A simple model for scalar relativistic corrections to molecular total atomisation energies

ABSTRACT

Scalar relativistic corrections to atomisation energies of first- and second-row molecules can be rationalised in terms of a simple additive model, linear in changes in atomic s populations. In a sample of 200 first-and second-row molecules, such a model can account for over 98% of the variance (99% for the first-row subset). The remaining error can be halved again by adding a term involving the change in atomic p populations: those coefficients need not be fitted but can be fixed from atomic electron affinity calculations. This model allows a fairly accurate a priori estimate for the importance of scalar relativistic corrections on a reaction energy, at essentially zero computational cost. While this is not a substitute for explicit calculation of Douglas–Kroll–Hess (DKH) or exact two-component (X2C) relativistic corrections, the model offers an interpretative tool for the chemical analysis of scalar relativistic contributions to reaction energies.

GRAPHICAL ABSTRACT

KEYWORDS:

• Thermochemistry
• scalar relativistic effects
• population analysis
• nature of the chemical bond

Acknowledgements

The authors would like to thank Dr. Kenneth G. Dyall (Schrödinger, Inc.) for enlightening discussions at the 58th Sanibel Symposium, and Prof. Pekka Pyykkö (U. of Helsinki) for helpful comments and for bringing the early work of Anders Fröman [39,40] to our attention. This paper is dedicated to the memory of Prof. Israel Rubinstein OBM (1947–2017), outstanding scientist, friend and Renaissance man.

Supporting information

The computed and model-generated scalar relativistic corrections for the W4-17 dataset, as well as the population analyses, are freely available online in the FigShare data repository at http://doi.org/10.6084/m9.figshare.6154418, reference number 6154418.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. In the process, we found that the W4-17 dataset contains a typo: the DKH2 scalar relativistic correction for PF5 in the ESI of Ref. [34] should read −2.57 kcal/mol rather than −3.52 kcal/mol (which was obtained using a smaller basis set). We thank Prof. Amir Karton (U. of Western Australia) for clarifying this.

Additional information

Funding

This work was supported by Israel Science Foundation: [Grant Number 1358/15], the Minerva Foundation, and the Helen and Martin Kimmel Center for Molecular Design (Weizmann Institute of Science).