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

Abstract

In recent work, force-based canonical approaches have given a unified but different viewpoint on the nature of bonding in pairwise interatomic interactions. The concept of a pairwise canonical potential in these cases was defined for a class of molecules referred to a dimensionless function obtained from each molecule by a readily invertible algebraic transformation. Differing molecular categories (covalent, ionic, van der Waals, hydrogen and halogen bonding) of representative interatomic interactions in which binding energies ranging from 1.01 to 1072.03 kJ/mol have been modeled canonically giving a rigorous semi-empirical verification to high accuracy. However, the fundamental physical basis that is expected to provide the inherent characteristics of these canonical transformations have not yet been elucidated. We now show that canonical force distributions can be formulated from the perspective of the HellmannFeynman Theorem and discuss how such canonical approaches can be used to further explain the nature of chemical bonding in pairwise interatomic interactions.

Canonical Approach To Generate Multidimensional Potential Energy Surfaces

“…The first observation is that the radial slices of the full H 2 O PES corresponding to fixing the two angular variables (Q,F) possess the same canonical shape seen in the wide array of diatomic molecules studied in Refs. [17][18][19][20][21][22][23][24][25][26]. The direct interpolation method described above (Section III.A) exploits the canonical nature of these radial slices to construct an approximation of the full H 2 O PES (for 44° < Q < 180° and 5° < F < 45°) that utilizes nine values for F and ten values for Q along with fourteen of the special radial values defined by the associated (radial) force.…”

“…This aspect of the canonical transformation methodology was recently extensively explored in the setting of diatomic molecules (see Refs. [17][18][19][20][21][22][23][24][25][26]. In particular, it was shown that through consideration of force (through which the key radial separation distances Rj are defined) rather than just potential energy the canonical structure of diatomic potential curves is revealed.…”

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

“…Recently developed canonical approaches to understanding molecular and intermolecular potentials and forces demonstrate "…that there is no very fundamental distinction between van der Waals binding and covalent binding", 2 or by extension, between covalent and hydrogen or halogen binding. [28][29][30][31][32][33][34][35][36] 3.…”

“…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.…”

“…Recently, we introduced explicit force-based transformations to canonical forms for potentials corresponding to both diatomic and two body intermolecular interactions. [28][29][30][31][32][33][34][35][36] The term canonical form for a class of molecular potentials refers to a dimensionless function obtained from each molecular potential within the defined class by a readily invertible piecewise affine (a function that performs a uniform scaling and translation of one interval of real numbers onto another interval) transformation. Furthermore, to be deemed canonical, the dimensionless forms obtained from all of the molecular potentials within the defined class by the canonical transformation must agree to within a specified order of high accuracy.…”