An update to the MARVEL dataset and ExoMol line list for 12C2
Laura K. McKemmish, Anna-Maree Syme, Jasmin Borsovszky, Sergei N. Yurchenko, Jonathan Tennyson, Tibor Furtenbacher, Attila G. Csaszar
MMNRAS , 1–17 (2020) Preprint 11 September 2020 Compiled using MNRAS L A TEX style file v3.0
An update to the MARVEL dataset and ExoMol line list for C Laura K. McKemmish, (cid:63) Anna-Maree Syme, Jasmin Borsovszky, Sergei N. Yurchenko, Jonathan Tennyson, Tibor Furtenbacher and Attila G. Császár School of Chemistry, University of New South Wales, 2052 Sydney Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom Institute of Chemistry, ELTE Eötvös Loránd University and MTA-ELTE Complex Chemical Systems Research Group, H-1518 Budapest 112, P.O. Box 32, Hungary
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
The spectrum of dicarbon (C ) is important in astrophysics and for spectroscopic studiesof plasmas and flames. The C spectrum is characterized by many band systems with newones still being actively identified; astronomical observations involve eight of these bands.Recently, Furtenbacher et al. (2016, Astrophys. J. Suppl., 224, 44) presented a set of 5699empirical energy levels for C , distributed among 11 electronic states and 98 vibronic bands,derived from 42 experimental studies and obtained using the M ARVEL (Measured ActiveRotational-Vibrational Energy Levels) procedure.Here, we add data from 13 new sources and update data from 5 sources. Many of thesedata sources characterize high-lying electronic states, including the newly detected 3 Π g state. Older studies have been included following improvements in the M ARVEL procedurewhich allow their uncertainties to be estimated. These older works in particular determinelevels in the C Π g state, the upper state of the insufficiently characterized Deslandres–d’Azambuja (C Π g –A Π u ) band.The new compilation considers a total of 31 323 transitions and derives 7047 empirical(M ARVEL ) energy levels spanning 20 electronic and 142 vibronic states. These new empir-ical energy levels are used here to update the C ExoMol line list. This updatedline list is highly suitable for high-resolution cross-correlation studies in astronomical spec-troscopy of, for example, exoplanets, as 99.4% of the transitions with intensities over 10 − cm molecule − at 1000 K have frequencies determined by empirical energy levels. Key words: molecular data; opacity; astronomical data bases: miscellaneous; planets andsatellites: atmospheres; stars: low-mass; comets: general.
The spectroscopy of the dicarbon molecule, C , has a long his-tory. Interestingly, C was originally observed by Wollaston (1802),which represents the pre-history of spectroscopy. This observationwas followed by the identification (Swan 1857) of the well-knownSwan d Π g – a Π u band system. The last decade has seen thespectroscopic characterization of several new bands of C , includ-ing the first observation of multiplicity-changing “intercombina-tion” bands linking both the singlet-triplet (Chen et al. 2015) andtriplet-quintet (Bornhauser et al. 2011) states. These observationshave allowed the determination of reliable frequencies of singlet-triplet transitions, which are thought to be important in comets(Rousselot et al. 2000) and are candidates for observation in the in-terstellar medium (Lebourlot & Roueff 1986). Detection of triplet-quintet transitions has led to the spectroscopic characterization of (cid:63) E-mail: [email protected] a number of quintet states for the first time (Schmidt & Bacskay2011; Bornhauser et al. 2015, 2017). In addition, recent experi-ments detected and characterized a number of new triplet bands(Welsh et al. 2017; Krechkivska et al. 2017).Astronomically, C is unusual in that it has been studiedvia a large number of band systems including the Swan, Phillips,Deslandres–d’Azambuja, Ballik–Ramsay, Mulliken and Herzberg-F bands, see Figure 1 for the band designations. The Swan (Swings1943; Gredel et al. 1989; Lambert et al. 1990; Rousselot et al. 2000)and the Deslandres–d’Azambuja (Gredel et al. 1989) band systemshave been discovered in the spectra of comets when models ofcometary emission have been found to require no less than two sin-glet, X Σ + g and A Π u , and four triplet, a Π u , b Σ − g , c Σ + u , andd Π g , electronic states to explain the observations. Indeed, two ofthe intercombination bands mentioned above, a Π u → X Σ + g andc Σ + u → X Σ + g , are needed to explain the observed intensities inthe Swan band (Rousselot et al. 2000). c (cid:13) a r X i v : . [ a s t r o - ph . E P ] S e p McKemmish et al. C has a strong presence in the solar photosphere where it hasbeen observed using the Swan (Asplund et al. 2005), the Phillips,and the Ballik–Ramsay (Brault et al. 1982) bands. The Phillipsand Ballik–Ramsay bands have also been observed in carbon stars(Goebel et al. 1983; Goorvitch 1990), while Swan bands have beenobserved in peculiar white dwarfs (Hall & Maxwell 2008; Kowal-ski 2010) and the coronae borealis star V coronae australis (Rao &Lambert 2008).Interstellar C has been observed via the infrared Phillips band(Gredel et al. 2001; Iglesias-Groth 2011), while the Swan bandemissions can be seen in the Red Rectangle (Wehres et al. 2010).Absorption in the Phillips, Mulliken and Herzberg-F bands can beseen in translucent clouds (Sonnentrucker et al. 2007).These astronomical observations require high-quality labora-tory data for their analysis and interpretation. Recent spectroscopicstudies have probed new bands with well-known band systems(Nakajima 2019; Krechkivska et al. 2018), providing new data onthem. In addition, recent spectroscopic studies on C have usedtechniques yielding improved ionization (Krechkivska et al. 2016)and dissociation energies (Visser et al. 2019). Theoretical studiesalso started to provide reliable association rates (Babb et al. 2019).Altogether work on the C molecule remains as lively as ever withthe interpretation of its bonding and spectroscopy remaining some-what as a puzzle to conventional chemical physics (Macrae 2016).Figure 1 gives an overview of the observed band systems for C with colour used to indicate those explicitly dealt with inthis study. In response to the needs of astrophysics and other ar-eas of physics, Yurchenko et al. (2018b) computed a comprehen-sive line list for C as part of the ExoMol project (Tennyson &Yurchenko 2012), called the line list. This line list wasgenerated by variational solution of the nuclear Schrödinger equa-tion for the states involved (Yurchenko et al. 2016) and covers theband systems linking the lowest eight electronic states, namely theSwan, Phillips, Ballik–Ramsay, Duck, Bernath B and B’ bands, andthe singlet-triplet intercombination lines. As a precursor to per-forming these calculations, Furtenbacher et al. (2016) performeda M ARVEL (Measured Active Rotational-Vibrational Energy Lev-els (Császár et al. 2007; Furtenbacher et al. 2007; Furtenbacher &Császár 2012a), see Section 2 for a description) analysis for the C isotopologue. The empirical energies generated by MARVELwere incorporated in the C line list giving, for exam-ple, the most accurate predictions available for the singlet-tripletintercombination lines.A number of advances has led us to review and update the C M ARVEL project. First, improvements in the M
ARVEL proce-dure, including significantly improved error handling (Tóbiás et al.2019), was found to influence the results of the original study. Sec-ond, while the original M
ARVEL study considered 42 sources ofspectroscopic C data, a number of largely older sources (Dieke& Lochte-Holtgreven 1930; Fox & Herzberg 1937; Herzberg &Sutton 1940; Phillips 1950; Herzberg et al. 1969; Goodwin & Cool1988, 1989) were not considered in 2016 as they did not con-tain any uncertainty estimates, a requirement for use in the M AR - VEL procedure. New combination difference approaches imple-mented in M
ARVEL allow these uncertainties to be accurately es-timated. These earlier works contain data on states that have notbeen observed in more recent studies; in particular the studies of40HeSu (Herzberg & Sutton 1940), 50Phillips (Phillips 1950) and67Messerle (Messerle 1967) contain the only published high res-olution C spectra of the Deslandres–d’Azambuja band. Finally,and most importantly, a series of new studies have provided ad-ditional data for known bands (Welsh et al. 2017; Krechkivska + Σ u D Π C g1 u Π F g B ∆ Π A Σ + E g Π g Σ − g g ∆ g e Π g d − ΠΣ Σ g + g3 a Π u b cDuckBallik− Π g Π g Π u Radi−SwanKable−Schmidt−SchmidtKrechkivskaHerzberg f Herzberg gRamsayHerzbergFox−f Bornhauser Σ g + − ene r g y ( x c m ) X Σ g + Π g B´C´6070 Bernathd’AzambujaDeslandres−PhillipsFreymarkMullikenHerzberg F ∆ u Messerle−KraussGoodwin−Cool
Figure 1.
The band system of C with its well-established names. Thedashed lines represent observed but unnamed intercombination bands;colours indicate newly considered bands (red) and updates (blue). TheMesserle–Krauss band and the associated C (cid:48) Π g state are depicted in dotsas doubts have been raised about their correctness. et al. 2017) and characterized several new bands for the first time(Schmidt & Bacskay 2011; Bornhauser et al. 2015, 2017). Thesesources are combined with those considered previously to producean updated set of empirical (M ARVEL ) rovibronic energy levelsduring this study. All (new and old) data sources are referencedby band in Table 5 ( vide infra ).In this work we also present an updated and improved versionof the C ExoMol line list, which incorporates the newand extended M
ARVEL -derived set of empirical energy levels. M ARVEL
PROCEDURE
Details about the M
ARVEL procedure (Furtenbacher et al. 2007;Furtenbacher & Császár 2012a; Tóbiás et al. 2019), built upon thetheory of spectroscopic networks (SN) (Császár & Furtenbacher2011; Császár et al. 2016), have been given in recent publications(Furtenbacher et al. 2014; Császár et al. 2016; Tóbiás et al. 2019,2020). Therefore, only a brief discussion is given here.The M
ARVEL protocol yields empirical rovibronic energieswith well-defined provenance and uncertainties; it starts with the
MNRAS , 1–17 (2020) n update to the MARVEL dataset and ExoMol line list for C construction of a SN using the dataset of measured and assignedtransitions collated from the literature. Each measured transitionmust have a unique (though not necessarily physically relevant) as-signment, which determines its place within the SN, and an uncer-tainty. What happens next is basically an inversion of the transitionsinformation, yielding empirically determined rovibronic energylevels within each component of the SN. Along this process valida-tion of the experimental information is performed, utilizing severalelements of network theory. Recently the algorithms employed byM ARVEL have been systematically improved, the relationship ofSNs to formal network theory considered (Császár & Furtenbacher2011; Furtenbacher & Császár 2012b; Árendás et al. 2016), andthe underlying methodology reviewed (Furtenbacher et al. 2014;Császár et al. 2016). M
ARVEL has been used to obtain accurateempirical rovibronic energy levels with statistically sound uncer-tainties for a considerable number of diatomic molecules of astro-nomical interest (Furtenbacher et al. 2016; McKemmish et al. 2017;Darby-Lewis et al. 2018; Yurchenko et al. 2018a; McKemmishet al. 2018; Darby-Lewis et al. 2019a,b; Furtenbacher et al. 2019).These M
ARVEL energy levels are crucial to enabling the generationof M
ARVEL ised line lists (e.g. McKemmish et al. (2019)) suitablefor high-resolution cross-correlation studies of low-signal objectssuch as exoplanets (e.g. Birkby et al. (2013)). M ARVEL
SET OF ASSIGNED TRANSITIONS3.1 Overview
We have updated the M
ARVEL set of assigned transitions for C through the inclusion of 13 new data sources (8 new sources fromprior to the original update and 5 post-2016 sources) and throughthe revision of transitions from six further data sources. The num-ber of included transitions has risen from the 2016 values of 23 251(22 937 validated) to 31 323 (30 792 validated).We usually added new data to the pre-existing M ARVEL set oftransitions and uncertainties, unless specified otherwise. The uncer-tainties used for each source were usually taken from the originalpaper, but increased as required, first for internal self-consistencyof the data within a single data source and then for self-consistencywith the full M
ARVEL compilation of data.The parity-defining quantum numbers used in the originalcompilation are not necessary given that lambda-doubling transi-tions have not been observed in C , and have thus been removedin the present study for simplicity.The new transitions file thus has the format shown in Table 1.The transitions file serves as both input to the M ARVEL procedureand as a single consolidated source of assigned transition frequen-cies and uncertainties for C .Salient details of each source of new and updated experimen-tal data are summarised in Tables 2 to 4, which specify, for eachincluded vibronic band, (1) the number of total and validated transi-tions, (2) the average and maximum uncertainty of the spectral linesafter self-consistency, and (3) the J and the wavenumber ranges ofthe transitions. The same details are provided in the supplemen-tary information for transitions retained from the original M ARVEL compilation (Furtenbacher et al. 2016).
The 2016 original M
ARVEL compilation of C spectroscopic datadid not incorporate sources that either (a) did not include an esti- mate of the transition frequency uncertainty, or (b) involved veryhigh-lying electronic states, e.g. , C Π g , F Π u , f Σ + g , and g ∆ g .Many of these new data sources include transitions in theultra-violet and have much higher uncertainties than other datasources. In most data sources, we limited the maximum uncertaintyto 0.5 cm − . Next, we provide information about these sources oneby one. (Dieke & Lochte-Holtgreven 1930) An early source ofDeslandres–d’Azambuja (C Π g − A Π u ) transitions for low-energy vibrational states, which have surprisingly not been remea-sured for C despite the high uncertainties of these data. Uncer-tainties were estimated using combination differences based on theuse of lower-state energy levels determined by M ARVEL , the esti-mated source uncertainties are 0.2 cm − . (Fox & Herzberg 1937) The first measurements of theFox–Herzberg (e Π g − a Π u ) band, all with upper vibrationalstate of v =
0. Uncertainties were estimated using combination dif-ferences based on the use of lower-state energies determined byM
ARVEL , the estimated source uncertainties are 0.2 cm − . Two ofthese bands, (0–3) and (0–6), have not been remeasured, thoughall involved energy levels are now well understood by other bandmeasurements. (Herzberg & Sutton 1940) Another source ofDeslandres–d’Azambuja (C Π g − A Π u ) transitions with anumber of vibrational bands. Uncertainties were estimated usingcombination differences based on the use of lower-state energiesdetermined by M ARVEL , the estimated source uncertainties are 0.2cm − . (Phillips 1950) Even another source of Deslandres–d’Azambuja (C Π g − A Π u ) transitions, with significantly ex-cited vibrational states involved. (Messerle 1967) Some data from Messerle’s 1967thesis was located (Nauta 2020); these data are relevant for theDeslandres–d’Azambuja (C Π g − A Π u ) band. Note that no datafrom the putative Messerle–Krauss bands (C (cid:48) Π g − A Π u ) werefound. (Herzberg et al. 1969) These data are the sole sourcefor many very high-lying bands, located above 70 000 cm − . Un-certainties were estimated using combination differences based onthe use of lower-state energies determined by M ARVEL , the esti-mated source uncertainties are 0.1 cm − , with blended lines givena starting uncertainty of 0.2 cm − . Lines with recommended M AR - VEL uncertainties higher than 0.5 cm − were not validated; thisprocess only removed a small number of lines and all bands mostlyconsisted of validated lines. (Goodwin & Cool 1988) To ensure reliable inclusion ofthe 88GoCo (Goodwin & Cool 1988), and in fact 89GoCo (Good-win & Cool 1989), data (the only source of data for the 1 ∆ u state),uncertainties up to 2 cm − were required to be permitted in thesetwo sources. These high uncertainty values can be attributed to thequality of the early ultraviolet studies, which have a stated abso-lute energy error of 2 cm − , though the relative uncertainties werestated as ± − . (Goodwin & Cool 1989) Following the considerationsof 88GoCo (Goodwin & Cool 1988), an earlier paper by the sameauthors, uncertainties for the 89GoCo data were initially set as 0.2cm − , but allowed to increase as required; all transitions were val-idated with uncertainties less than 1.2 cm − . MNRAS000
ARVEL , the estimated source uncertainties are 0.2 cm − . Two ofthese bands, (0–3) and (0–6), have not been remeasured, thoughall involved energy levels are now well understood by other bandmeasurements. (Herzberg & Sutton 1940) Another source ofDeslandres–d’Azambuja (C Π g − A Π u ) transitions with anumber of vibrational bands. Uncertainties were estimated usingcombination differences based on the use of lower-state energiesdetermined by M ARVEL , the estimated source uncertainties are 0.2cm − . (Phillips 1950) Even another source of Deslandres–d’Azambuja (C Π g − A Π u ) transitions, with significantly ex-cited vibrational states involved. (Messerle 1967) Some data from Messerle’s 1967thesis was located (Nauta 2020); these data are relevant for theDeslandres–d’Azambuja (C Π g − A Π u ) band. Note that no datafrom the putative Messerle–Krauss bands (C (cid:48) Π g − A Π u ) werefound. (Herzberg et al. 1969) These data are the sole sourcefor many very high-lying bands, located above 70 000 cm − . Un-certainties were estimated using combination differences based onthe use of lower-state energies determined by M ARVEL , the esti-mated source uncertainties are 0.1 cm − , with blended lines givena starting uncertainty of 0.2 cm − . Lines with recommended M AR - VEL uncertainties higher than 0.5 cm − were not validated; thisprocess only removed a small number of lines and all bands mostlyconsisted of validated lines. (Goodwin & Cool 1988) To ensure reliable inclusion ofthe 88GoCo (Goodwin & Cool 1988), and in fact 89GoCo (Good-win & Cool 1989), data (the only source of data for the 1 ∆ u state),uncertainties up to 2 cm − were required to be permitted in thesetwo sources. These high uncertainty values can be attributed to thequality of the early ultraviolet studies, which have a stated abso-lute energy error of 2 cm − , though the relative uncertainties werestated as ± − . (Goodwin & Cool 1989) Following the considerationsof 88GoCo (Goodwin & Cool 1988), an earlier paper by the sameauthors, uncertainties for the 89GoCo data were initially set as 0.2cm − , but allowed to increase as required; all transitions were val-idated with uncertainties less than 1.2 cm − . MNRAS000 , 1–17 (2020)
McKemmish et al.
Table 1.
Extract from the 12C-12C_2020update.marvel.inp input file for C .1 2 3 4 5 6 7 8 9 10 11˜ ν ∆ ˜ ν State (cid:48) v (cid:48) J (cid:48) F (cid:48) State (cid:48)(cid:48) v (cid:48)(cid:48) J (cid:48)(cid:48) F (cid:48)(cid:48) ID3345.6527 0.006132865 Bˆ1Deltag 1 9 1 Aˆ1Piu 1 10 1 16ChKaBeTa.1673347.987 0.0093071 bˆ3Sigmag- 4 26 3 aˆ3Piu 5 26 3 15ChKaBeTa.15943349.659 0.009250366 Bˆ1Deltag 1 16 1 Aˆ1Piu 1 16 1 16ChKaBeTa.1683349.8868 0.0015 Bˆ1Deltag 0 30 1 Aˆ1Piu 0 31 3 88DoNiBeb.1253350.6451 0.007 bˆ3Sigmag- 4 27 2 aˆ3Piu 5 27 2 15ChKaBeTa.15823351.6007 0.003 Bˆ1Deltag 1 8 1 Aˆ1Piu 1 9 1 16ChKaBeTa.1693352.8642 0.003 Bˆ1Deltag 0 39 1 Aˆ1Piu 0 39 1 16ChKaBeTa.1703354.5954 0.003 Bˆ1Deltag 1 15 1 Aˆ1Piu 1 15 1 16ChKaBeTa.1713356.9124 0.007 bˆ3Sigmag- 4 14 3 aˆ3Piu 5 15 3 15ChKaBeTa.15573357.1991 0.003176643 Bˆ1Deltag 1 7 1 Aˆ1Piu 1 8 1 16ChKaBeTa.172Column Notation1 ˜ ν Transition frequency (in cm − )2 ∆ ˜ ν Estimated uncertainty in transition frequency (in cm − )3 State (cid:48) Electronic state of upper energy level; also includes parity for Π states and Ω for triplet states4 v (cid:48) Vibrational quantum number of upper level5 J (cid:48) Total angular momentum of upper level6 F (cid:48) Spin multiplet component of upper level, labelled in energy order7 State (cid:48)(cid:48)
Electronic state of lower energy level; also includes parity for Π states and Ω for triplet states8 v (cid:48)(cid:48) Vibrational quantum number of lower level9 J (cid:48)(cid:48) Total angular momentum of lower level10 F (cid:48)(cid:48) Spin multiplet component of lower level, labelled in energy order11 ID Unique ID for transition, with reference key for source and counting number (Bornhauser et al. 2017) This paper provides newdata on the quintet bands and three assignments of the quintet-triplet spin-forbidden bands. However, two of these three new spin-forbidden bands were inconsistent with the rest of the M
ARVEL compilation without uncertainties of around 2.4 cm − and werethus excluded; in contrast, 67 spin-forbidden transitions betweenthe same two electronic states in 11BoSyKnGe (Bornhauser et al.2011) all validated with smaller uncertainties. (Welsh et al. 2017) Rotationally cool experimen-tal conditions enabled detailed study of low- J ultraviolet rovibronictransitions in the Fox–Herzberg (e Π g − a Π u ) band. No explicituncertainty was provided in this paper; anestimated source uncer-tainty of 0.035 cm − was used, though this seems to be a slightunderestimation based on the uncertainties M ARVEL found. (Krechkivska et al. 2017) This is the first study ofthe 3 Π g state, observed via the 3 Π g − a Π u transitions, withthe paper also substantially expanding on previously known dataon the 4 Π g state. The estimated source uncertainties are 0.035cm − . Detailed M ARVEL -based analyses of the data revealed thatthe original assignments were not self-consistent within this pa-per. Following these analyses, one of the original authors identified(Nauta 2020) a calibration error in the 4 Π g − a Π u (0 −
5) transi-tion frequencies, which can be corrected by decreasing all frequen-cies in this band by 0.9 cm − . Though it could not be confirmed,a calibration error was also suspected in the 4 Π g − a Π u (1 − ARVEL analysis showed the data setbecame self-consistent without unreasonably large uncertainties ifthese transition frequencies were decreased by 1.0 cm − . (Krechkivska et al. 2018) Rotationally cool exper-imental conditions enabled the detailed study of low- J rovibronictransitions in the Mulliken (D Σ + u – X Σ + g ) ∆ v = ± − was assigned, with reason-able results. (Nakajima 2019) The paper provides an estimatefor the line uncertainties as 0.01 cm − , which we adopted as theestimated source uncertainty. During the process of updating the compilation of C rovibronicdata, a number of issues with the original data were identified andcorrected. A source-by-source specification of the corrections fol-lows. (Phillips 1948b) A small number of digitisation errorswere identified and corrected following a thorough re-examinationof the band structure. (Phillips 1949) Significant errors with quantum num-bers, including incorrect band assignments, were identified and cor-rected, and the repetition of one band’s data identified and removed. (Hardwick & Winicur 1986) The 2016 compilation in-cluded only 100 of the spectral lines reported in this paper; theother 497 lines have been added to this update. (Tanabashi et al. 2007) The original data compilationincluded 3813 transitions, but some of these transitions were cal-culated rather than measured and many measured transitions wereexcluded. The source was reprocessed into M ARVEL format, givinga total of 4813 transitions, with calculated transitions (labelled “z”)excluded, blended lines given a starting uncertainty of 0.01 cm − and well resolved isolated lines given an estimated source uncer-tainty of 0.005 cm − . Note that the data from the 02TaAm (Tan-abashi & Amano 2002) source that was reproduced in 07TaHiAm MNRAS , 1–17 (2020) n update to the MARVEL dataset and ExoMol line list for C Table 2.
Newly included data sources (tags in bold). Given are details of thevibronic band, the vibrational states (Vib.) and the total angular momentumquantum numbers ( J ) involved, the number of transitions (Trans.) validated(V) and original accessed (A), the wavenumber (Wn) range of the band, andinformation about source uncertainties (Unc.), with their average (Av) andmaximum (Max) values. Band Vib. J -range Trans.(V/A) Wn range(cm − ) Unc. (cm − )(Av/Max) (Dieke & Lochte-Holtgreven 1930)C Π g − A Π u ( − ) Π g − A Π u ( − ) Π g − A Π u ( − ) Π g − A Π u ( − ) Π g − A Π u ( − ) Π g − A Π u ( − ) Π g − A Π u ( − ) (Fox & Herzberg 1937)e Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) (Herzberg & Sutton 1940)C Π g − A Π u ( − ) Π g − A Π u ( − ) Π g − A Π u ( − ) Π g − A Π u ( − ) Π g − A Π u ( − ) (Phillips 1950)C Π g − A Π u ( − ) (Messerle 1967)C Π g − A Π u ( − ) (Herzberg et al. 1969)F Π u − X Σ + g ( − ) Π u − X Σ + g ( − ) Σ + g − a Π u ( − ) Σ + g − a Π u ( − ) Σ + g − a Π u ( − ) ∆ g − a Π u ( − ) ∆ g − a Π u ( − ) (Goodwin & Cool 1988)1 ∆ u − A Π u ( − ) ∆ u − A Π u ( − ) ∆ u − A Π u ( − ) ∆ u − A Π u ( − ) ∆ u − A Π u ( − ) ∆ u − A Π u ( − ) ∆ u − A Π u ( − ) ∆ u − A Π u ( − ) ∆ u − A Π u ( − ) ∆ u − A Π u ( − ) ∆ u − A Π u ( − ) ∆ u − A Π u ( − ) ∆ u − A Π u ( − ) (Goodwin & Cool 1989)1 ∆ u − B ∆ g ( − ) was not included. Given the high resolution of the data, transitionswith uncertainties greater than 0.2 cm − were deemed misassign-ments and not validated (though they are still in the included M AR - VEL file with a "-" in front of the transition frequency, as usual); intotal 88 transitions were not validated, mostly at the beginning orend of a given band. When processing these data to determine op-timal uncertainties, the 48Phillips (Phillips 1948b) and 49Phillips(Phillips 1949) data were removed before being re-added; this en-sured the more recent data had a larger number of valid transitionswith lower uncertainties than the older data. (Chen et al. 2016) Due to late inclusion of this datasource, the lines from the B (cid:48) Σ + g – A Π u band were missed duringthe original compilation; these 104 missing lines have been addedin this update.Additionally, for 06PeSi (Petrova & Sinitsa 2006), we want tonote that we retained the 2016 M ARVEL values, but that these were
Table 3.
New experimental data sources for C which appeared since theoriginal M ARVEL study (Furtenbacher et al. 2016) was published. Detailsas in Table 2.
Band Vib. J -range Trans.(V/A) Wn range(cm − ) Unc. (cm − )(Av/Max) (Bornhauser et al. 2017)1 Π g − a Π u ( − ) Π u − Π g ( − ) Π g − a Π u ( − ) (Welsh et al. 2017)e Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) (Krechkivska et al. 2017)3 Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) (Krechkivska et al. 2018)D Σ + u − X Σ + g ( − ) Σ + u − X Σ + g ( − ) Σ + u − X Σ + g ( − ) Σ + u − X Σ + g ( − ) Σ + u − X Σ + g ( − ) Σ + u − X Σ + g ( − ) Σ + u − X Σ + g ( − ) Σ + u − X Σ + g ( − ) (Nakajima 2019)A Π u − X Σ + g ( − ) Π u − X Σ + g ( − ) Π u − X Σ + g ( − ) Π u − X Σ + g ( − ) Π u − X Σ + g ( − ) Π u − X Σ + g ( − ) Π u − X Σ + g ( − ) reassigned from the original paper’s assignments because the orig-inal contained unphysical assignments for the quantum numbers ofhomonuclear diatomics. The spread of uncertainties for every data source used for the up-dated M
ARVEL input is shown in Figure 2. The horizontal axis goesthrough each data source in chronological order. The colours ofthe data are assigned to the electronic bands of the transition, or-dered by transitions frequency. This plot clearly shows that for eachsource there are a significant number of transitions with uncertain-ties above the minimum uncertainty for that data set; these uncer-tainty increases were required to ensure self-consistency with thedata coming from other sources. The figure makes it also clear that
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Figure 2.
The range of transition frequency uncertainties for every source involved in the full M
ARVEL input file. See Table 5 for the citations to these sources. pre-1960 sources have much larger uncertainties than the later data,though there is no clear trend in improved accuracy since 1960.Most data sources since 1960 have minimum uncertainties between10 − to 10 − cm − . The post-1960 outliers with higher uncertain-ties, on the order of 0.1 cm − , are usually very-high-frequencytransitions in the ultraviolet region. These higher uncertainties areexpected as this region is more spectrally congested and UV in-struments are more expensive with lower spectral resolution thanvisible instruments due to decreased market demand.Colours in Figure 1, vide supra , demonstrate that the new datasources added to the C M ARVEL compilation in this paper in-crease the number of bands considered from 11 to 21, with updatesin data available for 7 of the originally included bands. The spe-cific experimental sources in our M
ARVEL compilation for eachelectronic transition band system are detailed in Table 5. It is clearthat some band systems, especially the b Σ − g − a Π u , d Π g − a Π u , e Π g − a Π u , A Π u − X Σ + g ones, have been extensivelyexplored with thousands of measured transitions in up to 16 differ-ent publications. These heavily explored band systems are strongabsorption bands in astrophysical environments. In contrast, someother systems have data only from a single paper. The triplet man-ifold is generally better explored than the singlet manifold, despitethe fact that the electronic ground state of C is a singlet. The num-ber of quintet and spin-forbidden intersystem lines remains quitesmall, but the latter in particular are very important for setting therelative energies of the singlet, triplet, and quintet manifolds accu-rately.Table 5 also provides details about the number of unique ver-sus total transitions measured. The high number of unique versustotal transitions in these data clearly demonstrates that most re-examinations of a particular band system produce data for differentvibronic bands rather than re-measuring existing data at a higheraccuracy. This result emphasises the need for a centrally-collated source of all available experimental data in one consistent format,as provided by this paper.With these new included data, every observed band hasM ARVEL -compiled rotationally-resolved data with two exceptions:the Kable–Schmidt (Nakajima et al. 2009) e Π g − c Σ + u bandaround 40 000 cm − and the Messerle–Krauss (Messerle & Krauss1967) C (cid:48) Π g − A Π u band around 30 000 cm − . Initial errors inthe e state constants prohibited a good fit to the Kable–Schmidtband in 2009; new constants (Welsh et al. 2017) obtained frombetter data in the Fox–Herzberg band allowed a much better fit ofthe e Π g − c Σ + u (4 −
3) band in that paper’s supplementary in-formation, although a full experimental assigned line list was notproduced. In the case of the Messerle–Krauss band, recent unpub-lished investigations (Nauta & Schmidt 2020) suggests that the ob-served lines of the Messerle–Krauss band are actually part of theDeslandres–d’Azambuja (C Π g − A Π u ) band and that the trueC (cid:48) Π g is much higher in energy, as consistently predicted by abinitio theory.The full M ARVEL input file with formatted assigned transi-tions includes 31 323 transitions with 6 quantum numbers follow-ing the formatting of the original C M ARVEL transitions file. Itis provided as supplementary information with the latest updateavailable online on M
ARVEL online, http://kkrk.chem.elte.hu/marvelonline/ . M ARVEL
DATA4.1 Spectroscopic Network
The experimental spectroscopic network of C built from as-signed transitions has one main component with 7047 energy lev-els, incorporating 2061 singlet, 4910 triplet, and 76 quintet states.These energy levels span 20 electronic states and 142 vibronic lev-els. There are 203 other spectroscopic networks, none of which MNRAS , 1–17 (2020) n update to the MARVEL dataset and ExoMol line list for C Table 4.
Updates to previously included data sources. Details as in Table 2.
Band Vib. J -range Trans.(V/A) Wn range(cm − ) Unc. (cm − )(Av/Max) (minor corrections) (Phillips 1948a)d Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) (re-processed) (Phillips 1949)e Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) (extended) (Hardwick & Winicur 1986)e Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) (re-processed) (Tanabashi et al. 2007)d Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) Π g − a Π u ( − ) (new lines) (Chen et al. 2016)B (cid:48) Σ + g − A Π u ( − ) (cid:48) Σ + g − A Π u ( − ) (cid:48) Σ + g − A Π u ( − ) have more than 12 energy levels. Therefore, they are not consid-ered further in this paper.Figure 3 visually demonstrates the connectivity of the experi-mental spectroscopic network of C . In all of the subfigures, thenodes are the energy levels, and the edges are the transitions be-tween them. The three subfigures show the SN at the resolution ofelectronic (top), vibronic (middle) and rovibronic (bottom) states,with the same colour scheme used for all figures.The top sub-figure of Figure 3 shows that the singlet and tripletmanifolds are largely independent, as expected, with two differentspin-forbidden bands connecting the manifolds. The quintet mani-fold is connected to the whole spectroscopic network via transitionsbetween the 1 Π g and a Π u states. Most of the triplet-bands stud-ies have a Π u as the lower-energy state, whereas for the singlet Figure 3.
Spectroscopic networks of C produced using the M ARVEL in-put and output data. Each electronic state is given a colour which is labelledin top subfigure (network of electronic states) and repeated in middle sub-figure (network of vibronic states) and bottom subfigure (network of rovi-bronic states). The bluer colours are singlets, the redder colours are tripletsand the green colours are quintets.MNRAS000
Spectroscopic networks of C produced using the M ARVEL in-put and output data. Each electronic state is given a colour which is labelledin top subfigure (network of electronic states) and repeated in middle sub-figure (network of vibronic states) and bottom subfigure (network of rovi-bronic states). The bluer colours are singlets, the redder colours are tripletsand the green colours are quintets.MNRAS000 , 1–17 (2020)
McKemmish et al.
Table 5.
All experimental data sources of rotationally-resolved assigned transitions (Trans.) for all investigated band system in C , where Tot refers tothe total number of transitions and Uniq refers to the number of unique transitions. Bold band names indicate bands newly included in this update, whileitalicized names indicate pre-existing bands with new data. Bold sources are newly included in this 2020 M ARVEL update, italicised sources are updated fromthe previous 2016 M
ARVEL compilation.
Multiplicity Band name Band System Trans. (Tot/Uniq) Sources
Singlet
Phillips A Π u − X Σ + g (Nakajima 2019)Bernath B B ∆ g − A Π u Bernath B’ B (cid:48) Σ + g − A Π u (Chen et al. 2016) Deslandres–d’Azambuja C Π g − A Π u (Dieke & Lochte-Holtgreven 1930), (Herzberg & Sutton 1940), (Phillips 1950), (Messerle 1967) Mulliken D Σ + u − X Σ + g (Krechkivska et al. 2018)Freymark E Σ + g − A Π u Herzberg F F Π u − a Π u (Herzberg et al. 1969) Goodwin–Cool ∆ u − A Π u (Goodwin & Cool 1988) Goodwin–Cool ∆ u − B ∆ g (Goodwin & Cool 1989) Triplet
Ballik–Ramsay b Σ − g − a Π u Swan d Π g − a Π u (Bornhauser et al. 2017)Duck d Π g − c Σ + u Fox-Herzberg e Π g − a Π u (Fox & Herzberg 1937), , (Hardwick & Wini-cur 1986), 98BrHaKoCr (Brockhinke et al. 1998), (Welsh et al. 2017) Herzberg f f Σ + g − a Π u (Herzberg et al. 1969) Herzberg g g ∆ g − a Π u (Herzberg et al. 1969) Krechkivska-Schmidt Π g − a Π u (Krechkivska et al. 2017) Krechkivska–Schmidt Π g − a Π u (Krechkivska et al. 2017) Quintet
Radi–Bornhauser Π u − Π g (Bornhauser et al. 2017) Intercombination X Σ + g − a Π u Π g − a Π u (Bornhauser et al. 2017)A Π u − b Σ − g bands the A Π u state is more connected than the X Σ + g state; thisfollows from the symmetries of the various states with Π states be-ing most connected.The separation of the singlet and triplet manifolds becomesmore pronounced in the middle sub-figure of Figure 3. This fig-ure also clarifies that vibronic states are strongly interconnected in C , i.e. , a given upper state can decay to many different vibrationalground states. These Franck–Condon transitions are numerous dueto significant variation in the bond lengths of the different elec-tronic states.The bottom sub-figure of Figure 3 shows clearly the sparsityof the intercombination bands in contrast to the other observedtransitions, yet highlights their importance in connecting the sin-glet, triplet, and quintet manifolds. The spiral networks of tran-sitions in both the singlet and triplet manifolds are multicolouredas they are between a variety of electronic states, with their linearstructure largely determined by angular momentum selection rules ∆ J = , ±
1. Note that we have excluded all energy levels and tran-sitions not in the main component from this figure for clarity. M ARVEL
Energy Levels
Figure 4 gives a summary of all 7047 empirical energy levels de-termined in this study, with each line representing energy levels ofa single vibronic state as a function of the total angular momentumquantum number J . These curves are clearly quadratic and smooth,suggesting that there are no major issues with the empirical energylevels.In Tables 6 to 8, we describe the updated M ARVEL datasetfor each vibronic level for low-lying singlet states, low-lying tripletstates and higher energy states respectively in terms of (a) the rangeof total angular momentum quantum numbers J and energies in-cluded; (b) the total number of quantum states included; (c) the av-erage uncertainty of the derived energies; and (d) the contributingdata sources.Low-lying states, particularly the X Σ + g ( v = − Π u ( v = − Π u ( v = −
5) ones, are very well characterisedto high J values with data from multiple sources leading to low un-certainties usually averaging less than 0.002 cm − . Higher-lying MNRAS , 1–17 (2020) n update to the MARVEL dataset and ExoMol line list for C [htpb!] Table 6.
Summary of experimentally-derived M
ARVEL energy levels, including uncertainties and data sources, for low-lying singlet states of C . Boldindicates new data sources, italics indicates updated data sources. No is the number of energy levels in that vibronic state. See Table 5 for the citations to thesesources. State v J -range No E -range Av Unc (cm − ) SourcesX Σ + g −
74 38 0 − , 77ChMaMa, 97SoBlLiXu, 04ChYeWoLi, 06PeSi,15ChKaBeTa, X Σ + g −
72 37 1827 − X Σ + g −
58 30 3627 − X Σ + g −
46 24 5397 − X Σ + g −
40 21 7136 − , X Σ + g −
30 16 8844 − , X Σ + g −
26 13 10518 − X Σ + g −
10 6 12155 − X Σ + g −
12 7 13751 − X Σ + g −
12 7 15303 − A Π u −
72 72 8272 − , 51Freymark, 63BaRab, 77ChMaMa, 88DoNiBeb, , 88DaAbPh,88DoNiBea, , 15ChKaBeTaA Π u −
79 77 9856 − , , 51Freymark,77ChMaMa, 88DoNiBeb, , 88DaAbPh,88DoNiBea, 06PeSi, 15ChKaBeTa, A Π u −
70 70 11415 − , , 51Freymark, 77ChMaMa, 88DaAbPh, 88DoNiBeb, ,97SoBlLiXu, 04ChYeWoLi, 06PeSi, 15ChKaBeTa, A Π u −
75 75 12951 − , , 51Freymark, 63BaRab, 77ChMaMa, 88DoNiBea, ,97SoBlLiXu, 04ChYeWoLi, 15ChKaBeTa, A Π u −
74 74 14462 − , 51Freymark, 63BaRab, 77ChMaMa, 88DoNiBea, , 04ChYeWoLi,15ChKaBeTa, A Π u −
59 59 15949 − , 63BaRab, 88DoNiBea, 04ChYeWoLi, 15ChKaBeTa, A Π u −
47 47 17411 − , 63BaRab, 04ChYeWoLi, 15ChKaBeTa, A Π u −
20 20 18849 − Π u −
19 18 20268 − Π u −
31 30 21650 − A Π u
10 1 −
30 30 23013 − A Π u
11 1 −
23 22 24352 − A Π u
12 1 − − Π u
13 1 − − Π u
14 1 − − Π u
15 1 − − Π u
16 1 − − ∆ g −
47 46 11868 − B ∆ g −
50 48 13252 − , B ∆ g −
42 40 14614 − B ∆ g −
39 37 15953 − B ∆ g −
36 35 17269 − B ∆ g −
33 31 18562 − B ∆ g −
36 32 19833 − B ∆ g −
34 33 21081 − B ∆ g −
24 20 22314 − B (cid:48) Σ + g −
32 17 15197 − (cid:48) Σ + g −
30 16 16617 − (cid:48) Σ + g −
28 14 18045 − (cid:48) Σ + g −
20 11 19458 − (cid:48) Σ + g −
30 16 20878 − states generally are characterised by far fewer sources and usu-ally exhibit a much more limited range in J . States with energieslower than approximately 30 000 cm − generally retain low me-dian uncertainties on the order of 0.002 cm − , while the higher-lying states detailed in Table 8 generally have median uncertaintiesof 0 . − . − , reflecting the lower accuracy of ultraviolet-spectroscopy measurements. Figure 5 shows the uncertainties of the energy levels in each elec-tronic state, ordered from left to right in order of increasing en-ergy. The eight low-lying electronic states, X Σ + g , a Π u , b Σ − g ,A Π u , c Σ + u , B ∆ g , B (cid:48) Σ + g , and d Π g , have uncertainties thatrange from less than 0.001 cm − to a small number of transitionswith uncertainties greater than 0.01 cm − . These low uncertaintiesare definitely suitable for the current needs of high-resolution as-tronomical spectroscopy. As an example, we note recent trends inusing cross-correlation of template and measured spectra to extract MNRAS000
30 16 20878 − states generally are characterised by far fewer sources and usu-ally exhibit a much more limited range in J . States with energieslower than approximately 30 000 cm − generally retain low me-dian uncertainties on the order of 0.002 cm − , while the higher-lying states detailed in Table 8 generally have median uncertaintiesof 0 . − . − , reflecting the lower accuracy of ultraviolet-spectroscopy measurements. Figure 5 shows the uncertainties of the energy levels in each elec-tronic state, ordered from left to right in order of increasing en-ergy. The eight low-lying electronic states, X Σ + g , a Π u , b Σ − g ,A Π u , c Σ + u , B ∆ g , B (cid:48) Σ + g , and d Π g , have uncertainties thatrange from less than 0.001 cm − to a small number of transitionswith uncertainties greater than 0.01 cm − . These low uncertaintiesare definitely suitable for the current needs of high-resolution as-tronomical spectroscopy. As an example, we note recent trends inusing cross-correlation of template and measured spectra to extract MNRAS000 , 1–17 (2020) McKemmish et al. [htpb!]
Table 7.
Summary of experimentally-derived M
ARVEL energy levels, including uncertainties and data sources, for low-lying triplet states of C . Boldindicates new data sources, italics indicates updated data sources. No is the number of energy levels in that vibronic state. See Table 5 for the citations to thesesources. State v J -range No E -range Av Unc (cm − ) Sourcesa Π u −
80 226 604 − , 79AmChMa, 83Amiot, 85RoWaMiVe, 85SuSaHi, 88DaAbSa, 94PrBe,98BrHaKoCr, 99LlEw, 06PeSi, 07TaHiAm, 15ChKaBeTa, a Π u −
70 192 2222 − , 79AmChMa, 85CuSa, 85RoWaMiVe, 85YaCuMeCa, 94PrBe, 03KaYaGuYu,06PeSi, 07TaHiAm, 15ChKaBeTaa Π u −
60 173 3816 − , , 79AmChMa, 85RoWaMiVe, 85YaCuMeCa, 94PrBe, 06PeSi,07TaHiAm, 15ChKaBeTa, 15KrBaTrNa, , a Π u −
58 163 5388 − , , , 79AmChMa, 85RoWaMiVe, 85YaCuMeCa, 94PrBe,07TaHiAm, 10BoKnGe, 15ChKaBeTa, 15KrBaTrNa, 16KrBaWeNa, , a Π u −
42 122 6936 − , , 79AmChMa, , 94PrBe, 07TaHiAm, 11BoSyKnGe, 15ChK-aBeTa, , a Π u −
42 121 8460 − , , , 07TaHiAm, 11BoSyKnGe, 15ChKaBeTa, a Π u −
36 104 9962 − , , 07TaHiAm, 15ChKaBeTa, , a Π u −
26 74 11440 − Π u −
34 100 12894 − , , 02TaAm, 07TaHiAm, 13BoSyKnGe, 13NaEn, 13YeChWaa Π u −
35 97 14326 − , 02TaAm, 07TaHiAm, 13NaEn, 13YeChWaa Π u
10 0 − − Π u
11 0 − − Π u
12 2 − − Π u
13 1 − − Π u
14 2 − − Σ − g −
75 106 6250 − Σ − g −
70 102 7698 − Σ − g −
70 104 9124 − Σ − g −
70 99 10528 − Σ − g −
60 87 11910 − Σ − g −
58 84 13270 − Σ − g −
58 80 14608 − Σ − g −
40 56 15924 − Σ − g −
30 42 17219 − Σ − g
19 17 −
22 8 30416 − Σ + u −
19 25 9280 − Σ + u −
24 33 11312 − Σ + u −
10 14 13315 − Σ + u − − Σ + u − − Σ + u − − Σ + u − − Π g −
81 224 19984 − , 83Amiot, 85CuSa, 94PrBe, 99LlEw, 03KaYaGuYu, 07TaHiAmd Π g −
53 159 21738 − , 85SuSaHi, 94PrBe, 07TaHiAm, 13ChYeWad Π g −
41 119 23454 − , 94PrBe, 07TaHiAm, 13ChYeWa, 13NaEnd Π g −
39 106 25130 − , 94PrBed Π g −
43 126 26761 − Π g −
36 105 28342 − Π g −
35 103 29865 − Π g −
34 93 31324 − Π g −
32 88 32709 − , 07TaHiAm, 13NaEn, d Π g −
33 85 34013 − , 07TaHiAmd Π g
10 0 −
34 94 35234 − , 07TaHiAm, 13NaEnd Π g
11 1 − − Π g
12 0 − − very small data signals, e.g. for non-dominant isotopologues (Mol-lière & Snellen 2019). The quintet states have uncertainties around0.002 cm − . In contrast, higher singlet and triplet electronic stateshave a higher uncertainty, generally 0 . − . − , with a smallerspread. These higher uncertainties can be attributed to the lowerresolution of the ultraviolet-spectroscopy experiments needed tocharacterise these high-lying states along with the smaller numberof experimental data sources.It is useful to consider how the source uncertainties of the tran-sitions (illustrated in Figure 2) propagate to the uncertainties of theenergy levels (illustrated in Figure 5). Overall, the uncertainty in the energy levels seems to be approximately an order of magni-tude lower than the uncertainty of the transitions. This relationshipis explored further in Figure 6, which plots the uncertainty of anenergy level (in logarithmic scale) as a function of the number oftransitions used in its determination. As expected, in general, as thenumber of transitions increases the uncertainty of the energy leveldecreases. MNRAS , 1–17 (2020) n update to the MARVEL dataset and ExoMol line list for C Table 8.
Summary of experimentally-derived M
ARVEL energy levels, including uncertainties and data sources, for highly-excited states of C . Bold indicatesnew data sources, italics indicates updated data sources. No is the number of energy levels in that vibronic state. See Table 5 for the citations to these sources. State v J -range No E -range Av Unc (cm − ) Sources1 Π g −
12 30 29861 − C Π g −
78 77 34241 − C Π g −
71 71 36005 − C Π g −
67 64 37719 − C Π g −
24 24 39306 − C Π g −
36 36 40775 − C Π g −
35 35 42033 − C Π g −
41 41 43030 − C Π g −
37 37 44631 − Π u −
13 35 51651 − Π u − − e Π g −
43 122 40420 − , , , e Π g −
55 159 41455 − , , 98BrHaKoCr, e Π g −
49 143 42433 − , e Π g −
48 138 43366 − , e Π g −
44 123 44260 − , e Π g −
15 41 45120 − e Π g −
16 40 45952 − e Π g −
12 32 46758 − e Π g −
15 40 47541 − e Π g −
14 35 48298 − e Π g
10 0 −
12 24 49035 − D Σ + u −
63 32 43231 − Σ + u −
65 33 45033 − Σ + u −
51 26 46806 − Σ + u −
37 18 48569 − Σ + u −
41 20 50268 − D Σ + u −
19 10 51956 − D Σ + u −
11 6 53616 − D Σ + u −
11 6 55247 − D Σ + u −
11 6 56849 − D Σ + u −
11 6 58422 − D Σ + u
10 1 −
11 6 59965 − D Σ + u
11 1 −
11 6 61478 − Π g − − Π g − − Π g − − Π g − − Π g − − E Σ + g −
66 32 54937 − Σ + g −
68 28 56529 − Σ + g −
32 15 58077 − Σ + g −
36 13 59550 − Σ + g −
46 15 60855 − Σ + g −
30 11 62305 − ∆ u −
33 61 57374 − , ∆ u −
37 35 58481 − ∆ u −
31 30 59546 − f Σ + g −
31 15 70819 − f Σ + g −
31 14 72176 − f Σ + g −
23 11 73452 − g ∆ g −
32 85 72268 − g ∆ g −
31 80 73741 − F Π u −
38 29 74713 − F Π u −
34 29 76100 − M ARVEL energy levels
Considering only the main component, the 2020 M
ARVEL compi-lation of C spectroscopic data added 1524 rovibronic states (765 singlets, 747 triplets, and 12 quintets) to the 2016 compilation andremoved 147 states (146 triplets and 1 quintet) due primarily to re-processing of the 07TaHiAm data to remove the predicted unmea-sured transitions previously incorrectly included. 55 of the removedstates are still present in the 2020 compilation as orphan energy lev- MNRAS000
ARVEL compi-lation of C spectroscopic data added 1524 rovibronic states (765 singlets, 747 triplets, and 12 quintets) to the 2016 compilation andremoved 147 states (146 triplets and 1 quintet) due primarily to re-processing of the 07TaHiAm data to remove the predicted unmea-sured transitions previously incorrectly included. 55 of the removedstates are still present in the 2020 compilation as orphan energy lev- MNRAS000 , 1–17 (2020) McKemmish et al.
Figure 4.
Summary of the energy levels from the M
ARVEL procedure. Each line is a unique spin-vibronic state, with each electronic state a unique colour.
Figure 5.
The distribution of uncertainties of the empirical energy levels generated for each electronic energy level. els ( i.e. , outside the main spectroscopic network), indicating thatthe connections between these energy levels and the main compo-nent were removed by the reprocessing.The new energy levels span 18 of the total of 20 electronicstates in the 2020 M
ARVEL C spectroscopic data compilation,and 79 of the 142 vibronic states. Six of these electronic states(C Π g , F Π u , f Σ + g , g ∆ g , 1 ∆ u , 3 Π g ) and 44 of these vi- bronic states are entirely new to this 2020 update. Increases in cov-erage were also notable for the e Π g state (increase of 333 levelsacross 11 vibrational states) and the A Π u state (increase of 106levels across 12 vibrational states). MNRAS , 1–17 (2020) n update to the MARVEL dataset and ExoMol line list for C Figure 6.
The relationship between the final uncertainty of the empirical energy levels and the number of transitions that contributed to the derived energylevel. []
Table 9.
Differences between old and new M
ARVEL compilations by elec-tronic state, quantified by MAD (mean absolute deviation) and Max (max-imum deviation). The "No" column specifies the number of states commonto the new and old compilations.2020 – 2016 EnergiesState No MAD Max 2016 Av uncX Σ + g
174 0.0034 0.0565 0.0006A Π u
512 0.0041 0.0566 0.0022B ∆ g
322 0.0013 0.0565 0.0022B (cid:48) Σ + g
58 0.0006 0.0019 0.0008D Σ + u
117 0.0888 0.5387 0.1643E Σ + g
113 0.0140 0.4942 0.1498a Π u Σ − g
762 0.0079 0.0829 0.0016c Σ + u
111 0.0038 0.0152 0.0015d Π g Π g
563 0.0498 1.4348 0.06594 Π g
32 0.4383 1.4070 0.08631 Π g
29 0.0067 0.0252 0.01161 Π u
35 0.0065 0.0252 0.0171
The old (2016) and new (2020) M
ARVEL rovibronic energy levelsfor C are different, though these differences are usually small.This difference is quantified in Table 9, which presents the averagechange in the energy levels of a given electronic state for quantumstates that are in both the 2016 and this 2020 M ARVEL compila-tions. The same data at vibronic resolution is provided in the Sup-plementary Information.Usually, the two M
ARVEL compilations predict energies thaton average agree to about 0.005 cm − for low-lying states, withmaximum deviations around 0.06 cm − . For higher electronic states, the differences in empirical energies between the two compi-lations is higher, up to an average of 0.44 cm − for the 4 Π g statefollowing the addition of significant new data in this 2020 M AR - VEL update. The main outliers to this trend are the a Π u , d Π g ,and e Π g states, which all have quite sizeable modifications from2016 to 2020. These changes can be traced primarily to a reprocess-ing of the 49Phillips and 07TaHiAm data, which corrected earliererrors. We carefully examined the states with large deviations andfound that the energies along a vibronic band were far smoother andmore reasonable in the 2020 update than the original 2016 compi-lation, indicating that these modifications improved the overall datacompilation.An integral part of the M ARVEL process is to provide pre-dictions for the accuracy of its empirical energy levels. Our datahere shows that the 2016 prediction of the average uncertaintiesgenerally is quite close to the changes in energy observed betweenthe 2016 and 2020 compilation, indicating that the original uncer-tainties were reasonable. The most notable underestimation in theoriginal uncertainties is for the X Σ + g state, which under-predictedchanges by about a factor of 5. Other significant deviations betweenthe 2016 prediction uncertainties and the 2020–2016 changes in en-ergy can be attributed to mis-assignments and processing errors inthe 2016 compilation. LINE LISTS
The supplementary information of this paper con-tains three updated states files for C , C C and C called , and respectively.The main modification to the original C line liststates file is that we re-M ARVEL ised the energy levels by replacingexisting energy levels with 4842 M
ARVEL ised energy levels from
MNRAS000
MNRAS000 , 1–17 (2020) McKemmish et al. this 2020 M
ARVEL update; these M
ARVEL ised energy levels aredenoted by a "m" while energy levels computed solely from theD UO spectroscopic model are denoted by "d". Note that there hasbeen no modifications to the underlying spectroscopic model of thisline list, i.e. , the potential energy and coupling curves were not re-fitted. For full details of the spectroscopic model for this linelist,one should refer to the original line-list paper (Yurchenko et al.2018b).Though we haven’t compiled a M ARVEL dataset for the C isotopologues, a reasonable assumption is that the line list errorsare similar between different isotopologues. Therefore, we followpast precedent (Polyansky et al. 2017; McKemmish et al. 2019) increating a pseudo-M ARVEL ised states file for C C and C byusing: E iso ≈ E Duoiso + ( E MARVELmain − E Duomain ) , (1)where E iso is the isotopologue energy for a given state in the finalline list, E Duoiso is the original spectroscopic model prediction usingD UO and E MARVELmain and E Duomain are the M
ARVEL and D UO predictedenergies of the state for the main isotopologue, in the case C .Energy levels modified in this way are labelled by "i" (for isotopo-logue pseudo-M ARVEL isation, in this way clearly distinguishedfrom M
ARVEL isation in the main isotopologue states file). For thecase of C , nuclear spin statistics means that some microstates arepresent in the isotopologue states files that are not present in themain C isotopologue states file, e.g. only one parity componentin a Π state is retained for each J in C while both are present for C and C C. To account for this, we used (M
ARVEL - D UO )energy differences from a single C parity state to correct bothparity states in the isotopologue files.The minor modification to the C states file is theinclusion of 71 energy levels that were predicted by 07TaHiAmdata but not otherwise included. These were based on 746 tran-sition frequencies from 07TaHiAm (Tanabashi et al. 2007) whichwere predicted (not experimentally measured), with some of theseinadvertently included in the 2016 compilation though none are inthis update. Given that the 07TaHiAm predictions are based onband-specific fits, they are likely more accurate than the original energy levels. Therefore, we found the associated energylevels of these additional lines by creating an extended M ARVEL input transitions file with these 746 additional frequencies (called in theSupplementary Information) and extracted 71 additional energylevels (compiled in
Predicted07TaHiAm.energies file in theSupplementary Information) which replaced the original energylevels in our updated C states file, with a label "p"(for perturbed).Note that the process of M ARVEL ising the linelistwas shown to help identify very subtle mistakes in the M
ARVEL compilation itself. For example, large errors in X Σ + g , v = J = −
54 energies between the line-list prediction and M AR - VEL energies helped identify a digitisation error where a "8" wasread as a "3" in the transition 77ChMaMa.558. These errors werecorrected in the final set of M
ARVEL transitions, energy levels andline lists provided by the Supplementary Information.As detailed in Table 10, this update increases the numberof M
ARVEL ised energy levels within the line list from 4555 to4916, increasing the coverage from 10.3% of all rovibronic lev-els to 11.1%. The new M
ARVEL ised energy levels are primarilyadditional vibrational levels ( ν = − , −
16) and expanded ro-tational coverage within the A Π u state, with data on b Σ − g , n = Table 10.
Summary of the overall proportion of energy levels and transi-tions that are M
ARVEL ised, i.e. based entirely on experimentally-derivedM
ARVEL energy levels.
Original Update
Energy levels
Number M
ARVEL ised 4 555 4 916*Total 44 189 44 189% M
ARVEL ised 10.3 11.1
All transitions (no intensity threshold)
Number M
ARVEL ised 258 729 307 076Total Num 6 080 920 6 080 920% M
ARVEL ised 4.3 5.0 ∗
71 of these M
ARVEL ised energy levels are found by combining the07TaHiAm predicted transition frequencies with the other M
ARVEL energy levels and running M
ARVEL . tions that are M ARVEL ised, i.e. , those with frequencies which areentirely determined by M
ARVEL energy levels, remains relativelylow, increasing from 4.3% to 5.2%.Looking at the strong to medium intensity transitions, how-ever, in Figure 7, we see that the bulk of the strong transitionsare M
ARVEL ised and that the 2020 update increases the per-centage of M
ARVEL ised transitions by about 5% when consider-ing the percentage of transitions with intensities above 10 − -10 − cm molecule − at 1000 K. The updated line list now hasexperimentally-derived (M ARVEL ised) transition frequencies forall strong transitions with intensities above 10 − cm molecule − (from 95.6% in original 8states) and 80.0% (from 75.7%) of alltransitions with intensities above 10 − cm molecule − at 1000 K.Due to the very high proportion of M ARVEL isation for strong-to moderate-strength transitions across the line list’s full spectralrange, this updated C line list is suitable for cross-correlationhigh-resolution studies of C in gaseous astrochemistry environ-ments such as exoplanets (de Kok et al. 2014). The 2016 M
ARVEL compilation has been significantly updated,with the addition of assigned transitions data from 8 old and 5 newexperiments on C to significantly extend the previous M ARVEL dataset for C , including an extra 8072 transitions and 1524 en-ergy levels spanning an extra six electronic states, and extra 44vibronic states. Data from five previously included sources havebeen updated and extended. The new data enabled a significant im-provement to the quality of the ExoMol C linelist by increasingthe M ARVEL isation-fraction of strong lines with frequencies above10 − cm molecule − from 94.2% to 99.4%. This increase in highaccuracy experimentally-derived (i.e., M ARVEL ) energy levels isextremely important astrophysically for very high resolution cross-correlation measurements that are now increasingly common withthe new generation of ground-based ultra-large telescopes.For laboratory spectroscopists, the existence of the M
ARVEL compilation, the M
ARVEL procedure and line lists have two mainbenefits: (1) a method to validate their data - for example, in thispaper, use of M
ARVEL enables calibration errors in 17KrWeBato be identified and corrected, (2) enables their new results to bereadily available to applications experts. Inclusion of new data isbest enabled by producing formatted assigned transitions, ideally
MNRAS , 1–17 (2020) n update to the MARVEL dataset and ExoMol line list for C Figure 7.
Proportion of strong-to-moderate intensity transitions that areM
ARVEL ised (based on experimentally-derived M
ARVEL energy levels) at1000 K in the updated line list compared to the original line list.Top panel considers the number of transitions (total number of transitionsvs the number M
ARVEL ised in the original and new versions of the linelist), whereas the bottom panel converts this to percentage of transitionsthat are M
ARVEL ised. The horizontal axis of both panels is an intensitylower threshold in a logarithmic scale; the vertical axis data gives data forall transitions with intensities above this threshold. adding their new data to pre-existing M
ARVEL compilations forthe molecule and contacting the creators of the most recent linelistfor their molecule. This strongly emphasizes the importance of au-thors providing their primary experimental data in the form of as-signed line lists rather than just supplying compound results suchas spectroscopic constants. M
ARVEL compilations currently existfor AlH (Yurchenko et al. 2018a), BeH (Darby-Lewis et al. 2018), C (Furtenbacher et al. 2016), NH (Darby-Lewis et al. 2019a),NO (Wong et al. 2017), O (Furtenbacher et al. 2019), Ti O(McKemmish et al. 2017), Zr O (McKemmish et al. 2018), iso-topologues of H O (Tennyson et al. 2009, 2010, 2013, 2014b,a;Clark et al. 2020), H
S (Chubb et al. 2018b), isotopologues ofH (Furtenbacher et al. 2013a,b), isotopologues of SO (Tóbiáset al. 2018), C H (Chubb et al. 2018a), H CCO (Fábri et al. 2011)and NH (Al Derzi et al. 2015; Coles et al. 2020), with ongoingwork on other molecules.For many diatomics accurate measurement of spin-forbiddenbands is very important for enabling the relative positioning of thespin manifolds, in the present case the singlet, triplet and quintetones. There are 88 of these transitions known for C ; however,the small T e of the lowest singlet state ( ≈
600 cm − ) increases theimportance of this information as this means that triplet absorptionis very important for the high-resolution spectroscopy of C .All allowed electronic bands from states below 12 000 cm − to a known electronic state have rotationally resolved data includedin this M ARVEL update except for the Messerle–Krauss band andthe Kable–Schmidt band. In the former case, the initial assignmentof the band is currently being questioned (Nauta & Schmidt 2020) with the C (cid:48) Π g expected by theory to be much higher in energy. Inthe latter case, the two electronic states involved are well charac-terised by other studies and so the updated ExoMol linelist can be expected to provide very accurate predictions of its spec-troscopy for users.A common trait of the higher lying states is the higher uncer-tainties in their energies, originating from lower resolution studiesin the ultraviolet region than other visible region studies. Of par-ticular note is the Deslandres–d’Azambuja band system which hasbeen seen in flames (Hornbeck & Herman 1949), plasma plumes(Camacho et al. 2008), laser ablation of graphite (Acquaviva &De Giorgi 2002) and astrophysics (Gredel et al. 1989; Berdyuginaet al. 2007). Yet remarkably the only modern, high resolution studyof these band was made of C (Anti´c-Jovanovi´c et al. 1985).A high resolution study of the Deslandres–d’Azambuja bands for C is overdue. ACKNOWLEDGMENTS
We thank Klaas Nauta, Tim Schmidt and Scott Kable for help-ful discussions and feedback. SNY and JT’s work was supportedby the STFC Projects No. ST/M001334/1 and ST/R000476/1. Thework performed in Budapest received support from NKFIH (grantno. K119658) and from the ELTE Excellence Program (1783-3/2018/FEKUTSTRAT) supported by the Hungarian Ministry ofHuman Capacities (EMMI).
DATA AVAILABILITY STATEMENT
The data underlying this article are available in the article and in itsonline supplementary material. These include the following file; • README_2020_C2_MARVEL - Explanation of all fileswithin the SI • ARVEL transitions file • ARVEL energies file • ARVEL input file that allows the predictions of 07TaHiAmto be incorporated into the final line list • Predicted07TaHiAm.energies - Theadditional energies predicted from12C2_experimentalplus07TaHiAmpredicted_MARVEL.inp • • SI_2020_C2MARVEL.pdf - Expanded analysis tables and fig-ures
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