A canonical approach to multi-dimensional van der Waals, hydrogen-bonded, and halogen-bonded potentials

Abstract

A canonical approach is used to investigate prototypical multi-dimensional intermolecular interaction potentials characteristic of categories in van der Waals, hydrogen-bonded, and halogen-bonded intermolecular potential energy functions. It is demonstrated that wellcharacterized potentials in ArHI, OCHI, OCHF, and OCBrCl, can be canonically transformed to a common dimensionless potential with relative error less than 0.010. The results indicate common intrinsic bonding properties despite other varied characteristics in the systems investigated. The results of these studies are discussed in the context of the previous statement made by J. C. Slater [J. Chem. Phys. 57 (1972) 2389] concerning fundamental bonding properties in the categories of interatomic interactions analyzed.

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

“…Once that explicit transformation was generated, there was no necessity for any adjustable parameters across a range of bonding types to which it was applied; which include the diatomic molecules N 2 , CO, We describe here a unifying principle for understanding pairwise interatomic interactions from the perspective of recently developed, force based, canonical approaches. [28][29][30][31][32][33][34][35][36] The key ideas will be introduced through the consideration of pairwise interatomic interactions from the point of view of force, echoing the seminal result of R. P. Feynman 37 that "…the force on a nucleus in an atomic system is … just the classical electrostatic force that would be exerted on this nucleus by other nuclei and by the electrons' charge distribution". In the next Section, we develop Feynman's idea into a new canonical model that unifies pairwise interatomic interactions and lends strong support to the previous assertions made by Slater.…”

Canonical Force Distributions in Pairwise Interatomic Interactions from the Perspective of the Hellmann–Feynman Theorem

“…In this contribution, we demonstrate that appealing to the Hellmann-Feynman theorem avoids this difficulty, and perhaps even more importantly, it gives valuable insight into the nature of the canonical shapes of potential curves and their associated Feynman force distributions that have been shown in [18,19,23,24,25]. Figure 1 For each section I, II and III, one defines the associated dimensionless canonical form for H 2 :…”

“…The key for selecting these sequences of points was shown in [18,19,23,24] to rest fundamentally upon the associated Feynman forces:…”

“…In a sequence of recent papers [18,19,23,24], a notion of piecewise affine transformation to dimensionless canonical form was developed and applied to potentials corresponding to a wide class of diatomic molecules and pairwise intermolecular complexes. The basic affine transformation of a dimensional section of a potential curve E(R) for R 1 ≤ R ≤ R 2 to a canonical dimensionless curve has the form:…”

“…More specifically, we will use the Hellmann-Feynman theorem to calculate the Feynman force acting at one of the two nuclei for each of these molecules. In our previous works [18,19,23,24] on canonical forms and transformations for these molecules, we showed the pivotal role the Feynman force plays in their construction, and to that end, the Feynman force was calculated by differentiation of accurate ground-state potentials taken from the literature. For the parameter λ , we take the interatomic separation distance R and we adopt a Cartesian coordinate system centered equidistant between the two nuclei located at (0,0,± R / 2) in the (x,y,z) Cartesian frame.…”