Noncovalent interactions and covalent bonds can be distinguished via quantum chemical topology analysis and molecular face theory, which are based on the potential acting on one electron in a molecule or molecular system (PAEM). A covalent bond forms when a PAEM bond critical point (BCP) occurs on the line connecting two atoms and when their molecular faces contact or fuse together, whereas a noncovalent interaction occurs between two adjacent atoms or chemical species when their molecular faces remain separate. The force acting on one electron within a molecule, which starts at infinity and ends at the BCP, forms nonoverlapping boundary surfaces that partition a molecule into distinct atomic regions. This is demonstrated with the following example reactions: H + H → H2, H + X → HX (X = F, Cl, Br, I), O (1D) + H2 → H2O, and S (1D) + H2 → H2S. The exploration of the physical quantities at PAEM critical points, such as the eigenvalues of the Hessian matrix, ellipticity, and electron interflow frequency, reveals their changing trends during the transition from a noncovalent interaction to a covalent bond or vice versa. These changes can help predict chemical bond formation or breakage, providing insight into chemical bonding.
The H2+ ion is the simplest example in which a chemical bond exists, created by one electron between two protons. As all chemical bonds, it is usually considered inexplicable in a classical frame. Here, in view of the extremely large velocities attained by the electron near the protons, we consider a relativistic extension of the standard classical three-body model. This has a great impact since the reference unperturbed system (clamped protons) is no more integrable, and indeed by molecular dynamics simulations, we find that the modification entails the existence of a large region of strongly chaotic motions for the unperturbed system, which lead, for the full system, to a collapse of the molecule. For motions of generic type, with the electron bouncing between the protons, there exists an open region of motions regular enough for producing a bond. Such a region is characterized by the property that the electron’s trajectories have an angular momentum pφ along the inter-nuclear axis of the order of the reduced Planck’s constant ℏ. Moreover, special initial data exist for which the experimental bond length and oscillation frequency of the protons (but not the dissociation energy) are well reproduced. Also, well reproduced is the quantum potential, albeit only in an extended interval about the minimum.
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