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Two-step emergence: the quantum theory of atoms in molecules as a bridge between quantum mechanics and molecular chemistry

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Like Cervantes’ tale of Sancho Panza, who loses his donkey in one chapter but a few chapters later, thanks to the forgetfulness of the author, is riding the dear little animal again, our story has contradictions.

Erwin Schrödinger (1953)

Abstract

By moving away from the traditional reductionist reading of the quantum theory of atoms in molecules (QTAIM), in this paper we analyze the role played by QTAIM in the relationship between molecular chemistry and quantum mechanics from an emergentist perspective. In particular, we show that such a relationship involves two steps: an intra-domain emergence and an inter-domain emergence. Intra-domain emergence, internal to quantum mechanics, results from the fact that the electron density, from which all the other QTAIM’s concepts are defined, arises from the wavefunction as a coarse-grained magnitude. Inter-domain emergence involves an analogical link, a map**, between QTAIM’s entities, such as topological atoms and bond paths, and the entities that populate the molecular-chemistry domain, such as chemical atoms and chemical bonds.

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Notes

  1. The wavefunction can be complex in case of the presence of an external magnetic field, for example.

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Acknowledgements

The authors are grateful to Professor Lou Massa (Hunter College) for several enlightening discussions. C.F.M. acknowledges the Natural Sciences and Engineering Research Council of Canada (NSERC), the Canada Foundation for Innovation (CFI), and Mount Saint Vincent University for funding. This study was also supported by Agencia Nacional de Promoción Científica y Tecnológica (Grant No. PICT-2018- 04519).

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  1. Department of Chemistry and Physics, Mount Saint Vincent University, Halifax, B3M 2J6, Canada

    Chérif F. Matta

  2. Department of Chemistry, Dalhousie University, Halifax, NS, B3H 4J3, Canada

    Chérif F. Matta

  3. CONICET, University of Buenos Aires, Buenos Aires, Argentina

    Olimpia Lombardi & Jesús Jaimes Arriaga

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Matta, C.F., Lombardi, O. & Jaimes Arriaga, J. Two-step emergence: the quantum theory of atoms in molecules as a bridge between quantum mechanics and molecular chemistry. Found Chem 22, 107–129 (2020). https://doi.org/10.1007/s10698-020-09352-w

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