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Register a new userOn the universality of spectroscopic constants of diatomic molecules
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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.
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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, which describes local anharmonic effects. From Eckart potential (EP) model, it is possible to find a connection with the GMP model, as well as obtain the analytical expression for the energy spectrum because it is based on $S,Oleft(2,1right)$ algebras. In this work we find the macroscopic properties such as vibrational mean energy $U$, specific heat $C$, Helmholtz free energy $F$ and entropy $S$ for a heteronuclear diatomic system, along with the exact partition function and its approximation for the high temperature region. Finally, we make a comparison between the graphs of some thermodynamic functions obtained with the GMP and the Morse potential (MP) for $H,Cl$ molecules.
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 Dirac equation. The first one is based on a min-max principle and uses a two-spinor formulation as a starting point. The second one is the Rayleigh-Ritz variational method combined with kinematically balanced basis functions. Both methods use a B-spline basis function expansion. We show that accurate results can be obtained with both methods and that no spurious states appear in the discretization process.
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 dipole moments of diatomic molecules can be learned, and hence predicted, with a relative error <5%. The dataset contains the dipole moment of 162 diatomic molecules, the most exhaustive and unbiased dataset of dipole moments up to date. Our findings show that the dipole moment of diatomic molecules depends on atomic properties of the constituents atoms: electron affinity and ionization potential, as well as on (a feature related to) the first derivative of the electronic kinetic energy at the equilibrium distance.
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 temperatures lower than a few tens of nanoKelvin. In this work we consider the benchmark ultracold reaction between, the most-celebrated ultracold molecule, KRb and K. For the first time we map out an accurate ab initio ground state potential energy surface of the KRbK complex in full dimensionality and report numerically exact quantum-mechanical reaction dynamics. The distribution of rotationally resolved rates is shown to be Poissonian. An analysis of the hyperspherical adiabatic potential curves explains this statistical character revealing a chaotic distribution for the short-range collision complex that plays a key role in governing the reaction outcome. We compare this with a lighter system with a smaller density of states (here the LiYbLi trimer) which displays random, and not chaotic, behavior.
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) and J. Chem.Phys. {bf 124}, 084905 (2006)). In the level-set method, a possible solute-solvent interface is represented by the zero level-set (i.e., the zero level surface) of a level-set function and is eventually evolved into the equilibrium solute-solvent interface. The evolution law is determined by minimization of a solvation free energy {it functional} that couples both the interfacial energy and the van der Waals type solute-solvent interaction energy. The surface evolution is thus an energy minimizing process, and the equilibrium solute-solvent interface is an output of this process. The method is implemented and applied to the solvation of nonpolar molecules such as two xenon atoms, two parallel paraffin plates, helical alkane chains, and a single fullerene $C_{60}$. The level-set solutions show good agreement for the solvation energies when compared to available molecular dynamics simulations. In particular, the method captures solvent dewetting (nanobubble formation) and quantitatively describes the interaction in the strongly hydrophobic plate system.
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