | 0.010 | 109607.963 | 0.003 | -0.009
7 | 0 | 127877.133 | 0.025 | 127877.131 | 0.004 | 0.002
7 | 1 | 127874.494 | 0.050 | 127874.504 | 0.004 | -0.010
10 | 3 | 182639.714 | 0.050 | 182639.724 | 0.011 | -0.010
10 | 2 | 182658.451 | 0.050 | 182658.469 | 0.006 | -0.018
10 | 1 | 182669.687 | 0.050 | 182669.719 | 0.005 | -0.032
10 | 0 | 182673.442 | 0.050 | 182673.470 | 0.005 | -0.028
11 | 3 | 200900.043 | 0.050 | 200900.014 | 0.012 | 0.029
11 | 2 | 200920.617 | 0.050 | 200920.630 | 0.007 | -0.013
11 | 1 | 200933.010 | 0.050 | 200933.002 | 0.006 | 0.008
11 | 0 | 200937.148 | 0.050 | 200937.127 | 0.006 | 0.021
12 | 3 | 219159.236 | 0.050 | 219159.253 | 0.013 | -0.017
12 | 2 | 219181.747 | 0.050 | 219181.737 | 0.008 | 0.010
12 | 1 | 219195.209 | 0.050 | 219195.232 | 0.006 | -0.023
12 | 0 | 219199.712 | 0.050 | 219199.731 | 0.006 | -0.019
13 | 3 | 237417.332 | 0.050 | 237417.345 | 0.014 | -0.013
13 | 2 | 237441.706 | 0.050 | 237441.696 | 0.008 | 0.010
13 | 1 | 237456.320 | 0.050 | 237456.311 | 0.007 | 0.009
13 | 0 | 237461.178 | 0.050 | 237461.184 | 0.007 | -0.006
14 | 3 | 255674.171 | 0.050 | 255674.193 | 0.015 | -0.022
14 | 2 | 255700.388 | 0.050 | 255700.410 | 0.009 | -0.022
14 | 1 | 255716.107 | 0.050 | 255716.145 | 0.007 | -0.038
14 | 0 | 255721.370 | 0.050 | 255721.391 | 0.007 | -0.021
16 | 3 | 292183.778 | 0.050 | 292183.777 | 0.017 | 0.001
16 | 2 | 292213.646 | 0.050 | 292213.722 | 0.010 | -0.075
16 | 1 | 292231.636 | 0.050 | 292231.694 | 0.008 | -0.058
16 | 0 | 292237.659 | 0.050 | 292237.685 | 0.008 | -0.026
17 | 3 | 310436.291 | 0.050 | 310436.322 | 0.019 | -0.031
17 | 2 | 310468.201 | 0.100 | 310468.127 | 0.011 | 0.074
17 | 1 | 310487.210 | 0.050 | 310487.216 | 0.009 | -0.006
17 | 0 | 310493.523 | 0.050 | 310493.580 | 0.009 | -0.057
18 | 3 | 328687.226 | 0.050 | 328687.241 | 0.020 | -0.015
18 | 2 | 328720.866 | 0.050 | 328720.905 | 0.012 | -0.039
18 | 1 | 328741.056 | 0.050 | 328741.110 | 0.010 | -0.054
18 | 0 | 328747.827 | 0.050 | 328747.846 | 0.010 | -0.019
21 | 6 | 383217.758 | 0.050 | 383217.721 | 0.096 | 0.037
21 | 5 | 383303.931 | 0.050 | 383303.862 | 0.064 | 0.069
21 | 4 | 383374.395 | 0.050 | 383374.396 | 0.041 | -0.001
21 | 3 | 383429.306 | 0.050 | 383429.289 | 0.025 | 0.017
21 | 2 | 383468.517 | 0.050 | 383468.517 | 0.015 | 0.000
21 | 1 | 383492.044 | 0.050 | 383492.060 | 0.012 | -0.016
21 | 0 | 383499.892 | 0.050 | 383499.910 | 0.012 | -0.018
22 | 6 | 401451.192 | 0.050 | 401451.205 | 0.103 | -0.013
22 | 5 | 401541.411 | 0.050 | 401541.408 | 0.069 | 0.003
22 | 4 | 401615.264 | 0.050 | 401615.268 | 0.044 | -0.004
22 | 3 | 401672.742 | 0.050 | 401672.750 | 0.027 | -0.008
22 | 2 | 401713.849 | 0.050 | 401713.827 | 0.017 | 0.022
22 | 1 | 401738.482 | 0.050 | 401738.481 | 0.014 | 0.001
22 | 0 | 401746.707 | 0.050 | 401746.700 | 0.014 | 0.007
23 | 6 | 419682.601 | 0.050 | 419682.598 | 0.111 | 0.003
23 | 5 | 419776.829 | 0.050 | 419776.858 | 0.074 | -0.029
23 | 4 | 419854.065 | 0.050 | 419854.039 | 0.048 | 0.026
23 | 3 | 419914.100 | 0.050 | 419914.106 | 0.029 | -0.006
23 | 2 | 419957.037 | 0.050 | 419957.031 | 0.018 | 0.006
23 | 1 | 419982.794 | 0.050 | 419982.794 | 0.015 | 0.000
23 | 0 | 419991.387 | 0.050 | 419991.383 | 0.015 | 0.004
24 | 6 | 437911.779 | 0.050 | 437911.807 | 0.119 | -0.026
24 | 5 | 438010.092 | 0.050 | 438010.117 | 0.080 | -0.025
24 | 4 | 438090.613 | 0.050 | 438090.615 | 0.052 | -0.002
24 | 3 | 438153.261 | 0.050 | 438153.263 | 0.032 | -0.002
24 | 2 | 438198.039 | 0.050 | 438198.033 | 0.020 | 0.006
24 | 1 | 438224.913 | 0.050 | 438224.903 | 0.016 | 0.010
24 | 0 | 438233.877 | 0.050 | 438233.861 | 0.016 | 0.016
25 | 6 | 456138.764 | 0.150 | 456138.735 | 0.129 | 0.029
25 | 5 | 456240.963 | 0.150 | 456241.090 | 0.087 | -0.127
25 | 4 | 456324.889 | 0.050 | 456324.900 | 0.056 | -0.011
25 | 3 | 456390.167 | 0.050 | 456390.126 | 0.034 | 0.041
25 | 2 | 456436.758 | 0.050 | 456436.737 | 0.022 | 0.021
25 | 1 | 456464.703 | 0.050 | 456464.712 | 0.018 | -0.009
25 | 0 | 456474.048 | 0.050 | 456474.039 | 0.018 | 0.009
26 | 5 | 474469.660 | 0.050 | 474469.681 | 0.094 | -0.021
26 | 4 | 474556.835 | 0.050 | 474556.798 | 0.061 | 0.037
26 | 3 | 474624.604 | 0.050 | 474624.597 | 0.037 | 0.007
26 | 2 | 474673.034 | 0.050 | 474673.048 | 0.024 | -0.014
26 | 1 | 474702.158 | 0.050 | 474702.127 | 0.020 | 0.031
26 | 0 | 474711.811 | 0.050 | 474711.821 | 0.020 | -0.010
27 | 5 | 492695.931 | 0.150 | 492695.796 | 0.102 | 0.135
27 | 4 | 492786.129 | 0.150 | 492786.214 | 0.066 | -0.085
27 | 3 | 492856.584 | 0.050 | 492856.582 | 0.041 | 0.002
27 | 2 | 492906.862 | 0.050 | 492906.869 | 0.026 | -0.007
27 | 1 | 492937.060 | 0.050 | 492937.050 | 0.022 | 0.010
27 | 0 | 492947.117 | 0.050 | 492947.112 | 0.022 | 0.005
Table 6: continued. Table 7: Frequency predictions for CH3CO+ ∗.

$J_{u}$a |  $K_{u}$a |  $J_{l}$a |  $K_{l}$a |  $\nu$(MHz)b | Unc(MHz)c | Eup(K)d |  $A_{ij}$(s-1)e |  $S_{ij}$f |  $g_{u}$g
---|---|---|---|---|---|---|---|---|---
1 | 0 | 0 | 0 | 18268.92826 | 0.00039 | 0.9 | 2.898$\times$10-07 | 1.0000 | 3
2 | 1 | 1 | 1 | 36537.00979 | 0.00072 | 9.5 | 2.086$\times$10-06 | 1.5000 | 5
2 | 0 | 1 | 0 | 36537.76068 | 0.00079 | 2.6 | 2.782$\times$10-06 | 2.0000 | 5
3 | 2 | 2 | 2 | 54801.89688 | 0.00115 | 32.8 | 5.587$\times$10-06 | 1.6667 | 7
3 | 1 | 2 | 1 | 54805.27517 | 0.00107 | 12.1 | 8.941$\times$10-06 | 2.6667 | 7
3 | 0 | 2 | 0 | 54806.40143 | 0.00117 | 5.3 | 1.006$\times$10-05 | 3.0000 | 7
4 | 3 | 3 | 3 | 73061.24457 | 0.00265 | 70.7 | 1.081$\times$10-05 | 3.5000 | 18
4 | 2 | 3 | 2 | 73068.74904 | 0.00151 | 36.3 | 1.854$\times$10-05 | 3.0000 | 9
4 | 1 | 3 | 1 | 73073.25310 | 0.00141 | 15.7 | 2.318$\times$10-05 | 3.7500 | 9
4 | 0 | 3 | 0 | 73074.75469 | 0.00154 | 8.8 | 2.473$\times$10-05 | 4.0000 | 9
5 | 4 | 4 | 4 | 91312.71293 | 0.00563 | 123.3 | 1.776$\times$10-05 | 1.8000 | 11
5 | 3 | 4 | 3 | 91325.83851 | 0.00326 | 75.1 | 3.159$\times$10-05 | 6.4000 | 22
5 | 2 | 4 | 2 | 91335.21824 | 0.00186 | 40.7 | 4.148$\times$10-05 | 4.2000 | 11
5 | 1 | 4 | 1 | 91340.84780 | 0.00173 | 20.0 | 4.741$\times$10-05 | 4.8000 | 11
5 | 0 | 4 | 0 | 91342.72461 | 0.00189 | 13.2 | 4.939$\times$10-05 | 5.0000 | 11
6 | 5 | 5 | 5 | 109553.96919 | 0.01021 | 190.5 | 2.644$\times$10-05 | 1.8333 | 13
6 | 4 | 5 | 4 | 109574.20539 | 0.00662 | 128.6 | 4.810$\times$10-05 | 3.3333 | 13
6 | 3 | 5 | 3 | 109589.95432 | 0.00384 | 80.4 | 6.496$\times$10-05 | 9.0000 | 26
6 | 2 | 5 | 2 | 109601.20873 | 0.00219 | 46.0 | 7.701$\times$10-05 | 5.3333 | 13
6 | 1 | 5 | 1 | 109607.96344 | 0.00203 | 25.3 | 8.425$\times$10-05 | 5.8333 | 13
6 | 0 | 5 | 0 | 109610.21536 | 0.00223 | 18.4 | 8.666$\times$10-05 | 6.0000 | 13
7 | 6 | 6 | 6 | 127782.68995 | 0.01698 | 272.3 | 3.683$\times$10-05 | 3.7143 | 30
7 | 5 | 6 | 5 | 127811.51930 | 0.01162 | 196.6 | 6.805$\times$10-05 | 3.4286 | 15
7 | 4 | 6 | 4 | 127835.12506 | 0.00755 | 134.7 | 9.361$\times$10-05 | 4.7143 | 15
7 | 3 | 6 | 3 | 127853.49637 | 0.00439 | 86.5 | 1.135$\times$10-04 | 11.4286 | 30
7 | 2 | 6 | 2 | 127866.62477 | 0.00249 | 52.1 | 1.278$\times$10-04 | 6.4286 | 15
7 | 1 | 6 | 1 | 127874.50422 | 0.00232 | 31.4 | 1.363$\times$10-04 | 6.8571 | 15
7 | 0 | 6 | 0 | 127877.13111 | 0.00254 | 24.5 | 1.391$\times$10-04 | 7.0000 | 15
999
$*$$*$footnotetext: The entire table is electronically available at the CDS
via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A
$a$$a$footnotetext: Upper and lower $J_{K}$ quantum numbers.
$b$$b$footnotetext: Predicted frequency (in MHz).
$c$$c$footnotetext: Uncertainty in the predicted frequency (in MHz).
$d$$d$footnotetext: Energy (in K) of the upper energy level of the transition.
$e$$e$footnotetext: Einstein coefficient of the transition (in s-1).
$f$$f$footnotetext: Line strength.
$g$$g$footnotetext: Degeneracy of the upper level. It is 2$J$+1 for all levels
except for those with $K$=3 $\times$ n (n=1,2,…), for which $g_{u}$ is
2$\times$(2$J$+1).