11institutetext: Grupo de Astrofísica Molecular, Instituto de Física
Fundamental (IFF-CSIC), C/ Serrano 121, 28006 Madrid, Spain. 11email:
<EMAIL_ADDRESS><EMAIL_ADDRESS>22institutetext: Observatorio
Astronómico Nacional (IGN), C/ Alfonso XII, 3, 28014, Madrid, Spain.
33institutetext: Centro de Desarrollos Tecnológicos, Observatorio de Yebes
(IGN), 19141 Yebes, Guadalajara, Spain.

# Discovery of a new molecular ion, HC7NH+, in TMC-1 ††thanks: Based on
observations carried out with the Yebes 40m telescope (projects 19A003,
20A014, 20D023, and 21A011). The 40m radiotelescope at Yebes Observatory is
operated by the Spanish Geographic Institute (IGN, Ministerio de Transportes,
Movilidad y Agenda Urbana).

C. Cabezas 11 M. Agúndez 11 N. Marcelino 2233 B. Tercero 2233 R. Fuentetaja 11
P. de Vicente and J. Cernicharo 3311

(Received; accepted)

We report the detection of the protonated form of HC7N in TMC-1. The discovery
of the cation HC7NH+ was carried out via the observation of nine harmonically
related lines in the Q-band using the Yebes 40m radiotelescope. The observed
frequencies allowed us to obtain the rotational constants
$B_{0}$=553.938802(160) MHz and $D_{0}$=3.6292(705) Hz. The identification of
HC7NH+ is further supported by accurate ab initio calculations. We derived a
column density of (5.5$\pm$0.7)$\times$1010 cm-2, which constitutes another
piece of evidence for the identification of the carrier. In addition, we
revised the HC7N column density and we derived a new value of
(2.1$\pm$0.2)$\times$1013cm-2. Hence, the abundance ratio HC7N/HC7NH+ is
$\sim$380, while those for HC3N/HC3NH+ and HC5N/HC5NH+ are $\sim$230 and
$\sim$240, respectively. Here, we discuss these results within the framework
of a chemical model for protonated molecules in cold dense clouds.

###### Key Words.:

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

##  1 Introduction

The cold dark cloud TMC-1 shows a rich and complex chemistry that leads to the
formation of a great variety of molecules. Among them, the unsaturated carbon
chains, including cyanopolyynes, acetylenic free radicals, and cumulene
carbenes stand out as the most prevalent type of molecules (Agúndez & Wakelam
2013). It was recently discovered that TMC-1 also contains a plethora of
carbon-based molecules of considerable complexity such as the partially
saturated carbon chains C5H4 (Cernicharo et al. 2021a) and C6H3N
(Shingledecker et al. 2021), the aromatic cycle benzyne (Cernicharo et al.
2021b), and polycyclic aromatic molecules like indene (Cernicharo et al.
2021c; Burkhardt et al. 2021), C6H5CN (McGuire et al. 2018), and C10H7CN
(McGuire et al. 2021).

Another distinctive aspect of TMC-1 is the presence of protonated species of
abundant neutral molecules. The list of protonated molecular species found
here consists of the widespread HCO+ and N2H+, such as HCS+ (Irvine et al.
1983), HCO${}_{2}^{+}$ (Turner et al. 1999), and the more recently discovered
species HC3O+ (Cernicharo et al. 2020a), HC3S+ (Cernicharo et al. 2021d),
CH3CO+ (Cernicharo et al. 2021e), and HCCS+ (Cabezas et al. 2022a). The list
is completed by the protonated nitriles HCNH+ (Schilke et al. 1991), HC3NH+
(Kawaguchi et al. 1994), NCCNH+ (Agúndez et al. 2015), and HC5NH+ (Marcelino
et al.  2020), which are observed in TMC-1 because their neutral counterparts
are abundant and have high proton affinities. The abundance ratio between a
protonated molecule and its neutral counterpart, [MH+]/[M], is sensitive to
the degree of ionization and thus to various physical parameters of the cloud,
and it is mainly set by the rates of formation and destruction of the cation
(Agúndez et al. 2015). The protonated form is mainly formed by proton transfer
to the neutral and destroyed by dissociative recombination with electrons. It
is interesting to note that both chemical models and observations suggest a
trend in which the abundance ratio [MH+]/[M] increases with the increasing
proton affinity of M (Agúndez et al. 2015).

The proton affinities of the nitriles whose protonated species have been
detected in TMC-1 are between 674.7 kJ mol-1 (for NCCN; Hunter & Lias 1998)
and 770 $\pm$ 20 kJ mol-1 (for HC5N; Edwards et al. 2009). These values are
larger than the proton affinities of molecules such as CO or N2 and smaller
than those of C3O or C3S. For cyanopolyynes, the longer the carbon chain, the
higher the proton affinity. That is, for HCN, HC3N, and HC5N, the proton
affinities are 712.9, 751.2, and 770 kJ mol-1, respectively (Hunter & Lias
1998; Edwards et al. 2009). Hence, larger members of the series of
cyanopolyynes are potential candidates to be detected in their protonated
form. One of them is HC7N, which is only two times less abundant than HC5N in
TMC-1 (Cernicharo et al. 2020b). However, laboratory microwave spectroscopy
information that allow for the astronomical identification of these protonated
species is not available. The use of high-level quantum chemical calculations
is a powerful alternative with which we may overcome the lack of laboratory
experimental data on transient molecules such as protonated species. The
combination of accurate calculations with high-resolution line surveys can be
used to carry out molecular spectroscopy in space, allowing for the detection
of elusive molecular species. In the recent years, we have employed this
method to identify, in space, MgC3N and MgC4H (Cernicharo et al. 2019), HC5NH+
(Marcelino et al.  2020), MgC5N and MgC6H (Pardo et al. 2021), H2NC (Cabezas
et al. 2021a), CH2DC3N (Cabezas et al.  2021b), HCCS+ (Cabezas et al. 2022a),
and CH2DC4H (Cabezas et al. 2022b). Here, we present a new case of molecular
spectroscopy carried out in space. Thanks to the sensitivity of our
QUIJOTE111Q-band Ultrasensitive Inspection Journey to the Obscure TMC-1
Environment line survey of TMC-1 (Cernicharo et al. 2021b), we have detected a
new series of harmonically related lines belonging to a molecule with a
${}^{1}\Sigma$ ground electronic state. Based on ab initio calculations and
the expected intensities of the lines for all the plausible molecular
candidates, we have confidently assigned the observed lines to HC7NH+.

##  2 Observations

The data presented in this work are part of the QUIJOTE spectral line survey
Cernicharo et al. (2021b) in the Q band towards TMC-1(CP)
($\alpha_{J2000}=4^{\rm h}41^{\rm m}41.9^{\rm s}$ and
$\delta_{J2000}=+25^{\circ}41^{\prime}27.0^{\prime\prime}$) that was performed
at the Yebes 40m radio telescope during various observing sessions between
November 2019 and January 2022. The survey was done using new receivers, built
within the Nanocosmos project222https://nanocosmos.iff.csic.es/ and consisting
of two cooled high electron mobility transistor (HEMT) amplifiers covering the
31.0-50.3 GHz band with horizontal and vertical polarizations. Fast Fourier
transform spectrometers (FFTSs) with $8\times 2.5$ GHz with a spectral
resolution of 38.15 kHz provide the whole coverage of the Q-band in both
polarizations. This setup has been described previously in Tercero et al.
(2021). The QUIJOTE observations are performed using the frequency-switching
observing mode with a frequency throw of 10 MHz in the very first observing
runs, during November 2019 and February 2020, 8 MHz during observations taking
place between January-November 2021, and 10 MHz again in the last observing
run between October 2021 and January 2022. After including all of the data,
the total on-source telescope time is 430 h in each polarization (twice this
value after averaging the two polarizations). This observing time can be split
into 200 and 230 hours for the 8 MHz and 10 MHz frequency throws. The main
beam efficiency of the Yebes 40m telescope varies from 0.6 at 32 GHz to 0.43
at 50 GHz.

The intensity scale used in this work, antenna temperature ($T_{A}^{*}$), was
calibrated using two absorbers at different temperatures and the atmospheric
transmission model ATM (Cernicharo 1985; Pardo et al. 2001). Calibration
uncertainties were assumed to be 10 % based on the observed repeatability of
the line intensities between different observing runs. All data were analyzed
using the GILDAS package333http://www.iram.fr/IRAMFR/GILDAS.

##  3 Results

The level of sensitivity of our QUIJOTE line survey is now three to four times
better than that used for the detection of HC5NH+ (Marcelino et al.  2020).
Due to the high abundance of HC7N in TMC-1, it is expected that its protonated
form, HC7NH+, can be detected within the forest of lines with an intensity of
$\leqslant$2 mK that remain unassigned in our line survey. The molecular
parameters for HC7NH+ have been estimated by Botschwina et al. (1997) using
accurate ab initio calculations. We used these parameters to predict the
rotational transition frequencies for HC7NH+ in the Q-band. Following these
predictions, we found a series of nine harmonically related lines $\sim$25 MHz
above the expected frequencies. The observed lines are shown in Figure 1,
whose frequencies and line parameters are given in Table 1. By fitting the
observed frequencies to the standard expression for a linear molecule
$\nu(J\rightarrow$$J-1)$=2$B_{0}J$ \- 4$D_{0}J^{3}$ in the ${}^{1}\Sigma$
electronic state, we derived the rotational parameters shown in the first
column of Table 2. The derived value for the $B_{0}$ rotational constant
agrees well with that predicted by Botschwina et al. (1997), 553.8 MHz.
However, in their paper, Botschwina et al. (1997) do not provide any
estimation for the centrifugal distortion constant, $D$ .

In addition to HC7NH+, the most promising candidates for acting as the carrier
for the observed lines are HC7O+ and NC6NH+. The $B$ rotational constant for
C7O is 572.94105 MHz, so its protonated form is expected to have a $B$ value
similar to that derived from our TMC-1 data. For NC6N, there are no
experimental data available in the literature, but the $B$ value for NC6NH+
should be on the order of that for HC7NH+ and HC7O+, as it occurs for the
smaller members HC5NH+, NC4NH+, and HC5O+ (Marcelino et al.  2020). Other
molecules that could be considered as candidates are H2C7O, H2C7O+, and H2C8.
However, no additional lines corresponding to $K_{a}$=1 transitions were
observed at higher and lower frequencies from this series, which excludes
these near-prolate molecules as plausible carriers of the observed lines.
Moreover, H2C8 can be discarded because its $K$=0 effective rotational
constant for H2C8 is 574.2267(4) MHz (Apponi et al. 2000), and H2C7O is
predicted (McCarthy et al. 2017) to have much smaller rotational constants $B$
and $C$, 517.0 and 516.1 MHz, respectively, while H2C7O+ is an open-shell
species and its rotational spectrum will display a complicated hyperfine
structure.

Table 1: Observed line parameters for HC7NH+ in TMC-1.

$J_{u}$-$J_{l}$ |  $\nu_{obs}$ a |  $\int T_{A}^{*}dv$ b |  $\Delta$v c | $T_{A}^{*}$
---|---|---|---|---
| (MHz) |  (mK km s-1) |  (km s-1) | (mK)
29-28 |  32128.095$\pm$0.010 |  1.46$\pm$0.12 |  0.74$\pm$0.07 |  1.86$\pm$0.16
30-31 |  32235.944$\pm$0.010 |  1.14$\pm$0.10 |  0.65$\pm$0.07 |  1.66$\pm$0.15
31-30 |  34343.775$\pm$0.010 |  0.70$\pm$0.10 |  0.66$\pm$0.11 |  1.00$\pm$0.14
32-31 |  35451.605$\pm$0.010 |  1.07$\pm$0.10 |  0.90$\pm$0.10 |  1.11$\pm$0.14
33-32 |  36559.437$\pm$0.010 |  0.78$\pm$0.10 |  0.74$\pm$0.11 |  1.12$\pm$0.14
34-33 |  37667.263$\pm$0.010 |  0.80$\pm$0.09 |  0.61$\pm$0.07 |  1.23$\pm$0.15
35-34 |  38775.097$\pm$0.010 |  0.66$\pm$0.09 |  0.77$\pm$0.13 |  0.80$\pm$0.15
36-35 |  39882.911$\pm$0.010 |  0.29$\pm$0.08 |  0.48$\pm$0.11 |  0.57$\pm$0.15
37-36 |  40990.727$\pm$0.010 |  0.38$\pm$0.09 |  0.53$\pm$0.15 |  0.67$\pm$0.16
444

Figure 1: Observed lines of HC7NH+ in TMC-1 in the 31.0-50.4 GHz range.
Frequencies and line parameters are given in Table 1. Quantum numbers for the
observed transitions are indicated in each panel. The red line shows the
synthetic spectrum computed for a rotational temperature of 8.5 K and a column
density of 5.5$\times$1010 cm-2 (see text). Blanked channels correspond to
negative features created in the folding of the frequency switching data. The
label U corresponds to unidentified features above 4$\sigma$.

To obtain accurate spectroscopic parameters, we performed ab initio
calculations for HC7NH+, HC7O+, and NC6NH+ and also for HC7N and C7O species
for which the rotational parameters are experimentally determined. In this
manner, we can scale the calculated values for the target species using
experimental/theoretical ratios derived for the related species. This
procedure has been found to provide rotational constants with an accuracy
better than 0.1 % (e.g. Cabezas et al. 2021a). We chose HC7N and C7O as
reference species to scale the HC7NH+ and HC7O+ calculations. The theoretical
values for NC6NH+ are not scaled because there is not any similar and
isoelectronic species for which the rotational parameters are experimentally
determined. The geometry optimization calculations for all the species were
done using the coupled cluster method with single, double, and perturbative
triple excitations with an explicitly correlated approximation (CCSD(T)-F12;
Knizia et al. 2009) and all electrons (valence and core) correlated together
with the Dunning’s correlation consistent basis sets with polarised core-
valence correlation triple-$\zeta$ for explicitly correlated calculations (cc-
pCVTZ; Hill et al. 2010). These calculations were carried out using the Molpro
2020.2 program (Werner et al. 2020). The values for the centrifugal distortion
constants and the vibration-rotation interaction constants were obtained using
harmonic and anharmonic vibrational frequency calculations, respectively, with
the second-order Møller-Plesset perturbation theory method (MP2; Møller &
Plesset 1934) and the correlation consistent with polarised valence
triple-$\zeta$ basis set (cc-pVTZ; Woon & Dunning 1993). These calculations
were carried out using the Gaussian09 program (Frisch et al. 2009). The
results obtained are presented in Table 2. The values for the $B_{e}$ constant
come from geometry optimization calculations and those for the $D$ constant
and the vibration-rotation corrections are taken from frequency calculations.
The $B_{0}$ values are the sum of $B_{e}$ and the vibration-rotation
correction terms. The values of $B_{0}$ and $D$ calculated for HC7NH+ and
HC7O+ were then scaled by the corresponding experimental/calculated ratios
obtained for HC7N and C7O, respectively.

##  4 Discussion

###  4.1 Identification of the carrier

Our comparison of the calculated and experimental rotational constants for
HC7N and C7O species reveals the good accuracy of the ab initio calculations
employed. The differences between the calculated $B_{0}$ values and the
experimental ones reach 0.08% and 0.03% for HC7N and C7O, respectively. Hence,
similar discrepancies should be expected between the $B_{0}$ value derived
from our fit and the calculated $B_{0}$ value for the carrier species. The
data from Table 2 show differences of 0.06%, 0.94%, and 0.26% for HC7NH+,
NC6NH+, and HC7O+, respectively, which indicates that the observed species in
TMC-1 is HC7NH+. When the scaled values are compared, the calculation errors
decrease down to 0.02% for HC7NH+, while for HC7O+ it is still high, 0.23%,
which confirms HC7NH+ as the carrier of the observed lines. The fact that the
$B_{0}$ constant for NC6NH+ cannot be scaled is irrelevant because the error
of the calculated value is almost ten times larger than the expected one for
this type of calculation, which rules out NC6NH+ as a possible candidate.
Another spectroscopic argument that supports the detection of HC7NH+ is the
good agreement found for the centrifugal distortion constant, $D$ . The scaled
value for HC7NH+ perfectly reproduces the $D$ value derived from the fit,
while that of HC7O+ is $\sim$25% larger. Hence, our ab initio calculations
provide conclusive arguments for the spectroscopic identification of HC7NH+
using our TMC-1 survey.

Table 2: Theoretical spectroscopic parameters for the different molecular
candidates for the observed lines in TMC-1 (all in MHz).

|  HC7NH+ |  HC7N |  NC6NH+ |  HC7O+ |  C7O
---|---|---|---|---|---
Parameter |  TMC-1aa$a$Observed frequencies towards TMC-1 for which we adopted a vLSR of 5.83 km s-1 (Cernicharo et al. 2020a). |  Calc.bb$b$Integrated line intensity in mK km s-1. |  Scaledcc$c$Line width at half maximum intensity derived by fitting a Gaussian function to the observed line profile (in km s-1). |  Exp.dd$d$Bizzocchi & Degli Esposti (2004). |  Calc.bb$b$This work; see text. |  Calc.bb$b$This work; see text. |  Calc.bb$b$This work; see text. |  Scaledee$e$This work; scaled by the ratio Exp/Calc. of the corresponding parameter for C7O species |  Exp.ff$f$Ogata et al. (1995). |  Calc.bb$b$This work; see text.
$B_{e}$ |  | 552.61 |  |  | 562.93 | 547.99 | 551.80 |  |  | 571.95
Vib-Rot. Corr. |  | 0.97 |  |  | 0.60 | 0.72 | 0.69 |  |  | 0.80
$B_{0}$ |  553.939070(140)gg$g$Values in parentheses denote 1$\sigma$ errors, applied to the last digit. | 553.58 | 554.05 | 564.0011225(44) | 563.53 | 548.71 | 552.49 | 552.67 | 572.94105(5) | 572.75
$D$ x 10-6 | 3.7602(619) | 3.15 | 3.64 | 4.04108(54) | 3.50 | 3.22 | 3.12 | 4.46 | 4.75(15) | 3.32
$\mu$ (D) |  | 6.4 |  |  |  | 12.4 | 1.7 |  |  |
555$a$$a$footnotetext: Parameters derived using the TMC-1 from Table 1.
$c$$c$footnotetext: This work; scaled by the ratio Exp/Calc. of the
corresponding parameter for HC7N species. .

Another point supporting this assignment concerns the very different dipole
moment of HC7NH+ and HC7O+. While HC7NH+ has a predicted dipole moment of
$\sim$6.4 D, the corresponding value for HC7O+ is $\sim$1.7 D, hence, the
abundance resulting from the observed line intensities would be significantly
different if the carrier is one or the other species. An analysis of the line
intensities through a line model-fitting procedure (Cernicharo et al. 2021c),
assuming that the carrier is HC7NH+, provides a rotational temperature of
$\sim\,8.5\pm 1.5$ K and a column density of
N(HC7NH+)=(5.5$\pm$0.7)$\times$1010cm-2. When HC7O+ is assumed as the line
carrier, the column density obtained is
N(HC7O+)=(7.1$\pm$0.6)$\times$1011cm-2. As previously discussed by Agúndez et
al. (2015), in cold dense clouds, protonated molecules MH+ are formed mainly
by reactions of proton transfer from a proton donor XH+, which is usually
HCO+, H3O+, or H${}_{3}^{+}$, to M, namely:

$\rm M+XH^{+}\rightarrow MH^{+}+X.$ (1)

The column density of HC7N in TMC-1 was found to be
(6.4$\pm$0.4)$\times$1013cm-2 (Cernicharo et al. 2020b). This value was
derived from observations of fourteen transitions from $J$=28-27 up to
$J$=44-43. These observations correspond to the first observing run in 2020.
We have revised these results taking into account the new data gathered until
January 2022. In these new estimations we have assumed a source of uniform
brightness and 80′′ in diameter (Fossé et al. 2001). We derive now a column
density for HC7N of (2.1$\pm$0.2)$\times$1013cm-2, and Trot=7.6$\pm$0.2K. The
previous estimate of N(HC7N) was unfortunately affected by an erroneous
assumption of the source diameter (40′′ instead of the value adopted in the
QUIJOTE line survey of 80′′). Hence, the HC7N/HC7N+ abundance ratio is
$\sim$380\. A correct estimation of the column density will require a measure
of the source size in order to compute the beam dilution of each line, which
could affect the derived rotational temperatures.

On the other hand, while C5O was recently discovered in TMC-1 (Cernicharo et
al. 2021f), the longest carbon chain C7O has not been observed in TMC-1 and
the derived upper limit to its column density using the QUIJOTE line survey is
$\leq$ $2.0$$\times$1010 cm-2, which would result in a ratio of C7O/HC7O+
$\leq$ 0.04. A neutral-to-protonated ratio lower than one seems extremely
unlikely. In light of this fact and the spectroscopic evidence mentioned
before we definitively conclude that the carrier of the unidentified lines
observed in TMC-1 is HC7NH+.

We estimated the proton affinities of HC7N, NC6N, and C7O because there are no
experimental values available in the literature. We used the energy balance,
at the CCSD/cc-pVTZ level of theory, between HC7N + H+ and HC7NH+, considering
HC7N and H+ as independent species. We found a proton affinity value for HC7N
of 798 kJ mol-1. Using analogue schemes, we obtained proton affinity values
for NC6N and C7O of 755 and 1059 kJ mol-1, respectively. The proton affinity
for C7O species is the highest, which makes it very favorable the formation of
HC7O+. However, as discussed previously, its detection seems unlikely given
that C7O has not been detected in TMC-1 and there is a stringent upper limit
to its column density. The proton affinity of 798 kJ mol-1 calculated for HC7N
is slightly larger than the experimental value measured for HC5N, 770$\pm$20
kJ mol-1 (Edwards et al. 2009). This is in line with the trend of increasing
proton affinity with increasing chain length found for cyanopolyynes.

###  4.2 Chemical model

Figure 2: Calculated abundances (bottom) and abundance ratios (top) as a
function of time for cyanopolyynes and their protonated forms. The horizontal
dotted lines correspond to values derived from observations of TMC-1.

The detection of HC7NH+ in TMC-1 contributes to the previous identifications
of protonated cyanopolyynes of a smaller size, namely, HC5NH+ and HC3NH+, in
this cloud. This allows us to have a view of the behavior of protonated
species for this family of molecules. The neutral-to-protonated ratios derived
in TMC-1 are HC3N/HC3NH+ = 230, HC5N/HC5NH+ = 240, and HC7N/HC7NH+ = 380.
Therefore, the ratios are of the same order for the three carbon chains.
Observations and chemical models suggest that the neutral-to-protonated ratio
decreases with increasing proton affinity towards the neutral (Agúndez et al.
2015). The proton affinities of cyanopolyynes increase with increasing chain
length. The values are 751.2, 770, and 798 kJ mol-1 for HC3N, HC5N, and HC7N,
respectively, which represents only a moderate enhancement and may not
translate to drastic variations in the neutral-to-protonated ratio. In fact,
HC7N has the higher proton affinity and the largest neutral-to-protonated
ratio, which does not fit into the trend between neutral-to-protonated ratio
and proton affinity mentioned above.

Figure 3: Abundance ratios between neutral and protonated forms for the family
of cyanopolyynes. Calculated values are obtained from the chemical model at a
time of 2 $\times$ 105 yr, while observed values are those derived in TMC-1.

To understand the chemistry of protonated cyanopolyynes, we ran a pseudo-time-
dependent gas-phase chemical model of a cold dark cloud using a chemical
network largely based on the RATE12 network from the UMIST database (McElroy
et al. 2013). The model is similar to those presented by Agúndez et al. (2015)
and Marcelino et al.  (2020). The only modification with respect to those
models is that here we have revised the rate coefficient of dissociative
recombination of HC7NH+ and longer protonated cyanopolyynes with electrons.
The value in the UMIST RATE12 network is a guess coming from Herbst & Leung
(1989), but in light of the more recent experiment involving DC3ND+ (Geppert
et al. 2004) and the critical evaluation of the rate coefficient of HC5NH+ \+
e- in the KIDA database666https://kida.astrochem-tools.org/ (Wakelam et al.
2015), we assumed the rate coefficient and branching ratios of the
dissociative recombination of HC5NH+ to also apply to longer protonated
cyanopolyynes.

According to the chemical model, the peak abundances were reached at a time of
$\sim$ 2 $\times$ 105 yr, which is thought to be the chemical age of TMC-1
(Agúndez & Wakelam 2013). The abundances calculated at this time show a trend
of decreasing abundance with increasing chain length (see dashed curves in the
bottom panel of Fig. 2) that is also observed for cyanopolyynes in TMC-1
(Cernicharo et al. 1987; Agúndez et al. 2008). The protonated forms of
cyanopolyynes are also predicted to be less abundant as the size of the chain
increases (solid curves in the bottom panel of Fig. 2). When focusing on the
abundances relative to H2, the agreement between the peak calculated abundance
and the value derived from observations is reasonably good, within one order
of magnitude.

While the abundances relative to H2 experience great variations over time, the
neutral-to-protonated ratios calculated for HC3N, HC5N, and HC7N remain nearly
constant for any time longer than a few 105 yr and they stick to the same
value for the three species, namely, around 103 (see top panel in Fig. 2). We
see that calculated neutral-to-protonated abundance ratios are significantly
lower than what has been observed for HC3N, HC5N, and HC7N. That is to say
that the chemical model underestimates the abundance of the protonated form
with respect to the neutral, which is something that occurs also for most
protonated molecules (Agúndez et al. 2015; Cernicharo et al. 2020a). As
previously discussed by Marcelino et al.  (2020), the rate coefficients of the
most important reactions that control the abundance of protonated molecules,
namely, proton transfer to the neutral and dissociative recombination with
electrons, are relatively well constrained from experiments based on HC3NH+
(Anicich 2003; Geppert et al. 2004), although they are not known for longer
protonated cyanopolyynes. We suspect that uncertainties in the low-temperature
rate coefficients of these reactions or missing reactions in the formation of
the cation could be at the origin of the discrepancies between the calculated
and observed neutral-to-protonated ratios for cyanopolyynes. In any case, the
order of magnitude of the neutral-to-protonated ratios is roughly reproduced
by the chemical model. The prediction is that protonated HC9N should be
present with a neutral-to-protonated abundance ratio that is similar to what
has been found for the smaller cyanopolyyne analogues (see Fig. 3).

##  5 Conclusions

Here, we present the first detection in space of a new molecular ion, HC7NH+,
toward the dark cloud TMC-1. Using the Yebes 40m radio telescope, we observed
a total of nine rotational transitions in the 31.0-50.4 GHz range. From ab
initio calculations and the expected intensities of the lines for all the
plausible molecular candidates, these transitions were assigned to HC7NH+. We
derived a column density of (5.5$\pm$0.7)$\times$1010 cm-2 and a HC7NH+/HC7N
abundance ratio $\sim$380\. The ratio is similar to those found for the
smaller analogue systems HC3NH+/HC3N and HC5NH+/HC5N, suggesting that a
similar chemistry regulates their abundances. A state-of-the-art chemical
model underestimates the HC7NH+/HC7N abundance ratio observed in TMC-1, which
is something that also occurs for other protonated molecules.

###### Acknowledgements.

We thank ERC for funding through grant ERC-2013-Syg-610256-NANOCOSMOS. The
Spanish authors thank Ministerio de Ciencia e Innovación for funding support
through projects PID2019-106235GB-I00 and PID2019-107115GB-C21 / AEI /
10.13039/501100011033. MA thanks Ministerio de Ciencia e Innovación for grant
RyC-2014-16277.

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