Canonical Approaches to Applications of the Virial Theorem

Abstract

Canonical approaches are applied for investigation of the extraordinarily accurate electronic ground state potentials of H2(+), H2, HeH(+), and LiH using the virial theorem. These approaches will be dependent on previous investigations involving the canonical nature of E(R), the Born-Oppenheimer potential, and F(R), the associated force of E(R), that have been demonstrated to be individually canonical to high accuracy in the case of the systems investigated. Now, the canonical nature of the remaining functions in the virial theorem [the electronic kinetic energy T(R), the electrostatic potential energy V(R), and the function W(R) = RF(R)] are investigated and applied to H2, HeH(+), and LiH with H2(+) chosen as reference. The results will be discussed in the context of a different perspective of molecular bonding that goes beyond previous direct applications of the virial theorem.

The electron delocalization range in stretched bonds

“…Figure shows a global picture of H 2 dissociation, plotting the bond energy Δ E bond , total electronic kinetic energy KE, and system‐averaged delocalization length D max as functions of bond length. Δ E bond and KE match previous work . Trends in D max mirror trends in KE: where the KE is large, D max is small, and vice versa.…”

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

“…were also shown recently to be individually canonical giving further perspectives into the nature of chemical bonding [21].…”

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.…”

“…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.…”

“…The definition of the endpoints R j and R rj as explained above is not unique and indeed it can be generalized as reported previously. 34,35 It should be emphasized that H 2 and H 2 + are two-electron and one-electron molecules,…”