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In this article, we describe an approach to teaching introductory quantum mechanics and machine learning techniques. This approach combines several key concepts from both fields. Specifically, it demonstrates solving the Schrödinger equation using the discrete-variable representation (DVR) technique, as well as the architecture and training of neural network models. To illustrate this approach, a Python-based Jupyter notebook is developed. This notebook can be used for self-learning or for learning with an instructor. Furthermore, it can serve as a toolbox for demonstrating individual concepts in quantum mechanics and machine learning and for conducting small research projects in these areas. 

Cross sections and thermally averaged rate coefficients for the vibrational excitation and de-excitation by electron impact on the HDO molecule are computed using a theoretical approach based entirely on first principles. This approach combines scattering matrices obtained from the UK R-matrix codes for various geometries of the target molecule, three-dimensional vibrational states of HDO, and the vibrational frame transformation. The vibrational states of the molecule are evaluated by solving the Schrödinger equation numerically, without relying on the normal-mode approximation, which is known to be inaccurate for water molecules. As a result, couplings and transitions between the vibrational states of HDO are accurately accounted for. From the calculated cross sections, thermally averaged rate coefficients and their analytical fits are provided. Significant differences between the results for HDO and H2O are observed. Additionally, an uncertainty assessment of the obtained data is performed for potential use in modeling non-local thermodynamic equilibrium (non-LTE) spectra of water in various astrophysical environments. 

This study presents Born–Oppenheimer energies and transition dipole moments of the 36 lowest electronic states of the N2+ ion as a function of internuclear distance in the interval between 1.5 and 10 bohrs obtained in first-principles calculations. The electronic states are of the total electronic spin S = 1/2, 3/2, and 5/2, dissociating toward to the lowest four N(4S0) + N+(3P), N(2P0) + N+(3P), N(2D0) + N+(3P), and N(4S0) + N+(1D) dissociation limits. Energies of the lowest states, dissociating toward to the N(4S0) + N+(3P) limit, are computed accounting for relativistic corrections. The obtained potential energy curves and the transition dipole moments are employed to compute vibrational energies in these states, vibronic transition dipole moments, and the Einstein coefficients for radiative transitions between the vibronic levels. 

This study presents calculations for cross sections of the vibrational excitation of H2O (X1A1) via electron impact. The theoretical approach employed here is based on first principles only, combining electron-scattering calculations performed using the UK R-matrix codes for several geometries of the target molecule, three-dimensional (3D) vibrational states of H2O, and 3D vibrational frame transformation. The aim is to represent the scattering matrix for the electron incident of the molecule. The vibrational wave functions were obtained numerically, without the normal-mode approximation, so that the interactions and transitions between vibrational states assigned to different normal modes could be accounted for. The thermally averaged rate coefficients were derived from the calculated cross sections for temperatures in the 10–10 000 K interval and analytical fits for rate coefficients were also provided. We assessed the uncertainty estimations of the obtained data for subsequent applications of the rate coefficients in modelling the non-local thermal equilibrium (non-LTE) spectra of water in various astrophysical environments. 

Energies, wavefunctions and lifetimes of vibrational resonances were computed for 18O-enriched isotopologue 50O_3=16O16O18O and 16O18O16O of the ozone molecule using hyperspherical coordinates and the method employing complex absorbing potential. 

This article presents a method of computing bound state potential curves and autoionizing curves using fixed-nuclei R-matrix data extracted from the Quantemol-N software suite. It is a method based on two related multichannel quantum-defect theory approaches. One is applying bound-state boundary conditions to closed-channel asymptotic solution matrices, and the other is searching for resonance positions via eigenphase shift analysis. We apply the method to the CH molecule to produce dense potential-curve datasets presented as graphs and supplied as tables in the publication supplement.