Explanation and theory formation in quantum chemistry
Tóm tắt
In this paper I expand Eric Scerri’s notion of Popper’s naturalised approach to reduction in chemistry and investigate what its consequences might be. I will argue that Popper’s naturalised approach to reduction has a number of interesting consequences when applied to the reduction of chemistry to physics. One of them is that it prompts us to look at a ‘bootstrap’ approach to quantum chemistry, which is based on specific quantum theoretical theorems and practical considerations that turn quantum ‘theory’ into quantum ‘chemistry’ proper. This approach allows us to investigate some of the principles that drive theory formation in quantum chemistry. These ‘enabling theorems’ place certain limits on the explanatory latitude enjoyed by quantum chemists, and form a first step into establishing the relationship between chemistry and physics in more detail.
Tài liệu tham khảo
Cohen-Tannoudji, C., Diu, B., Laloë, F.: Quantum Mechanics. Wiley. Translated from the French by Susan Reid Hemley, Nicole Ostrowsky and Dan Ostrowsky (1977)
Coulson, C.A., Haskins, P.J.: On the relative accuracies of eigenvalue bounds. J. Phys. B: Atom. Mol. Phys. 6, 1741–1750 (1973)
Courant, R., Hilbert, D.: Methoden Der Mathematischen Physik, Grundlehren der mathematischen Wissenschaften in einzeldarstellungen mit besonderer Beruücksichtigung der Anwendungsgebiete. J. Springer, Berlin (1931)
Dalgarno, A., Stewart, A.L.: On the perturbation theory of small disturbances. Proc. R. Soc. Lond. A Math. Phys. Sci. 238(1213), 269–275 (1956)
Dyall, K.G., Faegri, K.: Introduction to Relativistic Quantum Chemistry. Oxford University Press, Oxford (2007)
Feynman, R.P.: Forces in molecules. Phys. Rev. 56, 340 (1939)
Frost, A.A., Lykos, P.G.: Derivation of the Virial Theorem from the Generalized Hellmann-Feynman Theorem. J. Chem. Phys. 25, 1299–1300 (1956)
Goldstein, H.: Classical Mechanics, 2nd edn. Addison Wesley Publishing, Reading (1980)
Helgaker, T., Jørgensen, P., Olsen, J.: Molecular Electronic Structure Theory. Wiley, London (2000)
Hellmann, H.: Einführung in die Quantenchemie. F. Deuticke (1937)
Hempel, C.G.: Philosophy of Natural Sciences. Prentice Hall, Eaglewood Cliffs (1966)
Hempel, C.G.: Provisoes: a problem concerning the inferential function of scientific theories. Erkenntnis. 28, 147–164 (1988)
Hettema, H.: The calculation of frequency dependent polarizabilities. Ph.D. thesis, Katholieke Universiteit Nijmegen (1993)
Hettema, H.: Is quantum chemistry a degenerating research programme? Log. Philos. Sci. VI(1), 3–23 (2008)
Hirschfelder, J., Brown, W.B., Epstein, S.: Recent developments in perturbation theory. Adv. Quant. Chem. 1, 255–374 (1964)
Hylleraas, E. Über den Grundterm der Zweielektronenprobleme von H−, He, Li+, Be++ usw. Zeitschrift für Physik 65(3), 209–225 (1930)
Kato, T.: Fundamental properties of Hamiltonian operators of Schrödinger type. Trans. Am. Math. Soc. 70, 195–211 (1951a)
Kato, T.: On the existence of solutions of the helium wave equation. Trans. Am. Math. Soc. 70, 212–218 (1951b)
Kemeny, J.G., Oppenheim, P.: On reduction. Philos. Stud. VII, 6–19 (1956)
Kuipers, T.A.F.: From Instrumentalism to Constructive Realism, Vol. 287 of Synthese Library. Kluwer Academic Publishers, Dordrecht (2000)
Kuipers, T.A.F.: Structures in Science, Vol. 301 of Synthese Library. Kluwer Academic Publishers, Dordrecht (2001)
McWeeny, R.: Coulson’s Valence. Oxford University Press, Oxford (1979)
Nagel, E.: The Structure of Science: Problems in the Logic of Scientific Explanation. Routledge and Kegan Paul, London (1961)
Nakatsuji, H.: Structure of the exact wave function. J. Chem. Phys. 113(8), 2949–2956 (2000)
Nola, R., Sankey, H.: Theories of Scientific Method : An Introduction. Stocksfield, Acumen (2007)
Nooijen, M., Shamasundar, K.R., Mukherjee, D.: Reflections on size-extensivity, size-consistency and generalized extensivity in many-body theory. Mol. Phys. 103(15), 2277–2298 (2005)
Olsen, J., Jorgensen, P.: Linear and nonlinear response functions for an exact state and for an MCSCF state. J. Chem. Phys. 82, 3235–3264 (1985)
Paldus, J.: Diagrammatical Methods for Many-Fermion Systems. Lecture notes, University of Nijmegen (1981)
Paldus, J.: Coupled cluster theory. In: Wilson, S., Diercksen, G.H. (eds.) Methods in Computational Molecular Physics, vol. 293 of NATO ASI Series. Reidel. (1992)
Popper, K.: The Poverty of Historicism. Routledge, London (1957)
Primas, H.: Pattern recognition in molecular quantum mechanics: I. Background dependence of molecular states. Theoretica Chimica Acta (Berlin) 39, 127–148 (1975)
Primas, H.: Chemistry, Quantum Mechanics and Reductionism, 2 edn. Springer, Berlin (1983)
Scerri, E.: Popper’s naturalized approach to the reduction of chemistry. Int. Stud. Philos. Sci. 12, 33–44 (1998)
Scerri, E.R., McIntyre, L.: The case for the philosophy of chemistry. Synthese 111, 213–232 (1997)
Schlosshauer, M.: Decoherence and the Quantum-to-Classical Transition, The Frontiers Collection. Springer-Verlag, Berlin (2007)
Sinanoglu, O.: Relation of perturbation theory to variation method. J. Chem. Phys. 34(4), 1237–1240 (1961)
Slater, J.C.: The virial and molecular structure. J. Chem. Phys. 1(10), 687–691 (1933)
van Brakel, J.: Philosophy of Chemistry. Leuven University Press, Leuven (2000)
Van Vleck, J.H., Sherman, A.: The quantum theory of valence. Rev. Mod. Phys. 7(3), 167–228 (1935)
Weinhold, F.: Upper and lower bounds to quantum mechanical properties. Adv. Quant. Chem. 6, 299–331 (1972)
Wigner, E.P.: On a modification of the Rayleigh–Schrödinger perturbation theory. Matemat. és Természettud. Értesítö 53, 477–482 (1935)
Woody, A.I.: Putting quantum mechanics to work in chemistry: the power of diagrammatic representation. Philos. Sci. 67, S612–S627. Supplement. Proceedings of the 1998 Biennial Meetings of the Philosophy of Science Association. Part II: Symposia Papers (2000)
Yarkony, D.R. (ed.): Modern Electronic Structure Theory. World Scientific, Singapore (1995)