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.

# Cumulene carbenes in TMC-1: Astronomical discovery of $l$-H2C5 ††thanks:
Based on observations carried out with the Yebes 40m telescope (projects
19A003, 20A014, and 20D15). The 40m radiotelescope at Yebes Observatory is
operated by the Spanish Geographic Institute (IGN, Ministerio de Transportes,
Movilidad y Agenda Urbana).

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

(Received; accepted)

We report the first detection in space of the cumulene carbon chain $l$-H2C5.
A total of eleven rotational transitions, with $J_{up}$ = 7-10 and $K_{a}$ = 0
and 1, were detected in TMC-1 in the 31.0-50.4 GHz range using the Yebes 40m
radio telescope. We derive a column density of (1.8$\pm$0.5)$\times$1010 cm-2.
In addition, we report observations of other cumulene carbenes detected
previously in TMC-1, to compare their abundances with the newly detected
cumulene carbene chain. We find that $l$-H2C5 is $\sim$4.0 times less abundant
than the larger cumulene carbene $l$-H2C6, while it is $\sim$300 and $\sim$500
times less abundant than the shorter chains $l$-H2C3 and $l$-H2C4. We discuss
the most likely gas-phase chemical routes to these cumulenes in TMC-1 and
stress that chemical kinetics studies able to distinguish between different
isomers are needed to shed light on the chemistry of CnH2 isomers with $n$ $>$
3.

###### Key Words.:

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

##  1 Introduction

Cumulene carbenes are highly polar carbon-chains with elemental formula H2Cn.
They contain consecutive carbon-carbon double bonds and two nonbonded
electrons localized on the terminal C atom. These species play major roles as
reaction intermediates in combustion and plasma processes and they are also of
astrophysical interest since some of them have been detected in interstellar
and circumstellar environments. The first astronomical discovery of the
simplest cumulene carbene propadienylidene, $l$-H2C3, was carried out by
Cernicharo et al. (1991a) toward the cold dark cloud TMC-1. Butatrienylidene,
$l$-H2C4, was detected in the carbon-rich circumstellar envelope of IRC+10216
by Cernicharo et al. (1991b) and in TMC-1 by Kawaguchi et al. (1991) and
later, the larger cumulene carbene hexapentaenylidene, $l$-H2C6, was detected
in TMC-1, IRC+10216 and L1527 (Langer et al. 1997; Guélin et al. 2000; Araki
et al. 2017).

Cumulene carbenes are metastable isomers, lying 0.5-0.6 eV above the most
stable isomer, which is a polyacetylene (HCnH) for an even $n$ or a cyclic
structure when the number of carbon atoms is odd. Thus, their astronomical
detection demonstrates how far from thermochemical equilibrium is the
composition of interstellar clouds. The case of HNC, which is less stable than
HCN by about 0.6 eV but as abundant as HCN (Herbst  1978), illustrates this
point as well.

Pentatetraenylidene, $l$-H2C5, is the cumulene carbene from the isomeric
family with formula C5H2. $l$-H2C5 is a high energy isomer and lies 0.564 eV
above the most stable isomers, the nonpolar pentadiynylidene (HCCCCH) and
ethynyl cyclopropenylidene ($c$-C3HCCH), whose energy separation is very small
$\thicksim$0.043 eV. Other two species are part of this isomeric family,
HCCCHCC and $c$-C3H2C2, placed at 0.737 and 0.910 eV above the most stable
forms, respectively (Seburg et al. 1997). All these isomers, except the
nonpolar HCCCCH, have been studied in the laboratory (Travers et al.  1997;
McCarthy et al. 1997; Gottlieb et al. 1998) and, thus, their transition
frequencies are well known. However, until very recently none of them has been
observed in space. Cernicharo et al. (2021a) have reported the first
identification in TMC-1 of the most stable isomer of this family, $c$-C3HCCH,
using a high sensitivity line survey gathered with the Yebes 40m radio
telescope. This achievement opens the door to the identification of high
energy isomers of this family in TMC-1.

In this Letter we report the first identification of the $l$-H2C5 cumulene
carbene in space towards TMC-1 and a comparative study of the previously
detected cumulene carbenes in this source. The derived column densities for
these singular energetic species are interpreted by chemical models and used
to understand the chemical processes leading to their formation.

##  2 Observations

The data presented in this work are part of a deep spectral line survey in the
Q band towards TMC-1 ($\alpha_{J2000}=4^{\rm h}41^{\rm m}41.9^{\rm s}$ and
$\delta_{J2000}=+25^{\circ}41^{\prime}27.0^{\prime\prime}$) that was performed
at the Yebes 40m radio telescope between November 2019 and April 2021. The
survey was done using new receivers, built within the Nanocosmos
project111https://nanocosmos.iff.csic.es/ consisting of two HEMT cold
amplifiers covering the 31.0-50.4 GHz band with horizontal and vertical
polarizations. Fast Fourier transform spectrometers (FFTSs) with $8\times 2.5$
GHz bands per lineal polarization allow a simultaneous scan of a bandwidth of
18 GHz at a spectral resolution of 38.15 kHz. This setup has been described
before by Tercero et al.  (2021).

The observations were performed using the frequency switching technique with a
frequency throw of 10 MHz or 8 MHz (see, e.g., Cernicharo et al. 2021b, c).
The intensity scale, antenna temperature ($T_{A}^{*}$), for the two telescopes
used in this work was calibrated using two absorbers at different temperatures
and the atmospheric transmission model ATM (Cernicharo 1985; Pardo et al.
2001).Different frequency coverages were observed, 31.08-49.52 GHz and
31.98-50.42 GHz, which permitted us to check that no spurious ghosts are
produced in the down-conversion chain. The signal coming from the receiver is
downconverted to 1-19.5 GHz, and then split into 8 bands with a coverage of
2.5 GHz each of which are analyzed by the FFTs.

Pointing and focus corrections were obtained by observing strong SiO masers
towards nearby evolved stars (IKTau and UOri). Pointing errors were always
within $2^{\prime\prime}-3^{\prime\prime}$. Total calibration uncertainties
have been adopted to be 10 % based on the observed repeatability of the line
intensities between dif- ferent observing runs. All data have been analyzed
using the GILDAS package222http://www.iram.fr/IRAMFR/GILDAS.

##  3 Results and discussion

###  3.1 Detection of $l$-H2C5 in TMC-1

$l$-H2C5 was observed in the laboratory by McCarthy et al. (1997) and the
prediction of its rotational spectrum is available in the CDMS (Müller et al.
2005). This prediction, based in the laboratory data from McCarthy et al.
(1997), is implemented in the MADEX code (Cernicharo 2012) that was used to
identify the spectral features in our TMC-1 Q-band survey. McCarthy et al.
(1997) observed in the laboratory a total of nine rotational transitions for
$l$-H2C5 up to $J_{up}$=5 at 23 GHz. The derived parameters from McCarthy et
al. (1997) (see Table 1) allow to accurately predict the rotational
transitions for $l$-H2C5 in the Q-band. The molecule has a dipole moment of
5.9 D (Maluendes & McLean 1992) which makes it a very promising candidate to
be observed in our TMC-1 data. In this manner, we search for this species in
our TMC-1 survey and we found a total of eleven transitions ranging from
$J_{up}$ = 7-10, whose frequencies agree very well with those predicted,
discrepancies are smaller than 25 kHz. $9_{0,9}-8_{0,8}$ line is blended with
a negative feature produced in the folding of the frequency switching data
while $10_{0,10}-9_{0,9}$ transition is not detected due to the limited
sensitivity at the predicted frequency. In any case the non-detection is
consistent with the expected intensity. All the $l$-H2C5 lines observed in
TMC-1, shown in Fig. 1 and listed in Table 2, were analyzed, together with
those observed in laboratory, using an asymmetric rotor Hamiltonian with the
FITWAT code (Cernicharo et al. 2018) to derive the rotational and centrifugal
distortion constants. The results from this fit are shown in Table 1 together
with those obtained by McCarthy et al. (1997) only with laboratory data. With
this new global fit an improvement of the uncertainty in the rotational and
distortion constants is obtained. Hence, this fit is recommended to predict
the frequency of the rotational transitions of $l$-H2C5 with uncertainties
between 10 and 200 kHz in the 50-116 GHz frequency range.

As $l$-H2C5 has C2v symmetry, it is necessary to discern between
ortho-$l$-H2C5 and para-$l$-H2C5. The ortho levels are described by $K_{a}$
odd while the para levels by $K_{a}$ even. The nuclear spin-weights are 3 and
1 for ortho-$l$-H2C5 and para-$l$-H2C5, respectively. The $J_{K_{\rm a},K_{\rm
c}}$ = 11,1 is the lowest ortho energy state located 13.4 K above the para
ground level, $J_{K_{\rm a},K_{\rm c}}$ = 00,0. Hence, from the eleven
observed lines eight of them correspond to ortho-$l$-H2C5 and the remaining
three to para-$l$-H2C5. An analysis of the line intensities through a line
model fitting procedure Cernicharo et al. (2021a) provides a rotational
temperature of $\sim\,10$ K and column densities
N(ortho-$l$-H2C5)=(1.3$\pm$0.3)$\times$1010cm-1 and
N(para-$l$-H2C5)=(5.0$\pm$2.0)$\times$109cm-1. The ortho/para ratio is
calculated to be 2.6$\pm$1.5. We have assumed a linewidth of 0.6 km s-1 and a
source of uniform brightness temperature with a diameter of 80′′ (Fossé et al.
2001). Figure 1 shows, in red, the computed synthetic spectrum.

Figure 1: Observed lines of $l$-H2C5 in TMC-1 in the 31.0-50.4 GHz range. The
abscissa corresponds to the rest frequency assuming a local standard of rest
velocity of 5.83 km s-1. The ordinate is antenna temperature in millikelvins.
Curves shown in red are the computed synthetic spectra. U labels correspond to
features above 4$\sigma$. Frequencies and line parameters are given in Table
2. Table 1: New derived rotational parameters (in MHz) for $l$-H2C5.

Constant |  TMC-1+Laba |  Labb
---|---|---
$A$ |  277600.0c | 277600.0
$B$ | 2304.78432(27) | 2304.7844(3)
$C$ | 2285.80518(27) | 2285.8053(3)
$\Delta_{J}\times 10^{3}$ | 0.0978(19) | 0.104(6)
$\Delta_{JK}$ | 0.04647(19) | 0.0464(2)
$rms$d | 8.7 | 3.0
$J_{min}/J_{max}$ | 2/10 | 2/5
$K_{min}/K_{max}$ | 0/1 | 0/1
Ne | 20 | 9
333 $a$$a$footnotetext: Fit to the lines of $l$-H2C5 observed in TMC-1 and in
laboratory (McCarthy et al. 1997). $b$$b$footnotetext: (McCarthy et al. 1997).
$c$$c$footnotetext: Fixed to the value reported by McCarthy et al. (1997).
$d$$d$footnotetext: The standard deviation of the fit in kHz.
$e$$e$footnotetext: Number of lines included in the fit.

###  3.2 Column densities for $l$-H2C3, $l$-H2C4 and $l$-H2C6 in TMC-1

Table 2: Observed lines of $l$-H2C3, $l$-H2C4, $l$-H2C5, and $l$-H2C6 towards
TMC-1.

State | Transition | Rest Freq. | $E_{\rm up}$ | $S_{\rm ij}$ | $\int T_{\rm A}^{*}dv$ | $V_{\rm LSR}$ |  $\Delta$v | $T_{\rm A}^{*}$
---|---|---|---|---|---|---|---|---
| $(J_{K_{\rm a},K_{\rm c}})_{\rm u}-(J_{K_{\rm a},K_{\rm c}})_{\rm l}$ | (MHz) | (K) |  | (mK km s-1) | (km s-1) | (km s-1) | (mK)
$l$-H2C3
ortho | $2_{1,2}-1_{1,1}$ | 41198.335(2) | 2.0 | 1.50 | 72.0208(2) | 5.71(1) | 0.61(1) | 110.3(3)
para | $2_{0,2}-1_{0,1}$ | 41584.675(1) | 3.0 | 2.00 | 50.0199(4) | 5.75(1) | 0.58(1) | 81.11(3)
ortho | $2_{1,1}-1_{1,0}$ | 41967.671(2) | 2.0 | 1.50 | 72.2521(2) | 5.75(1) | 0.56(1) | 122.5(3)
$l$-H2C4
ortho | $4_{1,4}-3_{1,3}$ | 35577.008(2) | 3.8 | 3.75 | 137.590(1) | 5.71(1) | 0.70(1) | 185.3(2)
para | $4_{0,4}-3_{0,3}$ | 35727.379(1) | 4.3 | 4.00 | 91.6939(2) | 5.53(1) | 0.67(1) | 128.0(2)
ortho | $4_{1,3}-3_{1,2}$ | 35875.775(2) | 3.9 | 3.75 | 140.130(1) | 5.69(1) | 0.69(1) | 189.9(2)
ortho | $5_{1,5}-4_{1,4}$ | 44471.137(2) | 6.0 | 4.80 | 120.160(1) | 5.72(1) | 0.57(1) | 199.4(4)
para | $5_{0,5}-4_{0,4}$ | 44659.015(1) | 6.0 | 5.00 | 73.0765(2) | 5.58(1) | 0.58(1) | 119.2(4)
ortho | $5_{1,4}-4_{1,3}$ | 44844.590(2) | 6.4 | 4.80 | 117.010(1) | 5.70(1) | 0.59(1) | 186.6(4)
$l$-H2C5
ortho | $7_{1,7}-6_{1,6}$ | 32066.902(2) | 5.9 | 6.86 | 0.6759(5) | 5.83(7) | 0.69(17) | 0.9(2)
para | $7_{0,7}-6_{0,6}$ | 32133.937(2) | 6.2 | 7.00 | 1.3465(2) | 5.83(8) | 1.06(16) | 1.2(2)
ortho | $7_{1,6}-6_{1,5}$ | 32199.756(2) | 6.0 | 6.86 | 1.1423(2) | 5.83(5) | 0.77(12) | 1.4(2)
ortho | $8_{1,8}-7_{1,7}$ | 36647.836(3) | 7.7 | 7.88 | 0.7123(5) | 5.71(8) | 0.58(13) | 1.2(3)
para | $8_{0,8}-7_{0,7}$ | 36724.433(3) | 7.9 | 8.00 | 0.5152(11) | 5.83(8) | 0.53(23) | 0.9(3)
ortho | $8_{1,7}-7_{1,6}$ | 36799.669(3) | 7.7 | 7.88 | 0.5908(7) | 5.83(5) | 0.48(19) | 1.2(2)
ortho | $9_{1,9}-8_{1,8}$ | 41228.749(4) | 9.7 | 8.89 | 0.7447(6) | 5.83(8) | 0.54(16) | 1.2(4)
para | $9_{0,9}-8_{0,8}$ | 41314.902(5) | 9.9 | 9.00 | -(a) | … | … | …
ortho | $9_{1,8}-8_{1,7}$ | 41399.562(4) | 9.7 | 8.89 | 0.4890(14) | 5.83(9) | 0.59(29) | 0.8(4)
ortho | $10_{1,10}-9_{1,9}$ | 45809.639(6) | 11.9 | 9.90 | 0.5462(8) | 5.83(7) | 0.37(11) | 1.4(4)
para | $10_{0,10}-9_{0,9}$ | 45905.342(7) | 12.1 | 10.0 | -(b) | … | … | …
ortho | $10_{1,9}-9_{1,8}$ | 45999.431(6) | 11.9 | 9.90 | 0.6841(5) | 5.83(7) | 0.42(10) | 1.5(4)
$l$-H2C6
ortho | $12_{1,12}-11_{1,11}$ | 32232.270(6) | 9.9 | 11.9 | 3.89347(2) | 5.82(2) | 0.80(5) | 4.6(2)
para | $12_{0,12}-11_{0,11}$ | 32273.061(6) | 10.1 | 12.0 | 2.25233(5) | 5.86(3) | 0.73(7) | 2.9(2)
ortho | $12_{1,11}-11_{1,10}$ | 32313.117(6) | 10.0 | 11.9 | 4.17934(2) | 5.83(2) | 0.81(5) | 4.8(3)
ortho | $13_{1,13}-12_{1,12}$ | 34918.254(8) | 11.6 | 12.9 | 3.58530(2) | 5.84(2) | 0.66(4) | 5.1(3)
para | $13_{0,13}-12_{0,12}$ | 34962.439(8) | 11.7 | 13.0 | 2.61780(6) | 5.86(4) | 0.91(9) | 2.7(3)
ortho | $13_{1,12}-12_{1,11}$ | 35005.838(8) | 11.6 | 12.9 | 3.52717(2) | 5.83(1) | 0.70(4) | 4.7(2)
ortho | $14_{1,14}-13_{1,13}$ | 37604.22(1) | 13.4 | 13.9 | 2.95633(3) | 5.80(2) | 0.67(4) | 4.1(2)
para | $14_{0,14}-13_{0,13}$ | 37651.80(1) | 13.6 | 14.0 | 1.73602(10) | 5.83(4) | 0.70(9) | 2.3(3)
ortho | $14_{1,13}-13_{1,12}$ | 37698.54(1) | 13.4 | 13.9 | 2.87938(3) | 5.80(2) | 0.73(5) | 3.7(2)
ortho | $15_{1,15}-14_{1,14}$ | 40290.19(1) | 15.3 | 14.9 | 2.58873(5) | 5.75(2) | 0.56(5) | 4.4(4)
para | $15_{0,15}-14_{0,14}$ | 40341.16(1) | 15.5 | 15.0 | 1.95729(10) | 5.87(5) | 0.76(9) | 2.4(4)
ortho | $15_{1,14}-14_{1,13}$ | 40391.25(1) | 15.4 | 14.9 | 2.47566(5) | 5.91(3) | 0.65(8) | 3.6(2)
ortho | $16_{1,16}-15_{1,15}$ | 42976.15(2) | 17.4 | 15.9 | 1.2139(2) | 5.92(4) | 0.48(7) | 2.4(3)
para | $16_{0,16}-15_{0,15}$ | 43030.51(2) | 17.6 | 16.0 | 0.7463(4) | 5.80(6) | 0.50(12) | 1.4(3)
ortho | $16_{1,15}-15_{1,14}$ | 43083.94(2) | 17.4 | 15.9 | 1.61939(11) | 5.88(3) | 0.62(8) | 2.5(3)
ortho | $17_{1,17}-16_{1,16}$ | 45662.09(2) | 19.6 | 16.9 | 1.0792(4) | 5.86(9) | 0.68(23) | 1.5(5)
para | $17_{0,17}-16_{0,16}$ | 45719.84(2) | 19.7 | 17.0 | 1.3389(2) | 5.92(6) | 0.61(12) | 2.1(4)
ortho | $17_{1,16}-16_{1,15}$ | 45776.62(2) | 19.6 | 16.9 | 0.6063(12) | 5.85(9) | 0.45(24) | 1.3(6)
ortho | $18_{1,18}-17_{1,17}$ | 48348.02(2) | 21.9 | 17.9 | 1.3459(3) | 5.72(9) | 0.68(19) | 1.8(6)
para | $18_{0,18}-17_{0,17}$ | 48409.16(2) | 22.1 | 18.0 | 0.36152(11) | 5.82(9) | 0.23(90) | 1.4(6)
ortho | $18_{1,17}-17_{1,16}$ | 48469.29(2) | 22.0 | 17.9 | 0.37677(10) | 6.27(5) | 0.23(90) | 1.5(6)

444Numbers in parentheses indicate the uncertainty in units of the last
significant digits. For the observational parameters we adopted the
uncertainty of the Gaussian fit provided by GILDAS. $a$$a$footnotetext: One-
channel spectral feature. $b$$b$footnotetext: Spectral feature below the noise
level.

The carbene $l$-H2C3 is the smallest cumulene species studied in this work.
The laboratory spectroscopic data used to predict the $l$-H2C3 spectrum were
reported by Vrtilek et al.  (1990). The electric dipole moment calculated for
this molecule is 4.1 D (Defrees & McLean  1986). As for $l$-H2C5, $l$-H2C3 has
C2v symmetry and, thus, it is necessary to discern between ortho and para
$l$-H2C3. In the same manner than for $l$-H2C5 the ortho levels are described
by $K_{a}$ odd while the para levels by $K_{a}$ even, with 3/1 ratio for
ortho/para. Only three rotational transitions for $l$-H2C3 lie within the
31.0-50.4 GHz frequency range. One transition, 20,2-10,1, corresponds to
para-$l$-H2C3 and the other two, 21,2-11,1 and 21,1-11,0 are ortho-$l$-H2C3
transitions. The lines are shown in Fig.2 while the line parameters are
collected in Table 2. The position of the lines is consistent with the
calculated frequencies and the systemic velocity of the source, $V_{\rm LSR}$
= 5.83 km s-1 (Cernicharo et al. 2020). We assumed $T_{\rm r}=10$ K and the
column densities N(ortho-$l$-H2C3)=(1.5$\pm$0.5)$\times$1012cm-1 and
N(para-$l$-H2C3)=(4.0$\pm$1.2)$\times$1011cm-1. The ortho/para ratio is
calculated to be 3.8$\pm$1.1. Collisional rates are available for the system
l-H2C3/He (Khalifa et al. 2019). Adopting a volume density for TMC-1 of
4$\times$104 cm${}^{-}{3}$ (Cernicharo & Guélin 1987; Fossé et al. 2001) we
derive an excitation temperature for the two ortho transitions of $\sim$9 K,
and of $\sim$8.5 K for the para transition. Hence, the adopted rotational
temperature seems well adapted to the excitation conditions of this molecule.

Figure 2: Observed lines of $l$-H2C3 in TMC-1 in the 31.0-50.4 GHz range.
Curves shown in red are the computed synthetic spectra. Frequencies and line
parameters are given in Table 2.

The next member of the $l$-H2Cn family is $l$-H2C4. The rotational spectrum
for this cumulene was observed by Killian et al.  (1990) and Travers et al.
(1996). From ab initio calculations the dipole moment of $l$-H2C4 has been
estimated to be 4.1 D (Oswald & Botschwina 1995), similar to the smaller
cumulene carbene $l$-H2C3. The lines for ortho- and para-$l$-H2C4 are clearly
detected in our TMC-1 survey as can be seen in Fig. 3. However, it should be
noted that there are small discrepancies (of about 30 kHz for the para
species) between the observed and predicted frequencies from CDMS. We observed
a total of six rotational transitions with $J_{up}$ = 4 and 5 and $K_{\rm a}$
= 0 and 1. Four of them pertain to ortho-$l$-H2C4 and two to para-$l$-H2C4.
All the line parameters are given in Table 2. From the observed integrated
line intensities we obtained a $T_{\rm r}=10$ K and column densities for the
ortho and para species of N(ortho-$l$-H2C4)=(2.5$\pm$0.8)$\times$1012cm-1 and
N(para-$l$-H2C4)=(8.0$\pm$2.3)$\times$1011cm-1. The ortho/para ratio for
$l$-H2C4 is 3.1$\pm$0.9.

Figure 3: Observed lines of $l$-H2C4 in TMC-1 in the 31.0-50.4 GHz range.
Curves shown in red and green are the are the computed synthetic spectra using
the observed frequencies and the CDMS predictions, respectively. Frequencies
and line parameters are given in Table 2.

$l$-H2C6 is, to date, the larger cumulene carbene observed in space. Its
dipole moment is calculated (Maluendes & McLean 1992) to be larger than those
for the smaller cumulenes, with a value of 6.2 D. The rotational spectrum has
been investigated by McCarthy et al. (1997) and the derived spectroscopic
parameters are used to predict its transition frequencies. Due to its larger
molecular size, many rotational transition for $l$-H2C6 can be observed in the
31.0-50.4 GHz frequency range. As for all the other cumulene carbenes, and due
to its symmetry, it is necessary to discern between ortho- and para-$l$-H2C6.
Hence, we observed a total of twenty-one transitions for $l$-H2C6, fourteen
for ortho- and seven for para-$l$-H2C6 (see Fig. 4). Line parameters are
collected in Table 2. We derived from the observed integrated line intensities
a $T_{\rm r}=10$ K and the column densities
N(ortho-$l$-H2C6)=(6.0$\pm$1.8)$\times$1010cm-1 and
N(para-$l$-H2C3)=(2.0$\pm$0.6)$\times$1010cm-1. The ortho/para ratio is
calculated to be 3.0$\pm$0.9.

Figure 4: Observed lines of $l$-H2C6 in TMC-1 in the 31.0-50.4 GHz range.
Curves shown in red are the computed synthetic spectra. Frequencies and line
parameters are given in Table 2.

From our observations we obtain the following relative abundances for
$l$-H2C3/$l$-H2C4/$l$-H2C5/$l$-H2C6 in TMC-1, 344/561/1/4.4. $l$-H2C4 is the
most abundant cumulene carbene in TMC-1, followed by $l$-H2C3. The larger
species $l$-H2C5 and $l$-H2C6 are much less abundant compared to the shorter
cumulene chain, with $l$-H2C6 being 4.4 times more abundant than the odd
member $l$-H2C5. It is worth noting that, within the uncertainties, the four
cumelenes studied in this work have an ortho/para abundance ratio of 3. Hence,
no significant ortho to para conversion can be noticed for these molecules.

###  3.3 Chemistry of cumulene carbenes

In order to understand how cumulene carbenes $l$-H2Cn can be formed in TMC-1,
we carried out gas-phase chemical modeling calculations. We adopted typical
conditions of cold dark clouds, i.e., a volume density of H nuclei of 2
$\times$104 cm-3, a gas kinetic temperature of 10 K, a visual extinction of 30
mag, a cosmic-ray ionization rate of H2 of 1.3 $\times$ 10-17 s-1, and the so-
called set of low-metal elemental abundances (e.g., Agúndez & Wakelam 2013).
We used the chemical network RATE12 from the UMIST database (McElroy et al.
2013), updated with results from Lin et al. (2013), and expanded with the
subset of gas-phase chemical reactions revised by Loison et al. (2017) in
their study of the chemistry of C3H and C3H2 isomers.

Among the family of carbenes $l$-H2Cn, the one for which the chemistry is
better constrained is by far the smallest member $l$-H2C3, which has been
discussed in detail by Loison et al. (2017). This species is mainly formed
upon dissociative recombination with electrons of the linear and cyclic
isomers of C3H${}_{3}^{+}$, which in turn are formed through the radiative
association of C3H+ and H2. If we focus in the so-called early time, a few 105
yr, where gas-phase chemical models of cold dark clouds reproduce better TMC-1
observations (e.g., Agúndez & Wakelam 2013), the calculated abundance is about
one order of magnitude below the observed value (see Fig. 5), but the
calculated cyclic-to-linear abundance ratio agrees very well with the observed
value of 31 (Cernicharo et al. 2021a; this work). For members of the series
$l$-H2Cn with $n$ $>$ 3, information on the chemistry of the different
possible isomers is poorly known and thus chemical networks, such as UMIST
RATE12, do not distinguish between them. The calculated abundances of C4H2 and
C6H2 agree within a factor of 2-3 with the observed abundances of $l$-H2C4 and
$l$-H2C6, respectively (see Fig. 5), although one must keep in mind that
observations only refer to the cumulene while the model includes also other
isomers, in particular the more stable non-polar species HCnH. If the isomer
HCnH is significantly more abundant than H2Cn for n = 4,6 in TMC-1, then the
abundances calculated by the chemical model for C4H2 and C6H2 would be too
low. In the case of C5H2, the calculated peak abundance is about 30 times
lower than the observed abundance of $l$-H2C5 (see Fig. 5), although this may
not be a problem if the more stable isomer HC5H is substantially more abundant
than the carbene $l$-H2C5.

For $l$-H2Cn with $n$ $>$ 3, the chemical route analogous to that forming
$l$-H2C3 has variable degrees of efficiency. For example, formation of
C4H${}_{3}^{+}$ is relatively efficient thanks to the radiative association
between C4H${}_{2}^{+}$ and H (McEwan et al. 1999). For $n$ = 5, the route
does not work because C5H+ does not react with H2 (McElvany et al. 1987; Bohme
& Wlodek 1990), while formation of C6H${}_{3}^{+}$ is uncertain due to the
unknown reactivity of C6H${}_{2}^{+}$ with H2 (Anicich 2003). Further studies
of reactions involving hydrocarbon ions, in particular regarding isomer
differentiation, are highly desirable. According to the chemical model,
reactions of CnH- anions with H atoms are a major route to CnH2 molecules,
such as C4H2, C5H2, and C6H2. These reactions have been studied in the
laboratory for anions CnH- with $n$ = 2, 4, 6, and 7 and have been found to be
rapid and to yield CnH2 as main product (Barckholtz et al. 2001). The reaction
with $n$ = 5, although not studied, is likely to behave similarly. It is
however unknown whether the carbene isomer H2Cn or the more stable HCnH is
preferentially formed. It would be very helpful to investigate this particular
point.

Other formation routes, apart from CnH${}_{m}^{+}$ \+ e- and CnH- \+ H, can be
provided by neutral-neutral reactions. For example, the chemical model points
to the reaction between atomic C and the propargyl radical (CH2CCH), recently
detected in TMC-1 (Agúndez et al. 2021), as a source of C4H2 isomers. This
reaction is assumed to be fast by Loison et al. (2017), but calculations of
the rate coefficient and product distribution at low temperatures are needed.
Similarly, the reaction C + C4H3 is assumed to proceed fast by Smith et al.
(2004) and provides an important route to C5H2 isomers, but more detailed
studies on this reaction are necessary. Finally, we note that the cyclic C5H2
isomer $c$-C3HCCH recently detected by Cernicharo et al. (2021a) is most
likely formed through the reaction between CCH and $c$-C3H2.

Figure 5: Calculated fractional abundances of various hydrocarbons as a
function of time. The symbol $*$ in the legend means that the chemical model
does not distinguish between different isomers. The abundances observed in
TMC-1 for $c$-C3H2 (Cernicharo et al. 2021a) and $l$-H2Cn with $n$ = 3-6 (this
work) are indicated by dashed horizontal lines.

###### Acknowledgements.

This research has been funded by ERC through grant
ERC-2013-Syg-610256-NANOCOSMOS. Authors also thank Ministerio de Ciencia e
Innovación for funding support through projects AYA2016-75066-C2-1-P,
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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