Theoretical investigations on radiative opacity of OsO: contributions from the multiplet states

High-level relativistic quantum chemical calculations were performed with the BDF program package using the exact two-component (X2C) Hamiltonian, the ANO-R3 all-electron basis set, and the multi-reference second-order perturbation theory (MS-NEVPT2). Potential energy curves (PECs), spin–orbit coupling matrix elements, elec tronic angular momentum couplings, and electric dipole transition and permanent dipole mo ments as functions of internuclear distance were obtained for the 12 lowest Λ−S states of OsO, namely singlets, triplets and quintets.

These raw data are collected in the Excel file OsO.xlsx, which contains three worksheets: PECs (internuclear distance R in ˚ A and total energy in cm−1 relative to the minimum of the X1Σ+ state for each electronic state); PDMs (permanent dipole moments in Debye as a function of R); and TDMs (transition dipole moment components in Debye between different electronic states). Detailed input parameters and output information of these calculations are recorded in the text file OsO.log.Based on the electronic structure data, the nuclear motion (including electronic, vibra tional and rotational degrees of freedom) was solved by a variational coupled-channel method, as implemented in the DUO program.

This yielded all rovibronic energy levels, their quan tum numbers (total angular momentum J, parity, etc.), lifetimes, and Einstein A coefficients for electric-dipole transitions. The resulting line lists are provided in two files following the ExoMol standard format (Tennyson et al. 2013). OsO.states contains one row per unique rovibronic state.

The columns are: state index (n), energy term value E (in cm−1), total degen eracy gtot, total angular momentum J, lifetime τ (in seconds), total parity (p+/−), rotationless parity (pe/f), electronic state label, vibrational quantum number v, projection Λ of orbital an gular momentum, projection Σ of spin. The file contains several hundred thousand entries (the exact number is given in the file header).

OsO.trans lists every electric-dipole allowed transition. Each line gives the upper state index (f), the lower state index (i), and the Einstein Afi coefficient (in s−1). The total number of transitions is of the order of millions.

Finally, the line lists were fed into the EXOCROSS program (a radiative transfer code developed by the ExoMol project) to compute the absorption cross-section under local thermo dynamic equilibrium (LTE). A Voigt line profile was adopted. Calculations were performed for five temperatures: 300, 1000, 2000, 3000 and 5000 K, covering the wavenumber range 0 40000 cm−1.

All rotational levels up to J = 100 were included. The output files are named OsO T P.xsec (e.g., OsO 300K 10P.xsec) and contain two columns: wavenumber (in cm−1) and total absorption cross-section (in cm2).These cross-sections represent the complete radiative opacity of OsO at the given temperature and can be directly used in astrophysical models. All files are provided in open, standard formats.

OsO.xlsx is a Microsoft Excel file and can be opened with any spreadsheet software (Excel, LibreOffice Calc, etc.). OsO.log, OsO.states,OsO.transandtheEXOCROSSoutputfilesareplaintextandcanbeviewed with any text editor. The .states and .trans files are ready to be used as input for EX OCROSS,whichisopen-sourceandavailableatexomol.com/tools/exocross/.

They are also compatible with other programs that support the ExoMol line-list format. The data are derived from state-of-the-art relativistic quantum chemical calculations and subsequent variational nuclear-motion treatments. Nevertheless, theoretical approximations in evitably introduce uncertainties.

Sources of error include incompleteness of the one-electron basis set, truncation of the multi-reference perturbation theory, approximations in the treatmen t of spin–orbit coupling, and numerical extrapolation of potential energy curves and dipole moments. These factors may affect the accuracy of energy levels and transition probabilities. The line list is suitable for modelling opacity at elevated temperatures (e.g., above a few hun dred kelvin); for high-resolution spectroscopy at low temperatures a cautious evaluation of the uncertainties is recommended.