Large and Small Distances

Goodisman, Jerry

doi:10.1016/b978-0-12-290202-4.50006-3

Cited by 6 publications

(4 citation statements)

References 201 publications

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“…In the present contribution, it is demonstrated that the above notion of canonical potential or force curve shape plays an even more fundamental role in discussions of the nature of the molecular bond than just the energy E ( R ) and its associated force F ( R ). To illustrated that role, it proves helpful to express the virial theorem written in the form: ,, in which T ( R ), V ( R ), and W ( R ) denote the electronic kinetic energy, electrostatic potential energy and (virtual) work (done by the Feynman force). It can be shown that each of the energies T ( R ), V ( R ), and W ( R ) also are canonical in the sense described above.…”

Section: Methodsmentioning

confidence: 99%

Canonical Approaches to Applications of the Virial Theorem

et al. 2016

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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.

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Section: Methodsmentioning

confidence: 99%

Canonical Approaches to Applications of the Virial Theorem

et al. 2016

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“…Approaches to quantum mechanics that have the potential to improve the situation described in the previous paragraph are thus of particular interest. In this context, the method initially advocated by Slater to pairwise interatomic interactions to study molecular bonding through application of the virial theorem , and its subsequent relationship to the Hellmann–Feynman theorem , strictly within the Born–Oppenheimer approximation , is considered such an example.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2016

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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.

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“…Such accuracy is necessary if the algebraic Hamiltonians which generate fits to vibrational spectra are to be used subsequently in the construction of potential energy functions in coordinate space. Although well-known techniques exist for the inversion of spectroscopic data to generate diatomic potential functions, it is appropriate to study the applicability of the algebraic approach in this regard because of its capability of extension to polyatomic species for which the link between spectrum and potential by conventional methods is more difficult to achieve. To date, ab initio calculations have been used to calculate potential energy surfaces for triatomic molecules with spectroscopic accuracy, and vibrationally excited states of small polyatomic molecules have been analyzed by canonical Van Vleck perturbation theory…”

Section: Introductionmentioning

confidence: 99%