Impact of COVID-19 in Minas Gerais, Brazil: Excess deaths, sub-notified cases, geographic and ethnic distribution.

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.

Non-adiabatic effects in the H3+ spectrum.

The effect of non-adiabatic coupling on the computed rovibrational energy levels amounts to about 2 cm-1 for H3+ and must be included in high-accuracy calculations. Different strategies to obtain the corresponding energy shifts are reviewed in the article. A promising way is to introduce effective vibrational reduced masses that depend on the nuclear configuration. A new empirical method that uses the stockholder atoms-in-molecules approach to this effect is presented and applied to H3+. Furthermore, a highly accurate potential energy surface for the D3+ isotopologue, which includes relativistic and leading quantum electrodynamic terms, is constructed and used to analyse the observed rovibrational frequencies for this molecule. Accurate band origins are obtained that improve existing data. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H3+, H5+ and beyond'.

Core-valence stockholder AIM analysis and its connection to nonadiabatic effects in small 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-1 accuracy in molecular spectroscopy. The clear-cut determination of the core masses is exemplified for either homonuclear (H2+, H2) 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.