Carbon-Chain Chemistry in the Interstellar Medium

The presence of carbon-chain molecules in the interstellar medium (ISM) has been known since the early 1970s and $>130$ such species have been identified to date, making up $\sim 43$% of the total of detected ISM molecules. They are prevalent not only in star-forming regions in our Galaxy but also in other galaxies. These molecules provide important information on physical conditions, gas dynamics, and evolutionary stages of star-forming regions. Larger species of polycyclic aromatic hydrocarbons (PAHs) and fullerenes (C$_{60}$ and C$_{70}$), which may be related to the formation of the carbon-chain molecules, have been detected in circumstellar envelopes around carbon-rich Asymptotic Giant Branch (AGB) stars and planetary nebulae, while PAHs are also known to be a widespread component of the ISM in most galaxies. Recently, two line survey projects toward Taurus Molecular Cloud-1 with large single-dish telescopes have detected many new carbon-chain species, including molecules containing benzene rings. These new findings raise fresh questions about carbon-bearing species in the Universe. This article reviews various aspects of carbon-chain molecules, including observational studies, chemical simulations, quantum calculations, and laboratory experiments, and discusses open questions and how future facilities may answer them.


Brief Overview of Astrochemistry
Astrochemistry is an interdisciplinary research field concerning "study of the formation, destruction, and excitation of molecules in astronomical environments and their influence on the structure, dynamics, and evolution of astronomical objects" (Dalgarno 2008). Astrochemical studies can involve various approaches: astronomical observations; laboratory experiments on reactions and diagnostic spectroscopy; chemical simulations; and quantum chemical calculations. Fig. 1 Carbon-chain growth (for number of C ≤ 4) and formation processes of HC5N and CCS in early stages of molecular clouds (t < 10 4 yr). The dashed arrow from l, c−C3H to CCH indicates that this reaction is important around 10 5 yr. could efficiently form in young molecular clouds before carbon is locked into CO molecules.
In the 1990s, carbon-chain molecules were detected in many molecular clouds, beyond the previously well-studied examples, such as TMC-1. Survey observations revealed that carbon-chain molecules are evolutionary indicators of starless and star-forming cores in low-mass star-forming regions (Suzuki et al. 1992;Benson et al. 1998). These studies reinforced the view that these molecules are formed from ionic (C + ) or atomic (C) carbon in the early stages of molecular clouds, before CO formation, as predicted by chemical simulations. Figure 1 shows the carbon-chain growth and formation pathways of nitrogen-and sulfur-bearing species (HC3N, HC5N, and CCS), which have been frequently detected in lowmass starless cores in the early stages of molecular cloud cores. These reaction schemes are constructed from results of the latest chemical simulations with a constant temperature of 10 K and a constant density of nH = 10 4 cm −3 in t < 10 4 yr (Taniguchi et al. 2019b). Hydrocarbons can form efficiently from C + and C via ion-molecule reactions involving H2 and dissociative recombination reactions leading to the formation of neutral hydrocarbons. Such carbon-chain chemistry in cold molecular clouds is basically consistent with that proposed in the 1980s.
During the later stages of starless cores, carbon-chain species are adsorbed onto dust grains or destroyed by reactions with atomic oxygen. These processes result in the depletion of carbon-chain species by the later stages of prestellar cores and protostellar cores. Thus, carbon-chain molecules were classically known as "early-type species".
Subsequent studies found that carbon-chain species exist in lukewarm regions (T ≈ 25 − 35 K) around low-mass protostars, and a new carbon-chain formation mechanism starting from CH4 was proposed (see Section 2.4). This was named Warm Carbon-Chain Chemistry (WCCC) and a review article about it was published ten years ago (Sakai & Yamamoto 2013). More recently, carbon-chain chemistry around massive young stellar objects (MYSOs) has been explored (Section 2.5), and Hot Carbon-Chain Chemistry (HCCC) has been proposed. Furthermore, very complex carbon-chain species, branched-chain molecules, and molecules including benzene rings, have been discovered in the ISM in the last few years. These new findings bring fresh challenges and excite our curiosity for a deeper understanding of carbon-chain chemistry in the ISM.

Outline of This Review
In this review article, we summarize results from studies of carbon-chain molecules by astronomical observations, chemical simulations, quantum chemical calculations, and laboratory experiments. In Section 2, we overview the current status of the detected carbon-chain species in the ISM and the main concepts of carbon-chain chemistry around protostars. We review observational studies (Section 3), chemical models (Section 4), quantum chemical calculations (Section 5), and laboratory experiments (Section 6). Finally, we list current open and key questions regarding carbon-chain species and summarise in Section 7.
Here, we set a definition of "carbon-chain molecules" for this review article, as recent detections of new interstellar species complicates this categorization. We include linear carbon-chain species with more than two carbon atoms and cyclic species with more than three carbon atoms containing at least one double (-=-) or triple (-≡-) bond as carbon-chain molecules. Even if molecules meet the above criteria, species containing functional groups related to organic chemistry (e.g., -OH, -NH2) are excluded from carbon-chain molecules, because they are generally categorized as COMs. As an exception, cyclic-C2Si, which consists of a cyclic structure with two carbon atoms and one Si atom, is treated as a carbon-chain species. In addition to straight linear carbon-chain species, we also treat branched carbon-chain species (e.g., iso-propyl cyanide) as carbon-chain molecules. Molecules containing the structure of benzene, polycyclic aromatic hydrocarbons (PAHs), and fullerenes (C60 or C70) are also included. In the following sections, we abbreviate linearand cyclic-as l-and c-, if necessary to indicate the molecular structure (e.g., l-C3H2 and c-C3H2). This review article summarizes literature results until the end of December 2022.

Detection of Carbon-Chain Species in the ISM and CSEs
Cyanoacetylene (HC3N), the shortest cyanopolyyne (HC2n+1N), was the first carbon-chain molecule detected in space. It was found toward a high-mass star-forming complex, Sagittarius B2 (Sgr B2, Turner 1971). Following this, two new carbon chains, CH3CCH (Buhl & Snyder 1973) and C2H (Tucker et al. 1974) were detected, which belong to the hydrocarbons family. The next higher-order cyanopolyyne, cyanodiacetylene (HC5N), was identified toward Sgr B2, i.e., the same region where HC3N was first observed (Avery et al. 1976). In the following year, C2 was detected toward Cygnus OB2 No.12 via electronic spectra (Souza & Lutz 1977).
Observations of carbon-chain species also expanded to other star-forming regions and HC3N was detected toward various types of sources. For instance, it was identified toward Heiles cloud 2 (TMC-1 ridge is part of Heiles cloud) (Morris et al. 1976), and HC5N was found to be abundant in the same region (Little et al. 1977). The detections of the longer-chain, higher-order cyanopolyynes, HC7N, and HC9N, were also reported toward TMC-1 Broten et al. 1978). Around the same time, C3N, C4H, and CH3CCH were also found toward dark clouds, including TMC-1 (Friberg et al. 1980;Guelin et al. 1978;Irvine et al. 1981). The discoveries of several carbon-chain species in the ISM brought curiosity and opened a new field to be investigated further. Several years later, HC11N was tentatively identified toward TMC-1 (Bell & Matthews 1985). However, it took more than three decades to confirm its presence in the same source .

Different carbon-chain families and their present status
All of the carbon-chain species belonging to the various groups, Cn, CnH, CnH − , CnO, CnN, CnN − , CnS, CnP, HC2n+1N, HC2nN, HCnO, HCnS, HCnH, MgCnH, MgCnN, are summarized in Table 1. Here information is given on their electronic ground state, electric polarizability, electric dipole moment, and present astronomical status.

Pure carbon chains -Cn
All pure linear carbon chains are indicated as Cn (n > 1). The electronic ground state of all these species is singlet, and they do not have a permanent dipole moment (see Table 1). Hence, they do not show rotational transitions, and so are not detectable via rotational transitions using radio observations. Instead, they show emission in the infrared domain through their vibration-rotation transitions, and so far three chains (n = 2, 3, 5) are astronomically detected from this group (see Section 2.1). In diffuse and translucent environments, C2 formation starts with the reaction of C + + CH → C + 2 + H, followed by a series of hydrogen abstraction reactions and dissociative recombination reactions that yield C2 via several channels (Welty et al. 2013, and reference therein). C3 is formed via a dissociative recombination reaction of C3H + , though neutral-neutral reactions (e.g., C + C2H2 ) may also contribute (Roueff et al. 2002).

Hydrocarbons -CnH
The CnH group represents the simplest hydrocarbons and carbon-chain radicals. All carbon chains from this group have permanent dipole moments and show strong rotational transitions. To date, eight neutral (n = 1 − 8) carbon-chain species have been detected from this group. All of them have been identified towards both TMC-1 and IRC+10216. Apart from neutrals, three anions (C4H − , C6H − , and C8H − ) and two cations (C3H + and C5H + ) have also been identified. The anions belong to the even series (n = 2, 4, 6), while the cations belong to the odd series (n = 3, 5). In addition, two cyclic chains, c-C3H, and c-C5H, have been identified. All neutral species have a doublet ground state and show a trend of increasing dipole moment with the number of carbon atoms (n), especially for neutrals and anions (see Table 1). The CnH family is mainly formed through the atomic reactions in the following channel, C + Cn−1H2 → CnH + H (Remijan et al. 2023). Another two channels, which involve atomic and their related anions, can also form CnH family species efficiently: C + Cn−1H − → CnH + e − and H + C − n → CnH + e − .

Oxygen-bearing carbon chains -CnO
To date, three oxygen (O)-bearing carbon chains, CnO (n = 2, 3, 5) have been detected in the ISM. In this series, C3O was the first, detected toward TMC-1 in 1984, while C2O was identified in the same source in 1991. It took around three decades to detect the higher-order chain, C5O, in TMC-1. C4O is yet to be detected. Carbon chains in this group have alternate ground states, i.e., triplet and singlet, and show a trend of increasing dipole moment with the number of carbon atoms (see Table 1). A protonated species, HC3O + with singlet ground state, has been detected in TMC-1. The observed trend toward TMC-1 shows that C3O is the most abundant, followed by C2O and C5O, with C5O about 50 times less abundant than C2O and about 80 times less abundant than C3O (Cernicharo et al. 2021a). In addition, all these species have been identified towards the circumstellar envelope of IRC+10216. The formation of CnO and HCnO chains follows similar formation mechanisms as discussed above. The first step involves the radiative association of Cn−1H + , Cn−1H + 2 , and Cn−1H + 3 ions with CO, which is then followed by dissociative electron recombination reactions (Adams et al. 1989;Cernicharo et al. 2021a).

Sulfur-bearing carbon chains -CnS
Similar to CnO, several sulfur (S)-bearing carbon chains, CnS (n = 2, 3,4,5), have been identified in the ISM. These species have been detected toward TMC-1 and IRC+10216. Two protonated species, HCCS + and HC3S + , have only been detected towards TMC-1 so far. Carbon chains in this group have alternative ground states, i.e., triplet and singlet, and show a trend of increasing dipole moment with the number of carbon atoms, similar to the CnO group (see Table  1). The abundances of C2S and C3S are almost three orders of magnitude higher than C4S and C5S toward TMC-1 (Cernicharo et al. 2021f). On the other hand, the C5S column density is slightly less than those of C2S and C3S, with differences less than one order of magnitude, toward IRC+10216 (Agúndez et al. 2014). C2S and C3S are mainly produced via several ion-neutral reactions followed by electron recombination reactions and via several neutral-neutral reactions (Sakai et al. 2007). Higher order chains of this family, such as C4S and C5S, are thought to be formed via reactions of S + C4H and C + HC3S, and C4H + CS and S + C5H, respectively. However, the kinematics and product distribution of these reactions is poorly known (Cernicharo et al. 2021f).

Nitrogen-bearing carbon chains -CnN
In this group, C3N was the first detected species, done so tentatively toward IRC+10216 in 1977 and more robustly toward TMC-1 in 1980. The next higher order chain in this series, C5N was detected toward TMC-1 and tentatively detected toward IRC+10216 in 1998. The lower order chain, CCN, was found in 2014. Their anions, C3N − and C5N − , were discovered in the circumstellar envelope of the carbon-rich star IRC+10216 Cernicharo et al. 2008). They have also been identified toward TMC-1 by the QUIJOTE group, including their neutral analogs (C3N, C5N) (Cernicharo et al. 2020c). They measured similar abundance ratios of C3N − /C3N = 140 and 194, and C5N − /C5N = 2 and 2.3 in TMC-1 and IRC+10216, respectively, which may indicate similar formation mechanisms in these interstellar and circumstellar environments. However, physical conditions are completely different for TMC-1 and IRC+10216, and it might be a coincidence that there are similar abundance ratios of anion and neutral forms of CnN (n = 3,5). All carbon chains from this group have doublet ground state, and the two anionic forms have singlet state. The dipole moment of CCN is low compared to those of C3N, C5N, and their anionic forms, which helps explain the later, more challenging detection of CCN, even though it is of lower order in the chain (see Table 1). C4N, C6N, and C7N show even smaller values of their dipole moments, which suggests that much high sensitivity observations are required for their identification. C2N is produced through the reactions of N + C2 and C + CN. Similarly, C3N is produced in reactions of N + C3 and C + CCN, and C5N is produced through N + C5 on dust surfaces 3 . The production of C3N − mainly comes from the reaction between N atoms and bare carbon-chain anions C − n (Cernicharo et al. 2020c), whereas C5N − is produced via the electron radiative attachment to C5N (Walsh et al. 2009).

Phosphorus-bearing carbon chains -CnP
Although phosphorus (P) has a relatively small elemental abundance, it plays a crucial role in the development of life. Among the known eight phosphorus-bearing molecules, C2P (or CCP) is the only P-bearing carbon-chain species. It has been detected toward IRC+10216 (Halfen et al. 2008). All carbon chains in this group have doublet ground states (Table  1). Higher order chains, C3P and C4P, show a higher value of dipole moments, but they are yet to be detected in the ISM or circumstellar environments. Since the overall elemental abundance of phosphorous is small, higher-order phosphorous chains are expected to have very low abundances. CCP may be produced by radical-radical reactions, between CP and hydrocarbons (CCH and C3H), or ion-molecule chemistry involving P + and HCCH followed by the dissociative electron recombination reaction (Halfen et al. 2008).

HCnO family
Four neutral HCnO (n = 2, 3, 5, 7) chains have been identified toward TMC-1. The detection summary of this group indicates odd n chains are more abundant compared to their even n counterparts. This trend is the same as in the CnO family. All neutral chains have doublet ground states and dipole moment values are less than 3 Debye. The observed cation HC3O + has a singlet ground state and a dipole moment of 3.41 Debye (see Table 1). As mentioned before, CnO and HCnO are linked through their formation routes (sec Sec. 2.2.3).

HCnS family
This family is similar to HCnO but contains sulfur instead of oxygen. Only two neutral species, HCCS and HC4S have been identified toward TMC-1. Observed statistics suggest chains with even n have higher abundance than odd n species. All neutral chains of this group have doublet ground states (see Table 1). The dipole moments of neutral species are less than 2.2 Debye. HCCS is mainly formed through the reaction, C + H2CS (Cernicharo et al. 2021f). HC4S is produced through the reaction between C and H2C3S and by the dissociative recombination reaction of H2C4S + , which is formed via reactions of S + C4H + 3 and S + + C4H3 (Fuentetaja et al. 2022b). For HC3S + , proton transfer to C3S from HCO + and H3O + is the main formation route. The reactions of S + + c, l − C3H2 and S + c, l − C3H3 are also equally important and efficient (Cernicharo et al. 2021e).

Allenic chain family -HC2nN
HCCN was the first member of the allenic chain family, HC2nN, observed in space (Guelin & Cernicharo 1991), and HC4N was the second. These species have been identified toward IRC+10216. The allenic chain family has a triplet ground state and shows increasing dipole moment with size, similar to cyanopolyynes and other families ( Table 1). HC4N may form through the reactions of C3N + CH2 and C3H + HCN. For this family, ion-molecule paths are relatively slow (Cernicharo et al. 2004). HCCN is formed by the reactions between atomic nitrogen and HnCCH + .

Statistics of Detected Species
More than 270 individual molecular species have been identified in the ISM and circumstellar envelopes by astronomical observations (CDMS 4 , McGuire (2022)). Most of them are observed in the gas phase via their rotational transition lines, and very few of them are observed in the solid phase. Carbon is the fourth most abundant element in the Galaxy and plays a pivotal role in interstellar chemistry. A large part of interstellar dust grains is also made of carbon. A variety of carbon-chain species have been identified in the space ranging from simple linear chains to cyclic and PAHs. Figure 2 shows the cumulative plot of carbon-chain detection together with the histogram plot in each year starting from 1971, the first carbon-chain detection year, until 2022. The lower panel shows the carbon-chain species including molecules containing benzene rings and fullerenes, and the upper panel depicts the plot excluding these species. Following the definition mentioned earlier in Section 1.3, 118 carbon-chain species have been discovered so far. This accounts for 43% of all the known 270 molecules. If we exclude benzene ring and PAH-type molecules, the number goes down to 101, which means that 37% of all known molecules in the ISM and circumstellar shells belong to the linear/bending and cyclic carbon-chain species. Figure 3 illustrates the detection statistics of all known carbon-chain species per decade starting from the 1970s. We show the summary of all detected carbon-chain species in two pie charts, one including all detected carbon-chain species (right panel) and another including all species except molecules containing benzene rings and fullerenes (left panel). The left chart shows detection rates of 11% in the 1970s, 17% in the 1980s, 12% in the 1990s, 12% in the 2000s, 11% in the 2010s, and 37% in the 2020s (only 2020-2022). The right chart shows detection rates of 9% in the 1970s, 15% in the 1980s, 11% in the 1990s, 11% in the 2000s, 12% in 2010, and 42% in the 2020s (2020-2022). The detection rate in the 2020s becomes larger in the right chart compared to the left chart, meaning that molecules containing benzene ring(s) have been discovered in the last two years (Section 3.1.1).
In summary, there has been a dramatic change in discovered carbon-chain species in the 2020s. It shows the detection of carbon-chain species in each decade was almost similar starting from the 1970s to 2010s. Around 50 (38) molecular species (if we exclude molecules containing benzene rings and fullerenes) have been detected in the last three years (2020-2022), i.e., the detection rate is 42% (37%). Most of the PAH-type species are discovered in this period. A point that we would like to emphasize is that we have just only three years and the number in this decade is still increasing. All known/detected and unknown/possible candidates for future detection carbon-chain species are summarized and noted in Table 1.

Warm Carbon-Chain Chemistry (WCCC)
In Section 1.2, we mentioned that carbon-chain molecules have been classically known as early-type species, because they are abundant in young starless cores and deficient in evolved star-forming cores. Against this classical picture, Sakai et al. (2008) detected various carbon-chain molecules from IRAS 04368+2557 in the low-mass star-forming region L1527. The derived rotational temperature from the C4H2 lines is 12.3 ± 0.8 K, which is higher than excitation temperatures of carbon-chain species in the starless core TMC-1 (≈ 4 − 8 K). They proposed that evaporation of CH4 from ice mantles could be the trigger of formation of carbon-chain molecules in the lukewarm envelopes around low-mass protostars, and named such a carbon-chain formation mechanism "Warm Carbon-Chain Chemistry (WCCC)". A second WCCC source, IRAS 15398-3359 in the Lupus star-forming region, was discovered soon after (Sakai et al. 2009). This suggested that the WCCC mechanism may be a common feature around low-mass protostars.
Later studies using chemical simulations confirmed the formation mechanism of carbon-chain molecules starting from CH4 around temperatures of 25-30 K (Hassel et al. 2008). The CH4 molecules react with C + in the gas phase to produce C2H3 + or C2H2 + . The C2H2 + ion reacts with H2 leading to C2H4 + . Then, electron recombination reactions of C2H3 + and C2H4 + produce C2H2. Regarding WCCC, the review article by Sakai & Yamamoto (2013) summarized related studies in detail. We thus avoid duplication here.
However, an important question has been raised since the review of Sakai & Yamamoto (2013), namely, the origin(s) of WCCC sources, which is still controversial. The focus is on how CH4-rich ice is formed. This means that carbon atoms need to be adsorbed onto dust grains without being locked up in CO molecules. Sakai et al. (2008) proposed one possible scenario that shorter collapse times of prestellar cores may produce conditions needed for WCCC sources. On the other hand, Spezzano et al. (2016) suggested that variations in the far ultraviolet (FUV) interstellar radiation field (ISRF) could produce carbon-chain-rich or COM-rich conditions, based on their observational results toward the prestellar core L1544. They found a spatial distribution of c-C3H2 in a region relatively exposed to the ISRF, while CH3OH was found in a relatively shielded region. In this scenario, the FUV ISRF destroys CO, a precursor of CH3OH, leading to formation of C and/or C + , precursors of carbon-chain species. Spezzano et al. (2020) also found similar trends with observations of c-C3H2 and CH3OH toward six starless cores. They concluded that the large-scale effects have a direct impact on the chemical segregation; c-C3H2 is enhanced in the region more illuminated by the ISRF, whereas CH3OH tends to reside in the region shielded from the ISRF. Such chemical segregation observed in starless cores may be inherited to the protostellar stage and recognized as the different classes of WCCC protostars and COM-rich hot corinos. Recently, several authors investigated the effects of these factors on the abundances of carbon-chain species and COMs by chemical simulations (Aikawa et al. 2020;Kalvāns 2021). We discuss their model results in detail in Section 4.

Concept of Hot Carbon-Chain Chemistry
The discovery of the WCCC mechanism around low-mass protostars naturally raised a question: are carbon-chain molecules also formed around high-mass (m * > 8M ) protostars? With such a motivation, observations and chemi-

Excluding molecules including benzene rings and fullerene
All of the carbon-chain species Fig. 2 The number of detected carbon-chain species in each year (blue bars) and its cumulative plot (red curves and numbers). The upper panel shows those excluding molecules including benzene rings and fullerene, while the lower one shows those including them. Numbers indicated in the red font in 2022 are the total detected carbon-chain species until the end of 2022.

Excluding molecules including benzene rings and fullerene
All of the carbon-chain species   Taniguchi et al. (2019a). We distinguish HCCC from WCCC depending on the temperature. The HCCC mechanism refers to carbon-chain formation in the gas phase, adsorption onto dust grains, and accumulation in ice mantles during the warm-up phase (25 K < T < 100 K), followed by evaporation into the gas phase in the hot-core stage (T > 100 K). This mechanism is particularly important for cyanopolyynes (HC2n+1N). Cyanopolyynes are relatively stable species because of no dangling bond, and they are not destroyed by reactions with O or H2, which are destroyers of other carbon-chain species with dangling bonds. Instead, cyanopolyynes are consumed by reactions with ions such as HCO + and other protonated ions in the gas phase. Thus, the destruction rates of cyanopolyynes in the gas phase are lower than those of the other carbon-chain species, which enables cyanopolyynes to then be adsorbed onto dust grains.
During the warm-up stage, cyanopolyynes are efficiently formed by the gas-phase reactions between C2nH2 and CN.
The formed cyanopolyynes are then adsorbed onto dust grains and accumulated in ice mantles. When conditions reach their sublimation temperatures above 100 K, the species sublimate into the gas phase and their gas-phase abundances show peaks.
Other radical-type species, such as CCH and CCS, would not behave as cyanopolyynes do, because they are efficiently destroyed by the gas-phase reactions with O or H2 (Taniguchi et al. 2019a). Their gas-phase peak abundances are reached just after WCCC starts to form them around 25 K, and decrease as the temperature increases. Thus, we expect that radical-type carbon-chain species are abundant in the lukewarm regions and deficient in the hot-core regions, whereas the emission of cyanopolyynes is expected to show their peak at the hot-core regions, similar to the emission of COMs. If we admit these two types of carbon-chain species, then radical-type species would be recognized as "WCCC tracers", whereas cyanopolyynes would be regarded as "HCCC tracers". The difference between WCCC and HCCC is that WCCC only refers to the carbon-chain formation starting from CH4, which is important in lukewarm regions (25-35 K), while HCCC includes successive processes from the warm regions (T ≈ 25 − 100 K) to the hot-core region (T > 100 K).
The points of this section are summarized below.
1. Carbon-chain molecules account for around 40% of the interstellar molecules. These molecules have been detected in the ISM since the 1970s, and an increased number of reported detections made by recent Green Bank 100m telescope (GBT) and Yebes 40m telescope observations are astonishing. 2. WCCC refers to the carbon-chain formation mechanism in the lukewarm gas (T ≈ 25 − 35 K) starting from CH4 desorbing from dust grains around 25 K. The gas-phase reaction between CH4 and C + is the trigger of the WCCC mechanism. 3. HCCC refers to the gas-phase carbon-chain formation and adsorption and accumulation in ice mantles during the warm-up phase (T < 100 K), and their sublimation in the hot-core phase (T > 100 K).

Carbon-Chain Molecules in TMC-1
Taurus Molecular Cloud-1 (TMC-1) is one of the most well studied dark clouds (e.g., Kaifu et al. 2004). Its "Cyanopolyyne Peak" (hereafter TMC-1 CP) is the famous site where carbon-chain molecules are particularly abundant ( Figure 5). Many carbon-chain molecules were discovered from this dark cloud by radio astronomical observations (Section 2.1). Dobashi et al. (2018) identified four velocity components (vLSR = 5.727, 5.901, 6.064, and 6.160 km s −1 ) with very high velocity resolution (0.0004 km s −1 ) spectra of the CCS and HC3N lines in the 45 GHz band obtained by the Z45 receiver (Nakamura et al. 2015) installed on the Nobeyama 45m radio telescope. They revealed the gas kinematics of the TMC-1 filament and it was found that these velocity components are moving inward toward the center of the TMC-1 filament. Dobashi et al. (2019) identified 21 subfilaments in the TMC-1 filament using CCS (JN = 43 −32; 45.379033 GHz) line data. They found that the subfilaments have line densities that are close to the critical line density for dynamical equilibrium (∼ 17M pc −1 ). These results indicate that self-gravity is important in the dynamics of the subfilaments. The CCS (JN = 43 − 32) line was also used for measurement of the line-of-sight magnetic field strength by its Zeeman splitting (Nakamura et al. 2019). The derived magnetic field strength is ∼ 117 ± 21 µG, which leads to a conclusion that the TMC-1 filament is magnetically supercritical. As these studies show, rotational-transition lines of carbon-chain species are useful to investigate physical conditions of starless cores.
Two research groups have been carrying out line survey observations toward TMC-1 CP and have reported the detection of new interstellar molecules. Their discoveries are still ongoing during the writing of this review article. We briefly summarized the detection of carbon-chain molecules in Section 2.3, and here we mention their groundbreaking results in more detail.
One project is GOTHAM (GBT Observations of TMC-1: Hunting Aromatic Molecules 5 ) using the Green Bank 100m telescope led by Dr. Brett A. McGuire. This project is a high sensitivity (2 mK) and high velocity resolution (0.02 km s −1 ) spectral line survey in the X, K, and Ka bands (see Fig. 5). The beam sizes (FWHM) are 1.4 , 32 , and 26.8 for the X-Band receiver, KFPA, and Ka-Band (MM-F1) receiver, respectively 6 . They have analyzed spectra using the  spectral line stacking and matched filter methods (Loomis et al. 2018b utilizing the velocity information derived by Dobashi et al. (2018), and achieved detection of new, rare interstellar molecules.
McGuire et al. (2021) detected two polycyclic aromatic hydrocarbons (PAHs), 1-and 2-cyanonaphthalene, containing two rings of benzene via spectral matched filtering. Their molecular structures are shown in Figure 5. The nitrile bond (-CN) makes the dipole moment larger, thus aiding the detection of benzonitrile (c-C6H5CN), the first detected species with a benzene ring (McGuire et al. 2018). Benzonitrile has also been detected in other sources: Serpens 1A, Serpens 1B, Serpens 2, and L1521F (Burkhardt et al. 2021a). Although the detection of a pure PAH was considered to be difficult due to their small dipole moments, Burkhardt et al. (2021b) achieved the detection of indene (c-C9H8). McCarthy et al.

Revealing Main Formation Pathways of Carbon-Chain Molecules by 13 C Isotopic Fractionation
Since carbon-chain molecules are unstable even in vacuum chambers on the Earth, it is difficult to conduct laboratory experiments about their reactivity. Instead, the observed 13 C isotopic fractionation of carbon-chain molecules and the relative differences in abundance among the 13 C isotopologues was proposed to be a key method for revealing their main formation mechanisms (Takano et al. 1998). The 13 C isotopic fractionation is effective only in low-temperature conditions as it depends mainly on isotope exchange reactions, whose backward reactions can proceed only at warm or high temperatures. The elemental 12 C/ 13 C abundance ratio in the local ISM is around 60-70 (e.g., Milam et al. 2005). Hence, high-sensitivity observations are necessary to detect the 13 C isotopologues of carbon-chain molecules with high enough signal-to-noise (S/N) ratios to compare their abundances (i.e., S/N> 10). With these constraints, TMC-1 CP is the most promising target source, because of the low-temperature condition (T ≈ 10 K) and high abundances of carbon-chain molecules (Section 3.1.1). In fact, TMC-1 CP has the largest number of carbon-chain species investigated for 13 C isotopic fractionation. Thanks to developing observational facilities, larger molecules can be investigated within reasonable observing times. The same method has also been applied for other molecular clouds and envelopes around YSOs. In this subsection, we review such studies conducted in dark clouds.
Three cyanopolyynes have been investigated at TMC-1 CP; HC3N (Takano et al. 1998), HC5N (Taniguchi et al. 2016a), and HC7N . Takano et al. (1998) observed the three 13 C isotopologues of HC3N (H 13 CCCN, HC 13 CCN, and HCC 13 CN) using the Nobeyama 45m radio telescope. The relative abundance ratios of the three 13 C isotopologues were derived to be 1.  Table 2 summarizes correspondences of the possible main formation pathway of HC3N and its expected 13 C isotopic fractionation (Taniguchi et al. 2017a). Regarding the last one (the electron recombination reaction of HC3NH + ), various formation pathways of the HC3NH + ion should compete, and then clear 13 C isotopic fractionation would not be seen in HC3NH + , as well as HC3N. The reaction between of "C2H2 + CN → HC3N +H" can explain the observed 13 C isotopic fractionation in TMC-1 CP.
At the time five 13 C isotopologues of HC5N were detected (Takano et al. 1990) there was no evidence for the 13 C isotopic fractionation, because S/N ratios were low. More than 25 years later, Taniguchi et al. (2016a) successfully detected the lines of the five 13 C isotopologues of HC5N (J = 9 − 8 and 16 − 15 at 23 GHz and 42 GHz bands, respectively) with S/N ratios of 12-20. The derived abundance ratios among the five 13 C isotopologues of HC5N are 1.00 : 0  Taniguchi et al. (2016a) proposed that the reactions between hydrocarbon ions (C5Hm + ; m = 3 − 5) and nitrogen atoms, followed by electron recombination reactions are the most possible main formation mechanism of HC5N at TMC-1 CP. Burkhardt et al. (2018) detected six 13 C isotopologues of HC7N and five 13 C isotopomers of HC5N using the Green Bank 100m telescope. H 13 CC6N could not be detected in their observations. They found no significant difference among the 13 C isotopomers of HC7N, as similar to the case of HC5N. They concluded that the significant formation route for HC7N is the reaction of hydrocarbon ions and nitrogen atoms, which is the same conclusion for HC5N by Taniguchi et al. (2016a).
HC3N has been investigated in two other starless cores, L1521B and L134N (L183) (Taniguchi et al. 2017a). Their observational results show different fractionation patterns between the two sources. The 13 C isotopic fractionation in L1521B is similar to that in TMC-1 CP; HCC 13 CN is more abundant than the others, and the other two 13 C isotopologues have similar abundances. On the other hand, the results in L134N are different from TMC-1 CP and L1521B; the abundance ratios in L134N are 1.5 (±0.  Table 2 summarizes the names of molecular clouds that were suggested to have each main formation route. Based on these classifications (Table 2), the main formation mechanisms of HC3N are determined as the reactions of C2H2 + CN in L1521B and CCH + HNC in L134N. The C 13 CH/ 13 CCH abundance ratio was found to be > 1.4 in L134N (Taniguchi et al. 2019b), which agrees with the abundance ratio of 1.5 (±0.2): 1.0 for [H 13 CCCN]: [HC 13 CCN]. This is further supporting evidence for the conclusion that the main formation pathway of HC3N includes CCH in L134N. The difference between L134N and TMC-1CP/L1521B is probably brought about by different HNC/CN abundance ratios (HNC/CN = 35.6 and 54.2 in TMC-1 CP and L134N, respectively). The HNC/CN abundance ratio depends on the cloud's age, and then the main formation mechanism of cyanopolyynes likely changes over the course of the cloud's evolution.
In addition to cyanopolyynes, CnS (n = 2,3) and C2nH (n = 1,2) have been studied for 13 C fractionation in TMC-1 CP (Sakai et al. 2007(Sakai et al. , 2010. Sakai et al. (2007) detected the lines of 13 CCS and C 13 CS (JN = 21 − 10, F = 5/2 − 3/2). The abundance ratio of C 13 CS/ 13 CCS was derived to be 4.2 ± 2.3 (3σ). They proposed that the reaction between CH and CS is the main formation route of CCS in TMC-1 CP. The abundance ratio of C 13 CH/ 13 CCH was derived to be 1.6 ± 0.4 (3σ) (Sakai et al. 2010). To explain the abundance difference between the two 13 C isotopomers of CCH, Sakai et al. (2010) proposed that the reaction of CH + C is the main formation mechanism of CCH at TMC-1 CP.
Unlike cyanopolyynes, the 13 C isotopic fractionation of CCS and CCH does not necessarily provide information on their main formation mechanisms. Furuya et al. (2011) ran chemical simulations including 13 C and investigated effects of the isotopomer-exchange reactions. They considered the following two isotopomer-exchange reactions for CCH and CCS, respectively: 13 CCH + H C 13 CH + H + 8.1K; (1) and 13 CCS + S C 13 CS + S + 17.4K.
They also included the following neutral-neutral exchange reaction of CCS to reproduce the observed isotopomer ratio of CCS: 13 CCS + H C 13 CS + H + 17.4K.
This reaction is regarded as a catalytic reaction by the hydrogen atom. At low temperature conditions (T ≈ 10 K), C 13 CH and C 13 CS should be more abundant than the other 13 C isotopomers by Reactions (1) - (3). Their model results can explain the observed abundance differences between the two 13 C isotopomers of CCH and CCS in TMC-1 CP (Sakai et al. 2007(Sakai et al. , 2010. It was found that C 13 CH is more abundant than 13 CCH in the other starless cores (L1521B and L134N; Taniguchi et al. 2017a), and such a character may be common for cold dark clouds. Such exchange reactions may contribute to larger species such as C3S and C4H ).

Dilution of the 13 C species
From the observations deriving the 13 C isotopic fractionation of carbon-chain species in dark clouds, dilution of the 13 C species is inferred, i.e., the 12 C/ 13 C ratios of carbon-chain molecules are higher than the local elemental abundance ratio (60-70; Milam et al. 2005). The variations of the 12 C/ 13 C ratios of carbon-chain species could give another hint about carbon-chain chemistry in dark clouds. This is caused by the following reaction (e.g., Langer et al. 1984): The backward reaction is ineffective in cold-temperature conditions (∼ 10 K), and then the abundance of 13 C + should decrease. Ionic and atomic carbons (C + and C) are the main parent species of carbon-chain molecules and the low abundance of 13 C + results in deficient 13 C isotopologues of carbon-chain molecules. Table 3 summarizes the 12 C/ 13 C ratios of carbon-chain molecules derived in three starless cores: TMC-1 CP; L1521B; and L134N. From Table 3, the following tendencies can be inferred: 1. Cyanopolyynes (HC2n+1N) have relatively lower 12 C/ 13 C ratios compared to the other hydrocarbons. Especially, the 13 C isotopomers of CCH have high values.
2. The 12 C/ 13 C ratios are different among the dark clouds. The ratios in L134N are relatively low compared to the others.
The first point may be caused by the isotopomer-exchange reactions mentioned in Section 3.1.2. Such isotopomerexchange reactions are not expected for cyanopolyynes. In addition, Taniguchi et al. (2019b) proposed that the high 12 C/ 13 C ratios of CCH seem to be caused by reactions between hydrocarbons (CCH, C2H2, l, c-C3H) and C + . If 13 C + is diluted by Reaction (4), these reactions will produce hydrocarbons with high 12 C/ 13 C ratios. The second point may be related to the evolution of the starless cores; TMC-1 CP and L1521B are considered to be chemically younger than L134N (e.g., Dickens et al. 2000). Currently, the available data are limited, and such studies have been conducted mainly at TMC-1 CP. Thus, it is difficult to reach firm conclusions. Future high-sensitivity survey observations are needed to reveal the detailed mechanisms causing the dilution of 13 C species, which would give information about the chemical relationships among carbon-chain molecules in dark clouds.

Carbon-Chain Species around Low-Mass YSOs
Carbon-chain chemistry around low-mass young stellar objects (YSOs), namely WCCC, has been reviewed in Sakai & Yamamoto (2013), and we do not discuss WCCC in detail. Instead, we summarize observational results published after the review article of Sakai & Yamamoto (2013).
Several survey observations with single-dish telescopes targeting carbon-chain molecules and COMs have been conducted. Graninger et al. (2016) carried out survey observations of CH3OH and C4H using the IRAM 30m telescope. A tentative correlation between the gas-phase C4H/CH3OH abundance ratio and the CH4/CH3OH abundance ratio in ice was found. These results support the scenario of WCCC: sublimation of CH4 is a trigger of carbon-chain formation in lukewarm gas (e.g., Hassel et al. 2008). Higuchi et al. (2018) conducted survey observations of CCH, c-C3H2, and CH3OH toward 36 Class 0/I protostars in the Perseus molecular cloud using the IRAM 30m and Nobeyama 45m radio

+24
−16 Errors indicate the standard deviation. telescopes. They found that the column density ratio of CCH/CH3OH varies by two orders of magnitudes among the target sources, and the majority of the sources show intermediate characters between hot corino and WCCC. In other words, hot corino and WCCC are at opposite ends of a spectrum, and most low-mass YSOs could have both characters, in which carbon-chain molecules and COMs coexist. In addition, they found a possible trend that sources with higher CCH/CH3OH ratios are located near cloud edges or in isolated clouds. Similar trends were suggested by Lefloch et al. (2018) with data taken in the IRAM Large Program "Astrochemical Surveys At IRAM (ASAI)". The ASAI program is an unbiased line survey from 80 to 272 GHz toward 10 sources with various evolutionary stages. Lefloch et al. (2018) found a difference in environmental conditions between hot corino and WCCC sources: i.e., inside and outside dense filamentary cloud regions, respectively.
High-angular-resolution observations with interferometers, such as ALMA and NOEMA, have revealed spatial distributions of carbon-chain molecules around low-mass YSOs. As already mentioned, most low-mass YSOs appear to show characteristics of both hot corino and WCCC. Oya et al. (2017) detected both a carbon-chain molecule (CCH) and several COMs toward the low-mass Class 0 protostar L483. They confirmed that both WCCC and hot corino characters coexist in this source with their spatially resolved data. Zhang et al. (2018) found that CCH emission traces the outflow cavity with signatures of rotation with respect to the outflow axis toward the NGC 1333 IRAS 4C outflow in the Perseus molecular cloud, using ALMA. Tychoniec et al. (2021) analyzed ALMA data sets toward 16 protostars and investigated spatial distributions of each molecule. They found that CCH and c-C3H2 trace the cavity wall. This could be explained by the fact that the chemistry of the cavity wall is similar to photodissociation region (PDR) chemistry. The photodissociation of molecules by UV radiation keeps high gas-phase abundances of atomic carbon (C), which is a preferable condition for the formation of hydrocarbons. Pineda et al. (2020) found a streamer-like structure toward IRAS 03292+3039 in the Perseus star-forming region with NOEMA. Such a streamer may be well traced by carbon-chain molecules such as CCS and HC3N, if it is considered to be chemically young. The streamer in this source seems to bring fresh gas from outside of the dense core (> 10, 500 au) down to the central protostar where the disk forms. Thus the properties of such streamers are potentially important for the formation and evolution of protoplanetary disks.
Taking advantage of the characteristics of carbon-chain molecules, we can trace unique features around low-mass YSOs. Rotational-transition lines of carbon-chain molecules are now found to be useful tracers not only in early starless clouds but also around star-forming cores. ALMA Band 1 and the next generation Very Large Array (ngVLA) will cover the 7 mm band or lower frequency bands, which are suitable for observations of carbon-chain molecules, especially longer ones. Future observations using such facilities will offer new insights into the carbon-chain chemistry around protostars, including low-, intermediate-, and high-mass systems.

Chemical Evolutionary Indicators
As mentioned in Section 1.2, carbon-chain molecules classically have been known to be abundant in young starless cores and good chemical evolutionary indicators in low-mass star-forming regions. However, it was unclear whether carbonchain species can be used as chemical evolutionary indicators in high-mass star-forming regions and behave similarly as in the case of low-mass regions.
Survey observations of several carbon-chain species (HC3N, HC5N, CCS, and c-C3H2) and N2H + were carried out using the Nobeyama 45m radio telescope (Taniguchi et al. 2018a(Taniguchi et al. , 2019c. Taniguchi Figure 6). This column density ratio decreases as cores evolve from the starless (HMSC) to protostellar (HMPOs) stage. Sources that were categorized as HMSCs based on the IR observations but that are associated with molecular lines of COMs (CH3OH or CH3CN) and/or SiO (plotted as the blue diamond in Figure 6) tend to fall between HMSCs and HMPOs. These sources are considered to contain early-stage protostars in the dense, dusty cores, which are not easily detected with IR observations. Thus, these sources appear to be at an intermediate evolutionary stage between HMSCs and HMPOs.  Off-HMPO means that IRAS-observed positions were not at exact continuum peak positions, but the beam covered the continuum core in the beam edge. Blue diamond plots are sources that were identified as HMSCs based on the IR observations, but which are associated with molecular emission lines of COMs (CH3OH and/or CH3CN) or SiO.
The decrease of the N (N2H + )/N (HC3N) ratio means that HC3N is efficiently formed and N2H + is destroyed, as cores evolve. It is a notable point that the tendency of this column density ratio is the opposite to that in low-mass star-forming regions (Suzuki et al. 1992;Benson et al. 1998). This tendency could be explained by higher temperatures and extended warm regions around HMPOs compared to low-mass protostars. N2H + is destroyed by a reaction with CO, i.e., abundant in the gas phase after being desorbed from dust grains, and HC3N can be formed by CH4 via the WCCC mechanism or via C2H2 desorbed from dust grains. The desorption of CO, CH4, and C2H2 from dust grains occurs when temperatures reach around 20 K, 25 K, and 50 K, respectively. In summary, the gas-phase chemical composition is affected by the local heating from young massive protostars, and a chemical evolutionary indicator apparently shows an opposite trend compared to that of the low-mass case. Thus, carbon-chain species likely have the potential to become chemical evolutionary indicators even for high-mass protostars.

Cyanopolyynes around High-Mass Protostars
The survey observations mentioned in Section 3.3.1 show a possibility of different carbon-chain chemistry between highmass and low-mass star-forming regions. The detection rates of HC3N, HC5N, c-C3H2, CCS are 93%, 50%, 68%, and 46%, respectively, in high-mass star-forming regions (Taniguchi et al. 2018a(Taniguchi et al. , 2019c. On the other hand, Law et al. (2018) reported that the detection rates of HC3N, HC5N, l-C3H, C4H, CCS, and C3S are 75%, 31%, 81%, 88%, 88%, and 38%, respectively. Thus, cyanopolyynes (HC3N and HC5N) show higher detection rates, while CCS is relatively deficient in high-mass star-forming regions, compared to low-mass regions. These results imply that carbon-chain chemistry around MYSOs is different from WCCC found around low-mass YSOs. Taniguchi et al. (2017b) conducted observations of the multi-transition lines of HC5N using the Green Bank 100m and Nobeyama 45m radio telescopes toward four MYSOs. The derived rotational temperatures are around 20 -25 K, which are similar to the temperature regimes of the WCCC mechanism. However, the derived rotational temperatures are lower limits due to contamination from extended cold components covered by the single-dish telescopes. The MYSO G28.28-0.36 shows a particular unique chemical character: carbon-chain species are rich, but COMs are deficient (Taniguchi et al. 2018b). This source may be analogous to the WCCC source L1527. These results are suggestive of the chemical diversity around MYSOs, as similar to low-mass cases (hot corino and WCCC).
Since the above HC5N excitation temperatures derived with single-dish data are lower limits, it could not be concluded that carbon-chain molecules exist in higher temperature regions around MYSOs compared to the WCCC sources. Taniguchi et al. (2021) derived the CCH/HC5N abundance ratios toward three MYSOs and compared the observed ratio with the results of their chemical simulations to constrain temperature regimes where carbon-chain species exist. The CCH/HC5N abundance ratio is predicted to decrease as the temperature increases, because CCH shows a peak abundance in the gas phase around 30 K, while the gas-phase HC5N abundance increases as the temperature rises up to around 100 K (Taniguchi et al. 2019a). Details about the chemical simulations are presented in Section 4. The observed CCH/HC5N abundance ratios toward all of the three MYSOs are ∼ 15, which is much lower than that toward the low-mass WCCC source L1527 (625 +3041 −339 ). The observed abundance ratios around MYSOs agree with the simulations around 85 K, while the ratio in L1527 matches with the simulations around 35 K. Therefore, carbon-chain species, at least HC5N, around MYSOs appear to exist in higher temperature regions than the locations where the WCCC mechanism occurs. Such results indicate that carbon-chain chemistry around MYSOs may be different from the WCCC mechanism.
More recently, spatial distributions of the HC5N line (J = 35 − 34; Eup = 80.5 K) around MYSOs have been revealed by ALMA Band 3 data (Taniguchi et al., submitted). This line has been detected from three sources among five target sources. Figure 7 shows the comparison of spatial distributions among HC5N, CH3OH, and continuum emission in Band 3 toward the three MYSOs. The HC5N emission shows single peaks associated with the continuum peaks and is consistent with the emission of the CH3OH line (10,1 − 21,2, vt = 1; Eup = 302.9 K) which should trace hot core regions with temperatures above 100 K. These results also support the "Hot Carbon-Chain Chemistry" scenario.
Carbon-chain molecules are formed even around MYSOs. However, the WCCC mechanism does not match the observational results around MYSOs, and carbon-chain species, especially cyanopolyynes, exist in hot regions with temperatures above 100 K. Figure 8 shows a summary of chemical types found around low-mass and high-mass YSOs, respectively. Currently, a candidate of pure HCCC sources is the MYSO G28.28-0.36, in which COMs are deficient but HC5N is abundant (Taniguchi et al. 2018b). Larger sources samples are needed to clarify the apparent chemical diversity around MYSOs.

Carbon-chains around Intermediate-Mass Protostars
Observations have revealed WCCC and HCCC in low-mass and high-mass star-forming regions, respectively. However, the carbon-chain chemistry around intermediate-mass protostars (2 M < m * < 8 M ) has not been well studied. It is essential to understand the carbon-chain chemistry around protostars comprehensively because large physical gaps between low-mass and high-mass protostars prevent us to compare them straightforwardly.
Survey observations of several carbon-chain molecules in the Q band are ongoing with the Yebes 40m telescope. Twelve target intermediate-mass YSOs were selected from the source list of the SOFIA Massive (SOMA) Star Formation Survey project (De Buizer et al. 2017;Liu et al. 2019). At the writing stage of this review article, we have data toward the five target sources. We briefly demonstrate the initial results here. Table 4 summarizes the detection of molecules toward five intermediate-mass protostars. Not only carbon-chain molecules, but also several COMs and sulfur-bearing species have been detected. We derived the rotational temperatures using seven HC5N lines (from J = 12 − 11 to J = 18 − 17; Eup = 9.97 K -21.9 K). The derived rotational temperatures are around 20 K, which agrees with the WCCC mechanism. In the fitting procedure, we note that the J = 12 − 11 line The " √ " mark indicates detection with S/N ratios above 5.
cannot be fitted simultaneously, with the flux of this line being too high. This likely indicates that the J = 12 − 11 line traces mainly outer cold gas which is a remnant of molecular clouds, whereas the other lines trace the lukewarm gas where carbon-chain molecules could efficiently form by the WCCC mechanism. COMs and carbon-chain molecules have been found to coexist, indicating that hybrid-type sources are common also in the intermediate-mass regime.
In summary, carbon-chain formation occurs around intermediate-mass protostars, as well as low-mass and high-mass protostars. Future detail analysis combined with physical parameters and observations with interferometers will reveal whether the HCCC mechanism occurs around intermediate-mass protostars.

Carbon-Chain Species in Disks
Before the ALMA era, there were only a few reported detections of carbon-chain species in the protoplanetary disks around T Tauri stars and Herbig Ae stars. Henning et al. (2010) detected CCH from two T Tauri stars, DM Tau and LkCa 15, with the IRAM Plateau de Bure Interferometer (PdBI). The first detection of HC3N from protoplanetary disks was achieved using the IRAM 30m telescope and PdBI (Chapillon et al. 2012). They detected the HC3N lines (J = 12 − 11 and 16−15) from protoplanetary disks around two T Tauri stars, GO Tau and LkCa 15, and the Herbig Ae star MWC 480. Studies of disk chemistry have dramatically progressed, thanks to ALMA observations. In this subsection, we summarize studies related to carbon-chain species in protoplanetary disks. Qi et al. (2013) reported the first detection of c-C3H2 in a disk around the Herbig Ae star HD 163296 using the ALMA Science Verification data. Its emission is consistent with the Keplerian rotating disk and traces a ring structure from an inner radius of ∼ 30 au to an outer radius of ∼ 165 au. The HC3N HC3N and CH3CN show similarity; compact and typically well within the bounds of the dust continuum. HC3N is considered to be formed by only the gas-phase reactions: C2H2 + CN and CCH + HNC (see also Table 2).
The Molecules with ALMA at Planet-forming Scales (MAPS) ALMA Large Program has studied disk chemistry around five target sources (IM Lup, GM Aur, AS 209, HD 163296, and MWC 480)  2). They also found that the HC3N/HCN and CH3CN/HCN abundance ratios of the outer regions (50-100 au) in the target disks are consistent with the composition of cometary materials. The warmer disks, HD 163296 and MWC 480, likely have comet formation zones at correspondingly larger radii. Guzmán et al. (2021) presented distributions of CCH toward the five protoplanetary disks of the MAPS program. They proposed that the CCH emission comes from relatively warmer (20-60 K) layers. In HD 163296, there is a decrease in the column density of CCH and HCN inside of the dust gaps near ∼ 83 au, at which a planet has been considered to be located. The similar spatial distributions of CCH and HCN suggest that they are produced by the same chemical processes, and photochemistry is the most probable one.
ALMA observations have revealed the presence of disks around not only T Tauri and Herbig Ae stars, but also around more massive, O-/B-type stars. Csengeri et al. (2018) detected the vibrationally-excited HC3N line (J = 38 − 37, v7 = 1e) around the O-type star G328.2551-0.5321 (O5-O4 type star) with ALMA. This source is a high-mass protostar in the main accretion phase. Their data have spatial resolution of around 400 au. The position-velocity (PV) diagram of this HC3N vibrationally-excited line is consistent with a Keplerian disk rotation profile, and they proposed that such HC3N vibrationally-excited emission could be a new tracer for compact accretion disks around high-mass protostars. Taniguchi et al. (2022) detected the HC3N vibrationally-excited lines (J = 24 − 23, v7 = 2, l = 0 and 2e) from the hypercompact HII (HC HII) region G24.47-0.08 A1 using ALMA Band 6 data. Their emission morphologies are largely similar to those of CH3CN, which was suggested to trace Keplerian disk rotation around a central mass of 20 M in the previous study of Moscadelli et al. (2021). The column densities of HC3N and CH3CN were derived using lines of their 13 C isotopologues, and the CH3CN/HC3N abundance ratios were compared with those in protoplanetary disks around the lower-mass stars obtained by the MAPS program (Ilee et al. 2021). Figure 9 shows the comparisons of the CH3CN/HC3N abundance ratios in disks. It is clear that the ratio in the disk around the G24 HC HII region is higher than those around the lower-mass stars by more than one order of magnitude.
Such a difference in the CH3CN/HC3N abundance ratio was explained by the HC3N and CH3CN chemistry in the disk: efficient thermal sublimation of CH3CN from ice mantles and rapid destruction of HC3N by the UV photodissociation and/or reactions with ions (H + , H + 3 , HCO + ). In the protoplanetary disks, CH3CN is considered to be efficiently formed by dust-surface reactions: (1) the successive hydrogenation reactions of C2N; and (2) a radical-radical reaction between CH3 and CN (Loomis et al. 2018a). The derived excitation temperature of CH3CN in the G24 HC HII region (Tex ≈ 335 K) is much higher than its sublimation temperature (∼ 95 K), which suggests that CH3CN formed on dust surfaces efficiently sublimates by the thermal desorption mechanism. On the other hand, its excitation temperatures around the Herbig Ae and T Tauri stars were derived to be 30-60 K, which is suggestive of the non-thermal desorption mechanisms such as photodesorption (Loomis et al. 2018a;Ilee et al. 2021). This means that CH3CN sublimation is not efficient in disks around the Herbig Ae and T Tauri stars, leading to low gas-phase abundances of CH3CN. Both HC3N and CH3CN could be destroyed by the UV radiation, and the UV photodissociation rate of HC3N is higher than that of CH3CN by a factor of ∼ 2.4 (Le Gal et al. 2019). Thus, HC3N could be more rapidly destroyed by UV photodissociation. In addition, HC3N is destroyed by reactions with ions, which are expected to be abundant in the HII region. In summary, HC3N is likely destroyed rapidly in the G24 HC HII region.
Until now, there is only one O-type star disk in which the CH3CN/HC3N abundance ratio has been derived. We need similar data for an increased sample of sources, including T Tauri, Herbig Ae, and O/B type disks, including probing various evolutionary stages, to further test the apparent tentative trends that have been so far revealed. In addition, for such studies of disk structures, especially around the more distant massive protostars, it is important to conduct unbiased line survey observations with high angular resolution.

Carbon-Chain Species in Other Environments
Carbon-chain molecules have been detected not only from star-forming regions in our Galaxy, but also other environments of the ISM. We briefly summarize the carbon-chain species detected in these regions.
Small hydrocarbons have been known to be present in photodissociation regions (PDRs). Cuadrado et al. (2015) observed small hydrocarbons toward the Orion Bar PDR using the IRAM 30m telescope. They detected various small hydrocarbons (CCH, C4H, c-C3H2, c-C3H, C 13 CH, 13 CCH, l-C3H, and l-H2C3) and the l-C3H + ion. They found that the spatial distributions of CCH and c-C3H2 are similar but do not follow the PAH emission, and suggested that photodestruction of PAHs is not a necessary requirement for the observed abundances of the smallest hydrocarbons. Instead, the gas-phase reactions between C + and H2 produce the small hydrocarbons. Guzmán et al. (2015) observed small hydrocarbons (CCH, c-C3H2), l-C3H + , and DCO + toward the Horsehead PDR with the PdBI. They demonstrated that top-down chemistry, in which large polyatomic molecules or small carbonaceous grains are photo-destroyed into smaller hydrocarbon molecules or precursors, works in this PDR. Suggestions by these two studies (Cuadrado et al. 2015;Guzmán et al. 2015) seem in contradiction, but may imply that the carbon-chain chemistry in PDRs differs among regions. Thus, further study is needed of carbon-chain chemistry in PDRs.
The envelopes of the carbon-rich Asymptotic Giant Branched (AGB) star IRC+10216 are known as a carbon-chain-rich site. Several carbon-chain molecules have been discovered for the first time in this source in both radio and infrared regimes (see also section 2.3). For example, C4H2 has been detected in mid-infrared observations with the 3m Infrared Telescope Facility (IRTF) from this source (Fonfría et al. 2018). Pardo et al. (2022) conducted deep line survey observations in the Q band with the Yebes 40m telescope and summarized the detected carbon-chain species in this source. The rotational temperatures of the carbon-chain species are around 5-25 K, suggesting that carbon-chain species may exist in different regions. There remain a lot of unidentified lines (U lines), and future laboratory spectroscopic experiments are necessary for line identifications.
The planetary nebula CRL 618 is another carbon-chain-rich source, also studied by radio and infrared observations. Polyacetylenic chains (C4H2 and C6H2) and benzene (C6H6) have been detected here with the Infrared Space Observatory (ISO) (Cernicharo et al. 2001). The abundances of C4H2 and C6H2 are lower than that of C2H2 by only a factor of 2-4, while benzene is less abundant than acetylene by a factor of ∼ 40. These authors suggested that UV photons from the hot central star and shocks associated with its high-velocity winds affect the chemistry in CRL 618: i.e., the UV photons and shocks drive the polymerization of acetylene and the formation of benzene. These hydrocarbons likely survive in harsh regions compared to star-forming regions. Pardo et al. (2005) observed cyanopolyynes up to HC7N, and proposed rapid transformation from small cyanide to longer cyanopolyynes in this source.
Carbon-rich AGB stars or planetary nebulae, like IRC+10216 and CRL 618, appear to possess unique carbon-chain chemistry differing from that in star-forming regions and PDRs, and thus be important laboratories to study carbon chemistry, including PAHs and benzene. Future observations with infrared telescopes, such as James Webb Space Telescope (JWST), may give us new insights of carbon chemistry, in particular PAHs and fullerenes. Berné & Tielens (2012) investigated formation process of C60 by the infrared observations with Spitzer and Herschel toward the NGC 7023 nebula. They found that C60 is efficiently formed in cold environments of an interstellar cloud irradiated by the strong UV radiation field. The most plausible formation route is the photochemical processing of large PAHs.
ALMA observations have detected carbon-chain species in extragalactic sources. The ALMA Comprehensive Highresolution Extragalactic Molecular Inventory (ALCHEMI) large program has conducted line survey observations from 84.2 GHz to 373.2 GHz toward the starburst galaxy NGC 253. Several carbon-chain species (e.g., CCH, c-C3H2, HC3N, HC5N, HC7N, CCS) have been detected from this galaxy (Martín et al. 2021). The detection of more complex carbonchain species will be reported (Dr. Sergio Martin, ESO/JAO, private comm.). Shimonishi et al. (2020) detected CCH in a hot molecular core in the Large Magellanic Cloud (LMC), and found that the CCH emission traces outflow cavity, as also seen in the low-mass YSOs in our Galaxy (see section 3.2). Such observations toward extragalactic sources with different metallicities will be important for a comprehensive understanding of carbon chemistry in the ISM.
Summaries of this section are as follows:

Chemical Simulations
Modeling studies about carbon-chain chemistry in starless cores have tried to obtain good agreement with the observed abundances in the dark cloud TMC-1. Here, we review modeling studies covering various types of carbon-chain molecules in dark clouds. Loison et al. (2014) studied several carbon-chain groups (Cn, CnH, CnH2, C2n+1O, CnN, HC2n+1N, C2nH − , C3N − ) with gas-grain chemical models including updated reaction rate constants and branching ratios assuming two different C/O ratios (0.7 and 0.95). They added a total of 8 new species and 41 new reactions, and modified 122 rate coefficients taken from the KInetic Database for Astrochemistry (KIDA, kida.uva.2011). Their results clearly show that some carbonchain molecules depend on the C/O elemental abundance ratio (e.g., CnH where n = 4, 5, 6, 8). Their models with new parameters can obtain good agreement with the observed abundances in the dark cloud TMC-1 CP, and the models with two C/O ratios (0.7 and 0.95) obtain a similar agreement at different times. There are two ages that show better agreement between observations and models; 10 5 yr and around (1 − 2)×10 6 yr. The gas-phase chemistry is dominated at the earlier phase, whereas the grain surface chemistry and gas-grain interaction become more efficient at the later stages.
These authors also compared the modeled results to the observed abundances in another starless core, L134N. Here the models with a C/O ratio of 0.7 are in better agreement with the observed abundances compared to the case with the higher C/O ratio. Ages when the models agree with the observed abundances in L134N best are (3 − 5)×10 4 yr and ∼ 6×10 5 yr. Large amounts of free C, N, and O are available in the gas phase at the first age, while strong depletion effects are predicted at the later stage. They also suggested that experimental work for the determination of rate constants for the reactions of O + CnH and N + CnH, especially at low-temperature conditions, is necessary.
Most recent studies have focused on particular molecules that were newly detected at TMC-1 CP (Section 3.1.1). Classical models for dark clouds consider bottom-up chemistry starting from C + , with carbon-chain molecules considered to form mainly by gas-phase reactions (Section 1.2). However, such classical views need to be revisited. For example, it has been revealed that both gas-phase and grain-surface formation routes are important for the reproduction of the observed abundance of H2CCCHC3N . Some molecules detected by the GOTHAM project, especially cyclic molecules, have not been explained by the chemical simulations yet (e.g.,c-C9H8; Burkhardt et al. 2021b). These results suggest that small rings are formed through the destruction of PAHs or other unknown processes. Our knowledge about connections among different categories (e.g., linear, cyclic, PAHs) likely lacks important processes. Besides, we need to reveal the initial conditions of carbon-bearing species in molecular clouds. Further observations and chemical simulations are necessary to understand carbon-chain chemistry including the newly detected molecules.
Some recent studies with sophisticated chemical simulations focused on the origin of the chemical diversity around YSOs. Aikawa et al. (2020) demonstrated their results with two phases (the static phase and the collapse phase) and a multilayered ice mantle model, and investigated how the WCCC and hot corino chemistry depend on the physical conditions during the static phase. They found: 1. The lower temperatures during the static phase can produce the WCCC sources more efficiently. 2. The lower visual extinction during the static phase can form CH4 and carbon-chain molecules become more abundant. 3. A longer static phase is preferable for producing the WCCC sources. 4. It is difficult to produce the prototypical WCCC sources, where carbon-chain species are rich but COMs are deficient.
On the contrary, the hot corino sources and hybrid-type sources where both COMs and carbon-chain species are reasonably abundant could be reproduced.
In warm conditions, grains-surface formation and freeze out of CH4, which is a key species for WCCC, become less effective. Moreover, the conversion of CO to CO2 on grain surfaces becomes important, and the gaseous CO abundance decreases. These lead to a low abundance of C + , which is formed by the destruction of CO by He + . The C + ion is another key species for WCCC. Therefore, warm conditions are not suitable for the production of WCCC sources. In the model with a longer static phase, CH4 accumulates during the static phase, leading to a more favorable condition for WCCC. Kalvāns (2021) investigated the effects of the UV radiation field and cosmic rays on the formation of WCCC sources. They concluded that WCCC can be caused by exposure of a star-forming core to the interstellar radiation field (ISRF) or just to cosmic rays (with ζ ≥ 10 −16 s −1 ). Such a conclusion agrees with the observational results that hot corino type sources are located inside dense filamentary clouds, while the WCCC sources are located outside such structures (e.g., Lefloch et al. 2018). These two model studies show that various factors, including conditions before the onset of core collapse, are related to carbon-chain chemistry around low-mass YSOs. These factors likely are entangled in most sources. Taniguchi et al. (2019a) tried to reproduce the observed abundances of HC5N around the three MYSOs (Section 3.3.2) with chemical simulations of hot-core models with a warm-up period. They utilized three different heating timescales (t h ); 5 × 10 4 yr, 2 × 10 5 yr, and 1 × 10 6 yr, approximating high-mass, intermediate-mass, and low-mass star-formation, respectively (Garrod & Herbst 2006). They found that the observed HC5N abundances around the MYSOs can be reproduced when the temperature reaches its sublimation temperature (∼ 115 K) or the hot-core phase (T = 200 K).
These authors also investigated cyanopolyyne chemistry in detail during the warm-up and hot-core periods. Basically, formation and destruction reactions of HC3N, HC5N, and HC7N Fig. 10 The modeled HC5N abundances in the gas phase (red), dust surface (brown), and ice mantle (blue) during the warm-up and hot-core periods (Taniguchi et al. 2019a). The black line indicates the temperature evolution. Indicated molecules mark the times of efficient sublimation from dust grains.
example. Figure 10 shows the modeled HC5N abundances obtained by the 3-phase (gas, dust, ice) model with a heating timescale of 1 × 10 6 yr (Taniguchi et al. 2019a). The gas-phase HC5N abundance (red curves) shows a drastic change with time (or temperature) evolution. During the warm-up period, HC5N is mainly formed by the reaction between C4H2 and CN. In addition to this, the reaction between CCH and HC3N partly contributes to the HC5N formation. This reaction (CCH+HC3N) is important around t ≈ 8.5 × 10 5 yr, when the gas-phase HC3N abundance increases. At that time, the HC3N production is enhanced by the reaction between CCH and HNC. We indicate some molecules with green arrows in Figure 10. These indicate that each molecule directly sublimates from dust grains at these various ages. Methane (CH4) sublimates from dust grains around 25 K (t ≈ 7.2 × 10 5 yr), and carbon-chain formation starts, namely WCCC. After that, CN and C2H2 sublimate from dust grain at t = 7.7 × 10 5 yr (T ≈ 31 K) and t = 9.3 × 10 5 yr (T ≈ 55 K), respectively. The C4H2 species is formed by the gas-phase reaction of "CCH + C2H2 → C4H2 + H". When the temperature reaches around 73 K (t = 1.0 × 10 6 yr), C4H2 directly sublimates from dust grains. The enhancement of the gas-phase abundances of CN and C4H2 boosts the formation of HC5N in the gas phase.
We can see that the HC5N abundances in dust surface and ice mantles increase when the gas-phase HC5N abundance decreases. This means that the HC5N molecules, which are formed in the gas phase, adsorb onto dust grains and accumulate in ice mantles before the temperature reaches its sublimation temperature (T ≈ 115 K, corresponding to t = 1.2 × 10 6 yr). Their results are based on the concept of HCCC (Figure 4). This chemical simulation is supported by observations of the 13 C isotopic fractionation (c.f., Section 3.1.2) of HC3N toward the carbon-chain-rich MYSO G28.28-0.36 (Taniguchi et al. 2016b). The proposed main formation pathway of HC3N is the reaction between C2H2 and CN in this MYSO. This is consistent with the formation process seen in the chemical simulations during the warm-up stage. Taniguchi et al. (2019a) proposed that longer heating timescales of the warm-up stage could produce the carbonchain-rich conditions by comparisons of six modeled results, focusing on cyanopolyynes. In the HCCC mechanism, cyanopolyynes are formed in the gas phase, adsorb onto dust grains, and accumulate in the ice mantle. Their icemantle abundances just before sublimation determine the gas-phase peak abundances. Thus, longer heating timescales allow cyanopolyynes to accumulate in the ice mantle abundantly, leading to their higher gas-phase abundances in hot core regions. The long heating timescale of the warm-up stage (t h ) does not necessarily reflect the timescale of stellar evolution or accretion. It depends on the relationships between the size of the warm region (Rwarm) and the infall velocity (v infall ) as suggested by Aikawa et al. (2008): If Rwarm becomes larger or v infall becomes smaller, t h will be longer. The Rwarm and v infall values should be related to various physical parameters (e.g., protostellar luminosity, density structure, magnetic field strength). The conditions of Rwarm and v infall can be investigated by observations. Combined observations to derive chemical composition and the values of Rwarm/v infall are needed for a more comprehensive understanding of the chemical evolution and diversity around YSOs.

Role of Quantum Chemical Studies
Quantum chemistry is an indispensable tool to study structures and spectral properties of a given molecule, regardless of laboratory stability, and makes this a necessary component of astrochemical analyses. It is probably the best tool to explore and interpret chemical structures, properties, and, most importantly, detectable spectra of unusual molecules detected in space. In the 1960s and 1970s, when radio telescopes came into action with better sensitivity, many species were identified based on the laboratory data of their rotational spectra. However, there were also many unidentified signatures. Closed shell molecules can be easily handled in the laboratory and generate rotational spectra. The problem arises in the case of radical and charged species because of their highly unstable and reactive nature. Initial detection of HCO + and N2H + was in the 1970s and based on quantum chemistry (see Fortenberry 2015, and references therein). Following these, Patrick Thaddeus (Columbia University and then Harvard University) was a part of teams that detected nearly three dozen new molecular species (McCarthy & Thaddeus 2001). Thaddeus' group standardized the use of quantum chemistry in astrochemical detection.
Several carbon-chain species such C2H, C3N, and C4H were identified based on SCF (self-consistent field) computation. The usage of quantum chemistry in astrochemistry became popular and common if species had not been synthesized in a laboratory. Several carbon-chain species, such as l-C3H + and C6H − , were identified based on the insight of quantum chemistry. This has continued until recent times with the detection of the kentenyl radical (HCCO) towards various dark clouds in 2015. In another example, the detection of C5N − in the circumstellar envelope of the carbon-rich star IRC+10216 was based solely on quantum chemical data.
Modern quantum computations consider a lot of improvements with a wide range of quantum mechanical methods, basis sets, especially coupled cluster theory, at the single, double, and perturbative triples [CCSD(T)] level. The CCSD(T) method is exceptionally good in providing molecular structures and rotational constants, which give us very accurate rotational spectra. Over the years, many groups have made remarkable contributions to astrochemistry through quantum chemistry for astrochemical detection, understanding of the formation/destruction, and collisional excitation of different interstellar molecules (e.g., L. Allamandola, C. Bauschlicher, V. Barone, P. Botschwina, M. Biczysko, C. Puzzarini R. C. Fortenberry, J. Gauss, T. J. Lee, K. Peterson, H. F. Schaefer, J. Stanton, D. Woon, J-C Loison, J. Kästner , N. Balucani, A. Rimola). A comprehensive strategy for treating larger molecules with the required accuracy has been presented by Barone et al. (2015).

Ground State and Stability
The ground states of carbon-chain species are crucial because they decide their stability and eventually help us find the true state of the species either in laboratory experiments or in astrophysical environments via a spectral search. Table 1 summarizes the ground state of all the carbon-chain species included in this review article. The ground state, enthalpy of formation, rotational constants, dipole moment, and polarizability of many carbon-chain species can be found in KIDA database (https://kida.astrochem-tools.org/) as well as in several works in the literature (e.g., Woon & Herbst 2009;Etim et al. 2016;Etim & Arunan 2017;Bâldea 2019;Etim et al. 2020). For any particular carbon-chain species, the ground state can be found with the help of quantum chemical study.

Dipole moment and Polarizability
The dipole moment is an important parameter that decides whether a molecule is polar or non-polar. Non-polar molecules do not have a permanent electric dipole moment and do not show rotational transitions. On the other hand, polar molecules have a permanent electric dipole moment and they show rotational transitions. A higher dipole moment value means a higher intensity of rotational transitions. It is crucial because one can say whether it is detectable or not through their rotational transitions. The dipole moment values of all the carbon-chain species are summarized in Table  1. These can be measured theoretically with various quantum chemical methods and basis set by inclusion of structures of molecules.
The polarizabilities of all carbon-chain species, if available, are summarized in Table 1. The dipole moment and polarizability are crucial for the estimation of ion-neutral reaction rates. Ion-neutral reactions play a crucial role in the ISM, especially in cold dark clouds, for the formation and destruction of various species. For non-polar neutrals, the rate coefficient is given by the so-called Langevin expression: where e is the electronic charge, α pola is the polarizability, µ is the reduced mass of reactants, and cgs-esu units are utilized so that the units for the rate coefficient are cm 3 s −1 . For polar-neutral species, trajectory scaling relation is usually used. The best-known formula for the ion-dipolar rate coefficient kD in the classical regime and for linear neutrals is the Su-Chesnavich expression. The Su-Chesnavich (Su & Chesnavich 1982) formula is based on the parameter x, defined by where µD is an effective dipole moment of the neutral reactant, which is generally very close to the true dipole moment, and kB is the Boltzmann constant. The larger value of x takes, the larger the rate coefficient is. Apart from the estimation of the rate coefficient of ion-neutral reactions, the dipole moment is one of the key parameters to determine the column density of observed species. Accurate estimation of the dipole moments is essential to derive realistic values of column density. For instance, the dipole moment of C4H was used ∼ 0.87 Debye in previous literature, which was the value of mixed states, i.e., ground and excited states. The recent result suggests the dipole moment value is 2.10 Debye, which is 2.4 times larger than the values used before (Oyama et al. 2020). As a result, its column densities has been overestimated by a factor of ∼ 6.

Binding Energy of Carbon-Chain Species
A major portion of carbon-chain species is primarily formed in the gas phase. In addition, gas-grain exchange occurs, and many reactions occur on the grain surface. The binding energy (BE) plays a pivotal role in interstellar chemistry, especially grain surface chemistry, which eventually enriches the gas-phase chemistry. Here, we describe the role of binding energy in interstellar chemical processes.
The BE values of all carbon-chain species are provided (if available) in Table 5. Most of the BE values are mainly taken from KIDA (https://kida.astrochem-tools.org/). BE estimation of a species heavily depends on the methods and surface used for the calculations (e.g., Penteado et al. 2017;Das et al. 2018;Ferrero et al. 2020;Villadsen et al. 2022;Minissale et al. 2022). The BE values of all carbon-chain species, especially higher-order linear chains, are estimated based on the addition method that are provided in KIDA. In this method, for instance, the BE of HC7N is estimated by addition of binding energies of HC6N and C. 800 K is usually adopted as the BE of a carbon atom. However, we see a huge difference in BE of a carbon atom between the old value and newly measured values based on quantum chemical study (≥ 10000 K; Wakelam et al. 2017;Minissale et al. 2022). Thus, the addition method of BE may lead to large uncertainties to estimate BE of carbon-chain molecules, especially longer ones. If BE of a carbon atom is ≥10,000 K is correct, the addition method of BE may not be valid, because long carbon-chain species will have huge BE values. To overcome this issue, dedicated quantum chemical calculations or the temperature-programmed desorption (TPD) method are required to estimate the BE values of carbon-chain species with higher accuracy.
Gas-phase species accrete onto the grain surface depending upon their energy barriers with the surfaces. The species may bind to the grain surface via the physisorbed or chemisorbed processes. E d expresses the binding energy (or desorption energy) of the chemical species. Species attached to grain surfaces can migrate from one site to another depending on the barrier energy of migration (E b ). This is also known as a barrier against diffusion. The migration timescale by thermal hopping can be expressed as, where ν0 is the characteristic vibration frequency of the adsorbed species, and T d is the grain surface temperature. The theoretical expression for ν0 is, where m is the mass of the adsorbed particle, and ns is the number density of sites. The utilized values of ns are ∼ 2 × 10 14 cm −2 for olivine based grain and ∼ 5 × 10 13 cm −2 for the amorphous carbon grain, respectively (Biham et al. 2001). The characteristic frequency is ∼ 10 12 Hz. Diffusion time t diff required for an adsorbed particle over a number of sites is given by where S is the total number of sites on the grain surface.
Desorption is the release of species on the grain surface back into the gas phase. There are various desorption mechanisms that directly depend on the binding energy of the species. For instance, the thermal evaporation time of species on a grain surface is given by, Species on the grain surface attain sufficient thermal energy and evaporate from the surface after this characteristic time. Therefore, the thermal desorption rate can be written as where ν is the characteristics frequency that can be written as, where Ns is the density of the binding site, and mA is the mass of species A. The binding energy of the chemical species and the evaporation rate can be estimated from TPD experiments. Thermal desorption is a very efficient mechanism in hot cores, hot corinos, and other dense and high-temperature locations of star-forming regions.

Experimental Studies
Experimental studies are essential to measure the rotational or vibrational spectra of molecules with unprecedented resolution and accuracy. They can provide accurate molecular rotational spectra, which are used for their precise identification in data obtained from various radio and infrared telescopes. The first carbon-chain molecule, the simplest cyanopolyyne HC3N, was detected with NRAO 140-foot radio telescope in 1971 based on the laboratory rotational spectra measured by Tyler & Sheridan (1963). After that, the astronomical detection of many carbon-chain species was based on their laboratory rotational spectra. References to laboratory experiments of rotational or vibrational spectra of different molecules can be found in papers reporting their interstellar detection.
Laboratory experiments to investigate reactions have also been developed. Experimental investigations of carbonbearing molecule formation via neutral-neutral reactions are summarized in Kaiser (2002). Ion-molecule reactions producing carbon-chain species were also investigated via experiments (Takagi et al. 1999;Žabka et al. 2014). Recently, Martínez et al. (2020) investigated the growth of carbon-containing species from C and H2 in conditions analogous of circumstellar envelopes around carbon-rich AGB stars. They found that nanometer-sized carbon particles, pure carbon clusters, and aliphatic carbon species are formed efficiently, whereas aromatics are generated at trace levels and no fullerenes are detected. They also suggested that the formation of aromatic species must occur via other processes, such as the thermal processing of aliphatic material on the surface of dust grains.

Summary
We have reviewed carbon-chain chemistry in the ISM, mainly focusing on recent updates. A summary of our main points is as follows.
1. By the end of 2022, 118 carbon-chain species have been detected in the ISM. This accounts for almost 43% of 270 interstellar molecules detected in the ISM or circumstellar shells. These include various families of carbon-chain species, involving elements of O, N, S, P, and Mg. 2. Two line survey projects toward TMC-1 CP (GOTHAM and QUIJOTE) have recently reported detections of many new carbon-chain species. Abundances of some of these species are not yet reproducible in chemical simulations indicating a need for improved models. 3. In addition to the cold gas conditions of early-phase molecular clouds, carbon-chain formation also occurs around low-, intermediate-and high-mass YSOs. Warm Carbon-Chain Chemistry (WCCC) was found in 2008 around low-mass YSOs, while Hot Carbon-Chain Chemistry (HCCC) has been proposed based on observations around high-mass YSOs. 4. Recent chemical simulations aim to explain conditions forming hot corino and WCCC sources. There are several possible parameters to produce the chemical differentiation: e.g., UV radiation field and temperature during the static phase. 5. Thanks to high-angular resolution and high-sensitivity observations with ALMA, several carbon-chain species (e.g., CCH, c-C3H2, HC3N) have been detected from protoplanetary disks around Herbig Ae and T Tauri stars. Vibrationally-excited lines of HC3N have been found to trace disk structures around massive stars. 6. Circumstellar envelopes around carbon-rich AGB stars and planetary nebulae are unique factories of carbon chemistry.
Infrared observations have revealed the presence of PAHs and fullerenes in such environments. Recent laboratory experiments investigated chemistry in such regions. 7. Carbon-chain species have been detected even in extragalactic environments, such as the starburst galaxy NGC253 via the ALCHEMI project. In the Large Magellanic Cloud (LMC), CCH emission has been found to trace outflow cavities, as seen in low-mass YSOs in our Galaxy. 8. Theoretical and experimental studies are important for the observational detection of carbon-chain species and for obtaining an understanding of their formation and destruction processes. Developments of these techniques are important to reveal carbon-chain chemistry in various physical conditions in the ISM.
The presence of carbon-chain species in the ISM has been known since the early 1970s, and many researchers have investigated their features through observations, chemical simulations, laboratory experiments, and quantum calculations. Recent findings raise new questions about carbon-chain chemistry, and it is an exciting time of progress. To solve the newly raised questions, collaborative research involving observations, laboratory experiments, and chemical simulations is crucial.
To understand the carbon-chain chemistry better by observational methods, we need more dedicated low-frequency, high-sensitivity, and high angular resolution observations towards dark clouds, low-and high-mass YSOs, and other environments. In the near future, ALMA Band 1, ngVLA and the Square Kilometer Array (SKA) will become available. Observations using these facilities will be essential to reveal links between ISM physics and carbon-chain chemistry, the origin of chemical differentiation around YSOs, and relationships between WCCC and HCCC. In addition, future observational studies combining infrared data (e.g., from JWST, Thirty Meter Telescope (TMT), European Extremely Large Telescope (E-ELT)) and radio (ALMA, ngVLA, SKA, and future single-dish) telescopes have the potential from breakthrough results. For instance, relationships between PAHs/small dust grains and common carbon-chain species, which can be observed by infrared and radio regimes, respectively, can be studied by such a combination.

Open Key Questions
Recent new discoveries of carbon-chain molecules in the ISM have raised new questions, and we have realized that our knowledge about carbon-chain chemistry is far from complete. We highlight the following open questions: 1. How do large carbon-chain species, which have been found in TMC-1 CP, form? Is there a role for both bottom-up and top-down processes? 2. Which, if any, important formation/destruction processes of carbon-chain species are missing from current chemical models? 3. Can we estimate more accurate branching ratios for different species (e.g., isomers) in electron recombination reactions? 4. How are PAHs and fullerenes related to other carbon-chain species? 5. How can we obtain accurate binding energy of carbon-chain species?
Answers to these questions likely require combined efforts of observational, theoretical, and experimental study.