The Quantum Theory of Atoms in Molecules from a Bohmian perspective

J. A. JAIMES ARRIAGA; S. FORTIN

Bristol

Simposio; International Society for the Philosophy of Chemistry Summer Symposium 2018 (ISPC 2018); 2018

University Walk

One of the strongest arguments against the reduction of chemistry to physics is the one concerning the impossibility of recovering molecular structure from quantum mechanics. In this context, the Quantum Theory of Atoms in Molecules (QTAIM) (Bader 1990) has begun to attract the attention of chemists and philosophers of chemistry (see, e.g., Matta et al. 2011; Matta 2013), since it seems to be a rigorous formal proposal consistent with the principles and laws of quantum mechanics, which offers a theoretical foundation to the concept of molecular structure. This theory supports the idea that the physical manifestation of matter is given by the spatial distribution of the electron density and it is through this topology that the chemical concepts of atom, bond and structure can be defined. In particular, an atom in a molecule is bounded by a zero-flux surface in the gradient vector of electron density. This suggests that no electron can crossed such a surface and, hence, the electron density associated to each atom remains unchanged over time. In other words, it can be said that each particular electron belongs to a particular atom. However, this QTAIM view is completely alien to the conceptual world of standard quantum mechanics (SQM), where the picture of individual and distinguishable particles with defined though unknowable trajectories finds no place.On the other hand, the SQM perspective has prevailed to face the problem of the relationship between chemistry and physics, leaving aside other formalisms as the Bohmian Quantum Mechanics (BQM). A surprising fact when it is considered that the conceptual scheme of BQM is more consistent with the assumptions raised by the QTAIM. Actually, in a recent paper, Shan Gao (2013) argues that the electron density can be seen as an effective distribution originated by the ergodic motion of a charged particle, that is, an electron. According to Gao, in a one-charged particle system, the ergodic motion of the electron forms a ?cloud? of charge whose density is proportional to the square of the wave function. This argument reinforces the vision of QTAIM and is allied to the picture proposed by BQM, which can offer an adequate underlying ontology to recover charge density for quantum chemistry by appealing to Gao?s argument.In summary, unveiling the role played by the QTAIM in the intertheoretical relationships between chemistry and physics is of particular relevance. The possible connections or conceptual ruptures between the QTAIM and both the SQM and the BQM deserve to be analyzed. This analysis paves the way toward a possible explanation of the electron density as used by the QTAIM in terms of the fundamental dynamics of Bohmian particles.ReferencesBader, R. (1990). Atoms in Molecules. A Quantum Theory. Oxford: Oxford University Press.Gao, S. (2013). ?Is an electron a charge cloud? An reexamination of Schrödinger´s charge density hypothesis?. http://philsci-archive.pitt.edu/id/eprint/9696Matta, C. F. (2013). ?Special issue: Philosophical aspects and implications of the quantum theory of atoms in molecules (QTAIM)?. Foundations of Chemistry, 15: 245-251.Matta, C. F., Massa, L., and Keith, T. A. (2011). ?Richard F. W. Bader: a true pioneer?. Journal of Physical Chemistry A, 115: 12427-12431.