© The Authors 2025

1 Introduction

Over the past 15 years, our research has primarily focused on the measurement, assignment, and analysis of over 30 different molecular species exhibiting large amplitude motions (LAMs). We have employed various computational codes to fit and predict the molecular spectra associated with LAMs. These codes, while effective, produce outputs in diverse formats. This variability in data presentation poses a challenge, especially for the astrophysical community, which predominantly requires spectral predictions in the “.cat” format. The .cat format is the standard used by major spectral databases such as the Cologne Database for Molecular Spectroscopy (CDMS; Müller et al. 2005) and the Submillimeter, Millimeter, and Microwave Spectral Line Catalog (JPL catalog; Pickett et al. 1998). The variability in output data formats is also a primary reason why the spectral data for many species exhibiting LAMs and other molecules that we have studied during this period are absent from these databases. The available data have mostly been dispersed across the supplementary sections of various publications, limiting their accessibility and utility for the broader scientific community.

In response to these challenges, we decided to create the Lille Spectroscopic Database¹ (LSD) as a complementary repository to CDMS, the JPL catalog, and other data sources. This initiative aims to consolidate all of our data into a single accessible location, thus enhancing its availability to the scientific community. The data primarily consist of rotational spectra predictions for molecules of astrophysical and/or atmospheric interest that were studied by our team. From an astrophysical perspective, this includes both molecules already detected in the interstellar medium and those that may potentially be observed in the future. Our primary objectives with LSD are to adhere to the French national open access policy, which mandates public accessibility of research data, and to introduce several additional features that facilitate data utilization. These features include providing spectral data in various frequency and intensity units; offering absorption cross sections at different temperatures, as frequently requested by astrophysicists; and continuously updating and revising the data to ensure its accuracy and relevance.

2 Database infrastructure

2.1 Database content as of March 2025

The list of molecules and their corresponding entries available in LSD as of March 2025 is presented in Table 1. Each entry in the .cat format is uniquely tagged with a six-digit identifier. The first three digits denote the molecular weight in atomic mass units, while the last three specify a particular catalog entry (e.g., vibrational state or isotopic species). Following established conventions, the JPL catalog entries use 0 in the first out of the last three digits (e.g., CH₃CN ground state as 41001), CDMS entries use 5 (e.g., 41505), and LSD entries use 8.

High-resolution rotational spectra with a resolved hyperfine structure can be observed in specific regions of the interstellar medium using modern radio telescopes. These environments, characterized by low temperatures (10–20 K), low densities (10²−10⁶ cm⁻³), and narrow velocity dispersions (~0.1–1 km s⁻¹), include dark molecular clouds, prestellar cores, diffuse clouds, star-forming region envelopes, galactic center clouds, and circumstellar shells. Such conditions minimize Doppler and collisional broadening, enabling the resolution of hyperfine splittings (typically kilohertz to megahertz). For example, methylamine (CH₃NH₂) detections in the hot cores G10.47+0.03 and NGC 6334F, reported by Ohishi et al. (2019) using the Nobeyama 45 m telescope, exhibit partially or fully resolved hyperfine components in transitions near 80–100 GHz, facilitated by line widths (~2 km s⁻¹) comparable to the splitting. In contrast, observations toward three hot cores in NGC 6334I by Bøgelund et al. (2019) at higher frequencies failed to resolve the hyperfine structure mainly due to increased Doppler broadening. To account for these variations, LSD provides distinct entries for hyperfine-resolved and unresolved spectra of the same species when data permits. Hyperfine-resolved entries identified in the last column of Table 1 are useful for analyzing high-resolution spectra, enabling precise molecular identification and kinematic studies, while unresolved entries streamline data management when hyperfine resolution is not observable.

2.2 Data output

The initial iteration of LSD is designed to archive spectral predictions alongside theoretically computed rotational and rovibrational molecular spectra. Future versions will incorporate experimental data, including measured transition frequencies. The current implementation employs a relational database (MySQL 8.0.33) to facilitate efficient querying across diverse parameters. The LSD website is powered by a Java application built on the Java Spring framework and integrates a robust back-end with a user-friendly front-end.

Data access is provided through both a standard web interface and a suite of streamlined RESTful Application Programming Interface (API) functions designed for external tool integration. A RESTful API (Representational State Transfer) is a type of web service architecture that enables resource-oriented stateless communication between systems over the Internet. In the case of the LSD API, interactions are performed using the “HTTP GET” method, which allows users to retrieve resources by specifying parameters in the URL. The API returns data in multiple formats, including JavaScript Object Notation (JSON), a lightweight human-readable format widely used in web applications and data exchange, and Extensible Markup Language (XML), a structured format compatible with many legacy tools and systems. The .cat files are retrieved in a standard plain text format. Full documentation is provided². Key API endpoints and functions allow users to query molecular metadata, access predicted line lists within defined frequency ranges, retrieve absorption cross sections at various temperatures, and list available species and isotopologs. This programmatic access allows for the integration of LSD data into different external analysis workflows, radiative transfer models, and visualization pipelines.

The primary LSD output consists of an archive containing at least three files:

• A spectral prediction file in the .cat format, customizable for frequency units, intensity units, temperature, and frequency range constraints;

• A readme.txt file, offering a concise data overview and partition function values; and

• A .bib file, providing the recommended citation.

When available, a file detailing molecular energy levels is also provided. In the web interface, each entry is accompanied by a list of principal references, including available spectroscopic measurements, dipole moment values, and other relevant data such as results from quantum chemical calculations.

A global frequency search, accessible via both the web interface and API, enables the export of results in a unified .cat format file. The output is consistently sorted by frequency according to standard conventions. To avoid data redundancy, the search is performed separately for entries with and without a hyperfine structure. The selection between these entry types is available as an option in both the web interface and the corresponding API function. Additionally, the web interface supports metadata-based search capabilities, enabling users to locate entries by tag, molecular name, or chemical formula. This functionality is implemented via a live search dialog located in the main header of the web page. The same input field also supports quick frequency-based searches within a limited range, providing an efficient tool for rapid access to specific spectral regions.

In the generated .cat files, quantum numbers are represented according to the standard .cat format, where each quantum number is expressed as an integer. For molecules exhibiting LAMs, where additional symmetry group labels are required, specific conversion rules are applied to map symmetry species to integer values. These conversion rules are documented in the metadata associated with each entry on the LSD website as well as in the accompanying readme.txt file. Each transition in a .cat file is also accompanied by a quantum number format code, which is included in the LSD output. This format follows the general conventions outlined by Poynter & Pickett (1985).

2.3 Partition functions

Partition functions are reported as distinct rotational (Q_r) and vibrational (Q_v) components, and they ensure transparency when Q_v data are unavailable. In such cases, Q_v = 1, and the total partition function is always computed as Q = Q_r × Q_v. For molecules exhibiting internal rotation of a C_3v top, modeled using the RAM36 (Ilyushin et al. 2010) or RAM36hf (Ilyushin 2018) codes, Q_r incorporates the torsional mode contribution as derived from first principles up to v_t = 8, while Q_v is calculated excluding this mode.

3 Intensity units conversion

The primary output generated by LSD is a file containing the predicted molecular rotational or ro-vibrational spectrum in the .cat format. This format was first introduced in 1985 with the initial version of the JPL catalog of submillimeter, millimeter, and microwave spectral lines (Poynter & Pickett 1985). Today, the .cat format remains a standard in the astrophysical community, and it is widely used by the popular radiative transfer Weeds software (Maret et al. 2011). The .cat format is also a standard in the spectroscopic community since it is employed by the well-known SPFIT/SPCAT suite of programs (Pickett 1991).

In the .cat format, each spectral transition is recorded on an 80-character line that provides all necessary information for clear identification. In particular, a molecular energy level can be defined using up to six quantum numbers, which is adequate for the majority of cases. From the data performance point of view, the 80-character length of each line aids in efficient machine parsing and is also easy for human reading. The combination of the short line length and the potential for tens of thousands of transitions in a molecular spectrum also allows the overall size of the output file to be constrained.

However, in application to astrophysical observations, the .cat format contains a point to which particular attention should be drawn. When considering an |m⟩ →|n⟩ transition, where m and n represent a set of quantum numbers for each state, in a standard .cat file, the line intensity is represented by the integrated absorption cross section σ_mn in nm² MHz/molecule units. However, in the radiative transfer models and codes, the line intensity is typically expressed as the Einstein spontaneous emission coefficient, A_mn, in s⁻¹ units (Van der Tak et al. 2007; Maret et al. 2011) or as the line strength S_mn = g_m|⟨n|μ_x|m⟩|² in D² units (Hollis et al. 2004), where μ_x is the dipole moment projection on the molecular axis x and g_m is the degeneracy factor of m state.

For rotational transitions, it is convenient to represent the degeneracy factor as a product, g_m = g_Jg_i (Gordy & Cook 1984). Here, g_J = 2J + 1 is the degeneracy associated with the rotational quantum number J and g_i is associated with other quantum numbers as well as nuclear spins and large amplitude motions. The g_i values can vary based on the Hamiltonian model or experimental conditions. When employing the total angular momentum quantum number F, resulting from the coupling between rotational angular momentum and one or more nuclear spins, g_J is replaced by g_F = 2F + 1 in the calculation of g_m.

In LSD, the line intensity is stored in the form g_Jg_i|⟨n|μ_x|m⟩|², where g_i excludes the nuclear spin statistical weight factor g_s, which is stored separately but is nonetheless incorporated in the final calculation of g_m. Consequently, LSD generates .cat files in which σ_mn is calculated using an equation very similar to Eq. (1) of Pickett et al. (1998): $${\sigma }_{mn}=\frac{1}{4\pi {\epsilon }_0}\frac{8{\pi }^3}{3hc}{\nu }_{mn}(e^{-E_m/kT}-e^{-E_n/kT})\frac{g_m|⟨n|{\mu }_x|m⟩{|}^2}{Q}.$$(1)

Here, ν_mn is the transition frequency, E_m and E_n are respectively the energies of two states (E_m < E_n), and Q is the partition function. Compared to Eq. (1) of Pickett et al. (1998), we explicitly use the factor $\frac{1}{4\pi {\epsilon }_0}$ for conversion into SI units. The partition function Q in Eq. (1) may be defined from first principles as $$Q=\sum _j{g}_j{e}^{-E_j/kT},$$(2)

where the summation is taken over all molecular energy levels.

Given the intensity units, when using .cat files in radiative transfer codes, it is necessary to convert line intensities from σ_mn to S_mn or A_mn. For instance, converting σ_mn to S_mn can be done directly using Eq. (1). The conversion to the Einstein coefficient A_mn can be performed indirectly from S_mn using the following definition of A_mn: $$A_{mn}=\frac{1}{4\pi {\epsilon }_0}\frac{64{\pi }^4{\nu }_{mn}^3}{3h{c}^3}|⟨n|{\mu }_x|m⟩{|}^2.$$(3)

In both cases, one thus requires accurately calculating S_mn, which in turn requires using the same partition function and degeneracy factors g_m as for σ_mn. To highlight the challenges in correctly converting the line intensities from .cat files, we present three case studies in the following subsections.

3.1 Malononitrile CH₂(CN)₂

Malononitrile is an asymmetric top molecule that was recently detected in the interstellar medium (Agúndez et al. 2024). Its equilibrium structure belongs to the C_2v symmetry point group. Due to this symmetry, the intensities of its rotational transitions are influenced by nuclear spin statistics. In the ground vibrational state, the spin statistical weights are g_s = 15 for rotational levels with K_a + K_c even, and they are g_s = 21 for levels with K_a + K_c odd (Motiyenko et al. 2019). Furthermore, the presence of two equivalent ¹⁴N nuclei (each with a nuclear spin I₁ = I₂ = 1) gives rise to a rather complex nuclear quadrupole hyperfine structure, particularly at low values of the quantum numbers J and K_a. The LSD database provides predictions of the rotational spectrum of malononitrile with and without a hyperfine structure as two separate entries, 66802 and 66801, respectively (see Table 1).

Accurately calculating line intensities for malononitrile requires careful consideration of both spin statistics and hyperfine degeneracies. Table 2 presents the computed intensities of the 1_1,1 ← 0_0,0 transition, along with the partition functions used. For hyperfine-resolved transitions, the base intensity stored in LSD, g_Jg_i|⟨n|μ_x|m⟩|², is multiplied by a normalized relative intensity factor r. In this case, g_i = 9 reflects the total degeneracy associated with the nitrogen nuclear quadrupole hyperfine structure. By contrast, for unresolved pure rotational transitions, g_i = 1. Correspondingly, the total degeneracy factors are thus g_m = 9g_Fg_s and g_m = g_Jg_s.

Additionally, reduced statistical weights of g_s = 5 (for K_a + K_c even) and g_s = 7 (for K_a + K_c odd) are used for the pure rotational spectrum. However, this reduction cannot be applied to hyperfine-resolved data, primarily because the statistical weights are further redistributed among hyperfine components as 1:9:5 (for K_a + K_c even) and 3:3:15 (for K_a + K_c odd), corresponding to total nuclear spin states I = 0, 1, and 2, respectively, where I = I₁ + I₂ (Cox et al. 1985). Consequently, the partition functions calculated for the two entries differ and must not be interchanged when evaluating σ_mn.

Since g_i is constant across all transitions in either case, it can be factored out of both the numerator (g_m) and the denominator (Q) in Eq. (1). Consequently, σ_mn becomes proportional to the ratio between the statistical weight g_s and the weight factor averaged in the calculation of Q. This ratio remains the same in both the hyperfine-resolved and pure rotational cases. Therefore, the only difference between the intensity of a hyperfine component and that of the corresponding pure rotational transition is the relative factor r. As r is normalized to unity, the sum of the absorption cross-sections σ_mn of all hyperfine components equals the σ_mn value of the unresolved pure rotational transition. This equivalence can be confirmed by comparing the absorption cross section in the last row of Table 2 with the sum of the cross sections in all previous rows.

3.2 Methylamine CH₃NH₂

Methylamine was one of the first molecules detected in the interstellar medium back in the 1970s (Fourikis et al. 1974; Kaifu et al. 1974). The methylamine molecule exhibits two coupled large amplitude motions: torsion of the methyl moiety and inversion, or wagging, of the amine moiety. In the frame of the group-theoretical formalism developed by Ohashi & Hougen (1987), the torsion-wagging-rotational energy levels of methylamine are labeled according to the symmetry species of the G₁₂ permutation-inversion group: A₁, A₂, B₁, B₂, E₁, and E₂. The nuclear spin statistical weights are g_s = 4 for each of the torsional-wagging-rotational levels of symmetry, A₁, A₂, and E₂, and they are g_s = 12 for each of the levels of symmetry B₁, B₂, and E₁.

In the first published catalog of the rotational spectrum of methylamine in the ground vibrational state (Ilyushin & Lovas 2007), as well as in further studies of the parent (Motiyenko et al. 2014) and ¹³C isotopic species of methylamine (Motiyenko et al. 2016), reduced statistical weights g_s = 1 and g_s = 3 were respectively used. The LSD entries for methylamine 31801, 31802, 32801, and 32802 are based on these studies. Conversely, the SPFIT-based model, which is the basis of the JPL catalog entry 31008, adopted the full statistical weights g_s = 12, 4.

Table 3 shows a comparison of the entries from the JPL and LSD databases for the ground vibrational state of methylamine. Despite the differences in g_s (which can be spotted by comparing values in the g_up column) and the partition functions used, an examination of the absorption cross sections σ_mn in Table 3 revealed a striking similarity. One may thus assume that there is a consistency in the calculation of both datasets. This similarity can be explained by the fact that the partition functions in the LSD and JPL catalogs are different and account for different sets of g_s in such a way that g_s is effectively canceled out from both the numerator (g_m) and the denominator (Q) in the calculation of σ_mn in Eq. (1).

Given the present case and the case presented in Sect. 3.1, it is crucial to note that one should not use the .cat files and partition functions from different sources interchangeably, as they may employ different g_i and g_s values. Using mismatched .cat files and partition functions could lead to incorrect calculations of the line strengths, S_mn, and Einstein coefficients, A_mn, potentially resulting in significant errors in the derived molecular abundances and physical conditions of the interstellar medium. Therefore, one should always ensure consistency in the sources of .cat files and partition functions.

3.3 Dimethyl ether-d₁ and d₂ CH₃OCH₂D/CH₃OCHD₂

Dimethyl ether (CH₃)₂O, similar to methylamine, was first detected in the interstellar medium in the 1970s (Snyder et al. 1974). In hot corinos such as IRAS 16293-2422, many hydrogenated molecules exhibit remarkably high deuterium-to-hydrogen (D/H) abundance ratios, significantly higher than those observed in hot cores. This phenomenon, known as super-deuteration (Ceccarelli 2023), is believed to be linked to molecular depletion on grain surfaces during the cold prestellar phase. Our studies of deuterated dimethyl ether, DME-d₁ (Richard et al. 2013), and doubly deuterated dimethyl ether, DME-d₂ (Richard et al. 2021), have led to the detection of these species in IRAS 16293-2422, showing that dimethyl ether is highly deuterated in this source, with a D/H abundance ratio of approximately 15%.

The parent dimethyl ether molecule is characterized by the internal rotation of two equivalent methyl groups that are hindered by a relatively high barrier of V₃ = 900 cm⁻¹. Deuteration on one of the methyl groups reduces the symmetry and results in two conformations: symmetric and antisymmetric. For DME-d₁, the symmetric conformation features the deuterium atom lying in the plane of the C–O–C atom skeleton, while the antisymmetric conformation has the deuterium atom in an off-plane position. The antisymmetric conformation thus has two equivalent configurations. Since deuteration only slightly changes the torsional barrier, and given the relatively high barrier height, the splittings due to tunneling between the two equivalent configurations are small and were not resolved in Doppler-limited spectra, except in a few rare cases.

We thus considered the rotational states of antisymmetric conformation as doubly degenerate with a degeneracy factor of g_i = 2, whereas the rotational states of the symmetric conformations were attributed a degeneracy factor of g_i = 1. We also treated symmetric and antisymmetric conformers as two separate species, and each was given its own partition function, respectively Q_s and Q_a. We determined the column density for each species, respectively N_s and N_a, and the total column density as N = N_s + N_a.

While this approach leads to a correct determination of column densities and D/H ratios, it is not consistent with laboratory spectroscopy of DME-d₁ since it does not allow for accurate calculation of σ_mn. Given that g_i is the same for all energy levels of the antisymmetric conformer, it can be factored out of the sum in Eq. (2) and then canceled from both the numerator and the denominator in Eq. (1). Therefore, within this approach, the calculated intensities σ_mn of symmetric and antisymmetric conformers are approximately the same. However, in the laboratory, a 2:1 ratio of intensities is typically observed, with the lines of the antisymmetric conformation being twice as strong due to unresolved tunneling splittings.

Moreover, this approach is not physically consistent. First, the conformations cannot be truly separated, as they are inter-converted by tunneling through a finite-height barrier. Therefore, one cannot consider the two conformations and their abundances independently, except at very low temperatures. Second, the approach has also led to incorrect calculations of A_mn for the anti-symmetric conformer in our previous studies. By definition, A_mn depends only on the transition frequency ${\nu }_{mn}^3$ and the transition moment |⟨n|μ_x|m⟩|². Provided that |m⟩ and |n⟩ are the same, with relatively close values of rotational and centrifugal distortion constants, one expects to obtain similar |⟨n|μ_x|m⟩|² values for the two conformations. However, a close inspection of Table 4 in Richard et al. (2013) showed that, on average, A_mn values for the antisymmetric conformer are two times smaller compared to the corresponding values for the symmetric one when considering ν_mn.

The origin of the error is an incorrect calculation of |⟨n|μ_x|m⟩|² starting from σ_mn in the .cat file. As an intermediate stage of calculation, one first gets S_mn values that are equal for the two conformations due to factorization and division by g_i, as explained above. Then, to calculate |⟨n|μ_x|m⟩|², one divides S_mn by g_m = g_Jg_i, which is two times larger for the antisymmetric conformation since g_i = 2.

The physically correct interpretation of the problem is to consider that the two conformations share a common set of energy levels. In this case, the partition function that should be used in Eq. (1) is defined as $$Q=Q_s+e^{-E_a/kT}{Q}_a,$$(4)

where E_a is the relative energy of the antisymmetric conformer with respect to the most stable symmetric one. Compared to our previous studies, within this approach, column densities for the two conformers cannot be derived separately. Using this partition function, it becomes impossible to factorize g_i. This leads to σ_mn and S_mn values being two times larger for the antisymmetric conformer, which is consistent with observed laboratory spectra of deuterated DME. Consequently, it also yields consistently similar A_mn values from $|⟨n|{\mu }_x|m⟩{|}^2=\frac{S_{mn}}{g_m}$.

New partition functions for DME-d₁ and DME-d₂ are provided in LSD. The energy E_a is difficult to assess due to its relatively low value. In the calculation of Q according to Eq. (4), we used E_a = 10 cm⁻¹, the value adopted in the analysis of the rotational spectra of singly and doubly deuterated methyl formate (Margulès et al. 2009; Coudert et al. 2012). We also note that in these studies, we used partition functions calculated using the physically consistent approach of Eq. (4).

4 Data precision and extrapolation

Accurate spectral predictions are essential for the detection of molecules in the interstellar medium, as they allow for the identification of the specific spectral signatures of different chemical species. These signatures, which are often very faint and at the limit of spectral confusion, require precise modeling to be distinguished with certainty and to ensure unambiguous detection of new species. The most recent surveys (GOTHAM, McGuire et al. 2020; QUIJOTE, Cernicharo et al. 2023); particularly in cold environments (Remijan et al. 2024), have achieved the best experimental resolutions and precisions, which are measured in laboratories, at a few kilohertz.

The quality of rotational spectrum predictions is closely linked to how errors propagate through the different molecular Hamiltonian parameters used in the calculations. These parameters, such as rotational constants, distortion constants, and coupling terms, come from experimental measurements that carry uncertainties. They directly affect the quality of the rotational spectrum predictions. The uncertainties on the transitions are calculated using the classical error propagation method. It should be noted that this only takes into account parameters that are determined, not those that are undetermined and therefore set to zero with zero uncertainty. The indicated uncertainty is therefore optimistic, and its actual uncertainty may be up to ten times larger in the most extreme cases of highly flexible molecules, large amplitude motions, or strong ro-vibrational coupling.

Extrapolating predictions into ranges where there have been no laboratory measurements can be very delicate. Indeed, when extrapolating to higher frequencies, the transitions involve higher quantum numbers, which influence molecular parameters that are either undetermined or poorly determined. These parameters affect the quality of rotational spectrum predictions directly. Their absence or imprecision introduces uncertainties into the calculations, leading to errors in the position and intensity of the predicted spectral lines. These discrepancies can make it difficult to correctly identify molecular transitions and distort the interpretation of the data.

For these reasons, we restrict the available spectral predictions in LSD to frequency ranges close to those with experimental measurements, and we limit its catalog to transitions with predicted uncertainties no greater than 0.5 MHz, or 1 MHz in certain cases. This approach ensures a high level of reliability in molecular identifications and prevents misleading assignments due to excessive extrapolation errors. However, the full catalog, including all available data, is still used to compute rotational partition functions, which are essential for deriving accurate molecular abundances.

5 Conclusions

The Lille Spectroscopic Database provides a structured and accessible repository for rotational and ro-vibrational spectra of astrophysically and atmospherically relevant molecules. By integrating a relational database with API functionality, LSD facilitates efficient data retrieval and ensures compatibility with existing modeling tools.

In this work, we have highlighted the challenges associated with converting intensity units between different spectroscopic conventions. We demonstrated how variations in statistical weights and partition function definitions can impact intensity calculations and emphasized the importance of consistency in data usage. Additionally, we discussed the propagation of uncertainties in spectral predictions, particularly when extrapolating beyond measured frequency ranges. These factors are critical for ensuring the reliability of spectral data in astrophysical and laboratory applications.

The process of compiling and organizing the database also allowed us to identify and correct inconsistencies in previously published data. An example is the case of deuterated dimethyl ether, where intensity calculations were initially affected by incorrect statistical weight assignments. Through careful revision of partition functions and degeneracy factors, we corrected these discrepancies and removed the inconsistencies in the calculated intensities of rotational transitions.

Our future efforts will focus on expanding the database with additional experimental data, refining uncertainty estimates, and enhancing data retrieval tools. We intend to maintain an open-access policy and to continuously improve the data quality in LSD, with the aim being to support the scientific community in molecular spectroscopy and astrophysics.

Acknowledgements

We acknowledge the support of “Mésocentre de Calcul Scientifique Intensif de l’Université de Lille” for hosting the LSD. We also want to thank José Cernicharo and Arnaud Belloche for helpful discussions and debugging.

References

All Tables