From H2+ to the multidimensional potential of the intermolecular interaction Ar·HBr: A canonical approach

Abstract

A new approach to the accurate generation of multidimensional intermolecular interaction potentials is demonstrated. The basis for evaluating this application is the available very accurate 3-dimensional morphed potential of ArHBr. Starting from the well-defined potential of the simplest molecule, the diatomic H 2 + , a recently developed canonical approach is applied and used with sufficient additional polyatomic data to generate the adiabatic intermolecular interaction potential in ArHBr, with HBr in the vibrational ground state. This represents the first application of canonical transformations to a higher vibrationally dimensional molecular system, in this case, ArHBr. Results indicate intrinsic bonding characteristics inherent to both systems.

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

“…We then studied a generalized formulation of canonical transformations [4] and spectra, and used it to investigate the concept of a canonical potential strictly within the Born-Oppenheimer approximation [11]. However, until very recently when a proof-of-concept analysis of the van der Waals dimer ArHBr was investigated [12], corresponding canonical transformations have not been investigated for polyatomic systems which involve higher vibrational dimensions.…”

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.…”