Distributed molecular polarisabilities and asymptotic intermolecular interaction energies^†

Abstract

Strategies for obtaining distributed molecular polarisabilities and using them in calculations of interaction energies have been examined. A mathematically rigorous strategy applying constrained density fitting that practically removes the so-called charge-flow terms has been proposed. The resulting polarisabilities give asymptotic dispersion energies without the artefacts plaguing the previously used methods. In particular, since the charge-flow polarisabilities are extremely small in our approach, the terms in the distributed expansion of the dispersion energy which decay slower than the sixth inverse power of the intermonomer separation are negligible. Furthermore, we show that the usual practice of approximately locating or neglecting two-centre (nonlocal) distributed polarisabilities in calculations of these energies can now be abandoned since in the algorithm developed by us the inclusion of the nonlocal polarisabilities increases the computational requirements only by one power of the number of atoms and the summations can be restricted to within a small cutoff radius. Our method gives dispersion energies that are practically identical to the values computed from exact (unexpanded) formulas for all separations where charge-overlap effects are small, i.e. this approach gives the best possible asymptotic representation of dispersion energies. Thus, it should be possible to replace the current empirical dispersion functions by ab initio computed dispersion energies in a range of applications.

Keywords:

• distributed polarisability
• asymptotic expansion
• dispersion energy
• induction energy

Acknowledgements

The authors would like to thank Dr Bogumil Jeziorski, Dr Wojciech Cencek, Dr Alston Misquitta, Dr Rafal Podeszwa and Dr Anthony Stone for many helpful discussions and to Alston Misquitta and Anthony Stone for making their computer codes available to us. This research was supported by an ARO grant and the NSF Grant No. CHE-1152899.

^†This paper is dedicated to Trygve Helgaker.