Benchmark Spectroscopic Linelists of Primordial Molecules for Astrophysics and Astrochemistry

Small molecular systems like H₂⁺, H₂, HeH⁺, LiH, H₃⁺ and their isotopologues play a fundamental role in the study of the cooling of the primordial universe, interstellar matter and star and planet formation. Research in these fields demand very accurate linelists, that is, the full list of rovibrational transitions. Present experiments are quite accurate but are limited to few lines, so that theory is the only source of complete linelists.

Calculations start with the generation of very accurate Born-Oppenheimer (BO) potential energy curves (PECs) or surfaces (PESs), obtained with explicitly correlated Gaussian basis functions. Diagonal-BO, relativistic and QED corrections of increasing quality are then added to the PECs or PESs. Even though, the energy values are inaccurate by some cm^-1 (1 cm^-1=1.24 x 10^-4 eV), the same order of the effect of the diagonal-BO correction, the largest correction to the PECs. The reason is the absence of non-adiabatic corrections (NACs), which affect directly the energy levels. 

When the electronic ground-state is well isolated, the physical origin of NACs is the dragging of electrons by the nuclei in their motion. NACs are then simulated by the use of effective nuclear masses, containing distance-dependent fractions of electrons, in the rovibrational equation. After the appearance of some particular empirical recipes for effective masses, we introduced a general and very accurate ab initio approach for the electron fractions that follow the nuclei, based on the stockholder AIM (atoms-in-molecules) theory [1]. 

This approach seems to solve definitively the problem, in what concerns the vibrational effective mass, within the accuracy of 10^-1 cm^-1 and allowed us to obtain benchmark linelists, cooling functions and Einstein A-coefficients for LiH and isotopologues [2] and HD⁺, HD and HeH⁺ (and isotopologues) [3].

References

[1] P. H. R. Amaral and J. R. Mohallem, J. Chem. Phys. 146, 194103 (2017); [2] L. G. Diniz, A. Alijah and J. R. Mohallem, Astrophys. J. Supp. Ser. 235, 35 (2018); [3] P. H. R. Amaral et al., Astrophys. J. Supp. Ser., 878, 95 (2019). Supported by CNPq and Capes