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We show, through a machine learning approach, that the equilibrium distance, harmonic vibrational frequency, and binding energy of diatomic molecules are universally related. In particular, the relationships between spectroscopic constants are valid independently of the molecular bond. However, they depend strongly on the group and period of the constituent atoms. As a result, we show that by employing the group and period of atoms within a molecule, the spectroscopic constants are predicted with an accuracy of $lesssim 5%$. Finally, the same universal relationships are satisfied when spectroscopic constants from {it ab initio} and density functional theory (DFT) electronic structure methods are employed.
Due to one of the most representative contributions to the energy in diatomic molecules being the vibrational, we consider the generalized Morse potential (GMP) as one of the typical potential of interaction for one-dimensional microscopic systems, w
Two numerical methods are used to evaluate the relativistic spectrum of the two-centre Coulomb problem (for the $H_{2}^{+}$ and $Th_{2}^{179+}$ diatomic molecules) in the fixed nuclei approximation by solving the single particle time-independent Dira
We present a data-driven approach for the prediction of the electric dipole moment of diatomic molecules, which is one of the most relevant molecular properties. In particular, we apply Gaussian process regression to a novel dataset to show that dipo
A fundamental question in the study of chemical reactions is how reactions proceed at a collision energy close to absolute zero. This question is no longer hypothetical: quantum degenerate gases of atoms and molecules can now be created at temperatur
A level-set method is developed for numerically capturing the equilibrium solute-solvent interface that is defined by the recently proposed variational implicit solvent model (Dzubiella, Swanson, and McCammon, Phys. Rev. Lett. {bf 104}, 527 (2006) an