A Unified Perspective on the Nature of Bonding in Pairwise Interatomic Interactions

Force Based Canonical Approximation of Molecular Potentials: Average Force versus Pointwise Force

This work presents a new force-based canonical approach that utilizes the average force rather than the pointwise force, on which previously developed canonical approaches were based. Advantageously, the average force based method only requires the evaluation of the potential function and not its derivative. The average force and the pointwise force based methods are applied to a variety of diatomic molecules, and their accuracy is compared. It is demonstrated that the average force based method gives an improved accuracy compared to the pointwise force based method. This improved accuracy is attributed to the fact that the average force based method eliminates the need to use the numerical approximation of the derivative of the potential function that, in practice, is only known at discrete points. In addition, an algorithm is developed to apply the average force based method as a practical tool for generating potential curves for pairwise interatomic interactions utilizing the classical Lennard-Jones potential as reference. Moreover, application of the average force based method leads to a new canonical approximation paradigm. In this new paradigm, only the coordinates of the equilibrium configuration (the bottom of the potential well) of a molecule are required for accurate generation of the potential function. Moreover, theoretical results are presented, demonstrating the effectiveness of the canonical transformation procedure in producing highly accurate potential approximations. In particular, it is proved that a certain general set of qualitative conditions on potential-like functions are sufficient for a given potential function to be in the same canonical transformation class as a (dimensionless) Lennard-Jones potential. For functions satisfying these assumptions, it is shown that they have canonical approximations with arbitrarily small approximation errors.

Is there any fundamental difference between ionic, covalent, and others types of bond? A canonical perspective on the question

Canonical approaches demonstrate that pairwise interatomic interactions are fundamentally the same.

A general transformation to canonical form for potentials in pairwise interatomic interactions

Weakly bound (red; (i) Ar₂ (ii) Ar–HBr (iii) OC–Cl₂ (iv) OC–HF) and strongly bound (blue; (i) H₂ (ii) H₂⁺ (iii) LiH (iv) HF) pairwise interactions transformed to one canonical potential.