Complete benchmark rovibrational energy linelists calculated for the primordial polar molecules of the universe, namely HD + , HD, and the HeH + isotopologues, with accuracy up to 10 −2 cm −1 for low-lying states, are presented. To allow for these calculations to be performed, new high-accuracy potential energy curves, which include the diagonal Born-Oppenheimer adiabatic corrections and the leading relativistic corrections, are determined. Also, a new approach for calculating non-adiabatic corrections involving an effective vibrational nuclear mass obtained based on the atoms-in-molecules theory is employed. The vibrational and rotational masses are taken as being different and dependent on the nuclear distance. Accurate dipole moment curves are calculated and used to generate lists of Einstein A-coefficients. The energy linelists and the sets of Einstein A-coefficients for HD are upgrades of previous calculations including quasibound states, while for HD + and HeH + and its isotopologues the present results represent significant improvement over the previous calculations. The results obtained here suggest that, with the inclusion of the non-adiabatic corrections, the accuracy limit at least for low-lying states might have been reached. Thus, further progress should involve accounting for even smaller effects such as the quantumelectrodynamics corrections. The present results represent the state-of-the-art of theoretical spectroscopy of the primordial polar molecules.

A previous theory of separation of motions of core and valence fractions of electrons in a molecule [J. R. Mohallem et al., Chem. Phys. Lett. 501, 575 (2011)] is invoked as basis for the useful concept of Atoms-in-Molecules (AIM) in the stockholder scheme. The output is a new tool for the analysis of the chemical bond that identifies core and valence electron density fractions (core-valence stockholder AIM (CVSAIM)). One-electron effective potentials for each atom are developed, which allow the identification of the parts of the AIM which move along with the nuclei (cores). This procedure results in a general method for obtaining effective masses that yields accurate non-adiabatic corrections to vibrational energies, necessary to attain cm accuracy in molecular spectroscopy. The clear-cut determination of the core masses is exemplified for either homonuclear (H, H) or heteronuclear (HeH, LiH) molecules. The connection of CVSAIM with independent physically meaningful quantities can resume the question of whether they are observable or not.

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By analysing the evolution of the COVID‐19 epidemic in the state of Minas Gerais, Brazil, we showed the importance of considering the sub‐notification not only of deaths but also of infected cases. It was shown that the largely used criteria of a historical all‐deaths baseline are not approachable in this case, where most of the deaths are associated with causes that should decrease due to social distancing and reduction of economic activities. A quite simple and intuitive model based on the Gompertz function was applied to estimate excess deaths and excess of infected cases. It fits well the data and predicts the evolution of the epidemic adequately. Based on these analyses, an excess of 21.638 deaths and 557.216 infected cases is predicted until the end of 2020, with an upper bound of the case fatality rate of around 2.4% and a prevalence of 2.6%. The geographical distribution of cases and deaths and its ethnic correlation are also presented. This study points out the necessity of governmental and private organizations working together to improve public awareness and stimulate social distancing to curb the viral infection, especially in critical places with high poverty.