# Austere quantum mechanics as a reductive basis for chemistry

- 237 Downloads
- 3 Citations

## Abstract

This paper analyses Richard Bader’s ‘operational’ view of quantum mechanics and the role it plays in the the explanation of chemistry. I argue that QTAIM can partially be reconstructed as an ‘austere’ form of quantum mechanics, which is in turn committed to an *eliminative* concept of reduction that stems from Kemeny and Oppenheim. As a reductive theory in this sense, the theory fails. I conclude that QTAIM has both a regulatory and constructive function in the theories of chemistry.

### Keywords

Operational quantum mechanics Operationalism Atoms in molecules Electron density Reduction Explanation## Notes

### Acknowledgments

I would like to thank Richard Bader for a fruitful discussion about some of the topics discussed in this paper. The present paper contains my considered response to some of the topics we discussed during his visit to Auckland in September 2010. I would like to thank two referees of an earlier draft of this paper for constructive comments.

### References

- Bader, R.F.W.: Atoms in Molecules: A Quantum Theory. Oxford Science Publishers, Oxford (1990)Google Scholar
- Bader, R.F.W.: Principle of stationary action and the definition of a proper open system. Phys. Rev.
**49**(19), 348–356 (1994)Google Scholar - Bader, R.F.W.: The Lagrangian approach to chemistry. In: The Quantum Theory of Atoms in Molecules, Chap. 2, pp. 37–59. Wiley-VCH, New York (2007)Google Scholar
- Bader, R.F.W.: Bond paths are not chemical bonds. J. Phys. Chem.
**113**, 10391–10396 (2009)CrossRefGoogle Scholar - Bader, R.F.W.: Definition of molecular structure: by choice or by appeal to observation? J. Phys. Chem. A
**114**, 7431–7444 (2010)Google Scholar - Bader, R.F.W.: On the non-existence of parallel universes in chemistry. Found. Chem.
**13**, 11–37 (2011a). doi: 10.1007/s10698-011-9106-0 CrossRefGoogle Scholar - Bader, R.F.W.: Worlds apart in chemistry: a personal tribute to J. C. Slater. J Phys. Chem. A
**115**(45), 12667–12676 (2011b)CrossRefGoogle Scholar - Bader, R.F.W., Matta, C.F.: Atoms in molecules as non-overlapping, bounded, space-filling open quantum systems. Found. Chem.
**14**, 1 (2012)Google Scholar - Bader, R.F.W., Nguyen-Dang, T.T., Tal, Y.: A topological theory of molecular structure. Rep. Prog. Phys.
**44**(8), 893–948 (1981)CrossRefGoogle Scholar - Bokulich, A.: Reexamining The Quantum-Classical Relation: Beyond Reductionism and Pluralism. Cambridge University, Cambridge (2008)Google Scholar
- Bridgman, P.: The Logic of Modern Physics. Macmillan, New York (1932)Google Scholar
- Cassam-Chenaï, P., Jayatilaka, D.: Some fundamental problems with zero flux partitioning of electron densities. Theor. Chem. Acc.
**105**, 213–218 (2001)CrossRefGoogle Scholar - Cohen-Tannoudji, C., Diu, B., Laloë, F.: Quantum Mechanics. Wiley, Nwe York. Translated from the French by Susan Reid Hemley, Nicole Ostrowsky and Dan Ostrowsky (1977)Google Scholar
- Coulson, C.A.: Present state of molecular structure calculations. Rev. Mod. Phys.
**32**(2), 170–177 (1960)CrossRefGoogle Scholar - Dirac, P.: Quantum mechanics and the hydrogen atom. Proc. R. Soc. A
**110**, 561–579 (1926)CrossRefGoogle Scholar - Dirac, P.A.M.: The Lagrangian in quantum mechanics. Physikalische Zeitschrift der Sowjetunion
**3**(1), 64–72 (1932)Google Scholar - Dirac, P.A.M.: The Principles of Quantum Mechanics, 4th edn. Oxford University Press, Oxford (1958)Google Scholar
- Feynman, R.P., Hibbs, A.R.: Quantum Mechanics and Path Integrals, 4th edn. McGraw-Hill, New York (1965)Google Scholar
- Frank, P.G. (ed.): The Validation of Scientific Theories. American Association for the Advancement of Science, Washington (1954)Google Scholar
- Hempel, C.G.: The theoretician’s dilemma. In: Feigl, H., Scriven, M., Maxwell, G. (eds.) Concepts, Theories, and the Mind-Body Problem, Vol. 2 of Minnesota Studies in the Philosophy of Science, pp. 37–98. University of Minnesota Press, Minneapolis (1958)Google Scholar
- Hettema, H.: Reducing Chemistry to Physics: Limits, Models, Consequences. Createspace (2012)Google Scholar
- Jammer, M.: The Conceptual Development of Quantum Mechanics, 4th edn. Tomash Publishers, American Institute of Physics, Annapolis (1989)Google Scholar
- Kemeny, J.G., Oppenheim, P.: On reduction. Philos. Stud.
**VII**, 6–19 (1956)CrossRefGoogle Scholar - Lewis, G.N.: The atom and the molecule. J. Am. Chem. Soc.
**38**, 762–785 (1916)CrossRefGoogle Scholar - Matta, C.F., Bader, R.F.W.: An experimentalist’s reply to What Is an Atom in a Molecule? J. Phys. Chem. A
**110**(19), 6365–6371. PMID: 16686473 (2006)Google Scholar - Moffitt, W.: Atoms in molecules and crystals. Proc. R. Soc. Lond. A
**210**, 245–268 (1951)CrossRefGoogle Scholar - Nagel, E.: The Structure of Science: Problems in the Logic of Scientific Explanation, 4th edn. Routledge and Kegan Paul, London (1961)Google Scholar
- Nasertayoob, P., Shahbazian, S.: Revisiting the foundations of the quantum theory of atoms in molecules: toward a rigorous definition of topological atoms. Int. J. Quantum Chem.
**109**, 726–732 (2009)CrossRefGoogle Scholar - Pap, A.: Are physical magnitudes operationally definable? In: Churchman, C.W., Ratoosh, P. (eds.) Measurement: Definitions and Theories, Wiley, New York (1959)Google Scholar
- Russell, B.: A History of Western Philosophy, 4th edn. Simon and Schuster, New York (1945)Google Scholar
- Schwinger, J.: The theory of quantized fields. I. Phys. Rev.
**82**, 914–927 (1951)CrossRefGoogle Scholar - Srebrenik, S., Bader, R.F.W.: Towards the development of the quantum mechanics of a subspace. J. Chem. Phys.
**63**(9), 3945–3961 (1975)CrossRefGoogle Scholar - Styer, D.F., Balkin, M.S., Becker, K.M., Burns, M.R., Dudley, C.E., Forth, S.T., Gaumer, J.S., Kramer, M.A., Oertel, D.C., Park, L.H., Rinkoski, M.T., Smith, C.T., Wotherspoon, T.D.: Nine formulations of quantum mechanics. Am. J. Phys.
**70**(3), 288 (2002)CrossRefGoogle Scholar