A VSEPR-inspired force field for determining molecular properties of PF₅

ABSTRACT

Valence Shell Electron Pair Repulsion (VSEPR) theory, commonly taught in introductory chemistry courses, provides a basis for understanding the molecular structures of molecules of the type XY${}_m$, where X is a central atom surrounded by m Y ligands. While VSEPR is generally thought of only as a qualitative theory, Bartell and coworkers constructed a semi-quantitative model potential to address the physical underpinnings of VSEPR by introducing a points-on-a-sphere (POS) potential such that all X-Y bonds are of fixed length and all atoms Y${}_i$ repel each other. More than forty years ago, this simple model was shown to be effective in reproducing relative quadratic and cubic bending force constants for a variety of binary XY${}_m$ compounds when compared to values computed with semi-empirical and fairly primitive $\mathit{\text{ab}}$ $\mathit{\text{initio}}$ methods. The work presented here endeavours to go beyond the model used in the early investigations by Bartell and coworkers. Specifically, stretching force constants are clearly omitted from any POS model with a fixed radius, and are (primitively) included here by treating all X-Y bonds as simple (and equivalent) Morse oscillators. With the additional degrees of freedom in the parametrization that come from the Morse potential, the resulting model was investigated. The degree to which this simple mechanical model can reproduce quadratic and cubic force fields for PF${}_5$ is studied here, as well as how it works for a more difficult problem – the energetics and transition state properties for the intermediate in the (Berry) pseudorotation process that interchanges axial and equatorial fluorines in this prototype molecule. The five parameter Morse-POS model is shown to be do quite well in describing the quadratic and cubic force fields, as well as the pseudorotation process, a fairly impressive feat given the naivete of the model.

GRAPHICAL ABSTRACT

KEYWORDS:

• VSEPR
• force field
• points-on-a-sphere
• POS

Acknowledgments

This work is dedicated to our late friend, Dieter Cremer, whose work tended to recognise the simplicity and generalities that underlie complex phenomena associated with molecular structure and stereochemical dynamics. In addition, we also recognise the contributions of another recently late colleague and friend, L.S. Bartell, with the work presented here.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research was supported by the Zuckerman STEM Leadership Program as well as the U.S. National Science Foundation (Grant CHE-1664325).