A canonical approach to forces in molecules

Abstract

In a previous study, we introduced a generalized formulation for canonical transformations and spectra to investigate the concept of canonical potentials strictly within the Born-Oppenheimer approximation. Data for the most accurate available ground electronic state pairwise intramolecular potentials in H 2 + , H 2 , HeH + , and LiH were used to rigorously establish such conclusions. Now, a canonical transformation is derived for the molecular force F(R) from the Hellmann-Feynman Theorem with H 2 + , the simplest molecule as molecular reference. These transformations are demonstrated to be inherently canonical to high accuracy but distinctly different from those corresponding to the respective potentials of H 2 , HeH + , and LiH. Further applications of this methodology to Mg 2 , benzene dimer and to water dimer are also considered within the radial limit. The implications of these results for electrostatic model of chemical bonding will be considered and discussed using this fundamentally force-based canonical approach.

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.…”

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.…”

“…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,…”