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A new force-based canonical approach for the accurate generation of multidimensional potential energy surfaces is demonstrated. Canonical transformations previously developed for diatomic molecules are used to construct accurate approximations to the 3-dimensional potential energy surface of the water molecule from judiciously chosen (adopting the right coordinate system) 1-dimensional planar slices that are shown to have the same canonical shape as the classical Lennard-Jones potential curve. Spline interpolation is then used to piece together the 1-dimensional canonical potential curves, to obtain the full 3-dimensional potential energy surface of a water molecule with a relative error less than 0.01. This work provides an approach to greatly reduce the computational cost of constructing potential energy surfaces in molecules from ab initio calculations. The canonical transformation techniques developed in this work illuminate a pathway to deepening our understanding of chemical bonding.

Rovibrational transitions associated with tunneling states in the ν5 (water bending) vibration of the OC-H2O complex have been recorded using a supersonic jet mode-hop free quantum cascade laser spectrometer at 6.2 μm. Analysis of the resulting spectra is facilitated by incorporating fits of previously recorded microwave and submillimeter data accounting for Coriolis coupling. The theoretical basis of morphing a 5-D frozen monomers potential was initially developed and then extended to two 6-D morphed potentials. A combination of these spectroscopic results and previous rovibrational data for the ν5 vibration in OC-D2O are then used to generate a 6-D morphed potential surface for the intermolecular and the water bending vibrations. An alternative 6-D morphed potential of the intermolecular and the ν3 (CO stretching) vibrations was also generated. These determined morphed potentials then formed the basis for modeling the dynamics of the complex and prediction of accurate intermolecular rovibrational frequencies of the complex.

The concept of chemical bonding is normally presented and simplified through two models: the covalent bond and the ionic bond. Expansion of the ideal covalent and ionic models leads chemists to the concepts of electronegativity and polarizability, and thus to the classification of polar and non-polar bonds. In addition, the intermolecular interactions are normally viewed as physical phenomena without direct correlation to the chemical bond in any simplistic model. Contrary to these traditional concepts of chemical bonding, recently developed canonical approaches demonstrate a unified perspective on the nature of binding in pairwise interatomic interactions. This new canonical model, which is a force-based approach with a basis in fundamental molecular quantum mechanics, confirms much earlier assertions that in fact there are no fundamental distinctions among covalent bonds, ionic bonds, and intermolecular interactions including the hydrogen bond, the halogen bond, and van der Waals interactions.

Canonical approaches are applied to classic Morse, Lennard-Jones, and Kratzer potentials. Using the canonical transformation generated for the Morse potential as a reference, inverse transformations allow the accurate generation of the Born-Oppenheimer potential for the H2+ ion, neutral covalently bound H2, van der Waals bound Ar2, and the hydrogen bonded one-dimensional dissociative coordinate in a water dimer. Similar transformations are also generated using the Lennard-Jones and Kratzer potentials as references. Following application of inverse transformations, vibrational eigenvalues generated from the Born-Oppenheimer potentials give significantly improved quantitative comparison with values determined from the original accurately known potentials. In addition, an algorithmic strategy based upon a canonical transformation to the dimensionless form applied to the force distribution associated with a potential is presented. The resulting canonical force distribution is employed to construct an algorithm for deriving accurate estimates for the dissociation energy, the maximum attractive force, and the internuclear separations corresponding to the maximum attractive force and the potential well.

In previous studies, 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 H2+, H2, HeH+, and LiH were used to rigorously establish such conclusions. Now, a canonical transformation is derived for the molecular force, F(R), with H2+ 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 H2, HeH+, and LiH. In this paper, we establish the canonical nature of the molecular force which is key to fundamental generalization of canonical approaches to molecular bonding. As further examples Mg2, benzene dimer and to water dimer are also considered within the radial limit as applications of the current methodology.

Force-based canonical approaches have recently given a unified but different viewpoint on the nature of bonding in pairwise interatomic interactions. Differing molecular categories (covalent, ionic, van der Waals, hydrogen, and halogen bonding) of representative interatomic interactions with binding energies ranging from 1.01 to 1072.03 kJ/mol have been modeled canonically giving a rigorous semiempirical verification to high accuracy. However, the fundamental physical basis expected to provide the inherent characteristics of these canonical transformations has not yet been elucidated. Subsequently, it was shown through direct numerical differentiation of these potentials that their associated force curves have canonical shapes. However, this approach to analyzing force results in inherent loss of accuracy coming from numerical differentiation of the potentials. We now show that this serious obstruction can be avoided by directly demonstrating the canonical nature of force distributions from the perspective of the Hellmann-Feynman theorem. This requires only differentiation of explicitly known Coulombic potentials, and we discuss how this approach to canonical forces can be used to further explain the nature of chemical bonding in pairwise interatomic interactions. All parameter values used in the canonical transformation are determined through explicit physical based algorithms, and it does not require direct consideration of electron correlation effects.

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 interactions. It is demonstrated that well-characterized potentials in Ar·HI, OC·HI, OC·HF, and OC·BrCl, 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 Slater (1972) concerning fundamental bonding properties in the categories of interatomic interactions analyzed.

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.

A proof-of-concept for the accurate generation of multidimensional intermolecular interaction potentials is demonstrated. The basis for evaluating this application is the available very accurate 3-D morphed potential of Ar·HBr. Starting from the well-defined potential of the simplest molecule, the diatomic H2+, a recently developed 1-D canonical potential is used with selected 2-D polyatomic data to generate the adiabatic intermolecular interaction potential in Ar·HBr, 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, Ar·HBr. Results indicate intrinsic bonding characteristics inherent to both systems.