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BRILL eBooks

Models and Approximations in Quantum Chemistry

Robin Findlay Hendry

Published Jan 1, 1998• 68 citations
Publisher

Abstract

Idealization presents well known problems for realist views of theories: truth cannot be what we want in our theories if we knowingly introduce falsity into our theoretical treatments. One attractive defence of realism has it that, although idealized models themselves falsely represent their subjects, they stand in for intractable exact treatments in the theoretical deductions from true premises that constitute explanations and predictions. In this paper I will argue that on this proxy view of idealized models, certain relations are to be expected between theory and model, relations that fail to hold between quantum mechanics and its applications in quantum chemistry. What is needed is a view of what makes a molecular model a good one that is independent of its relation to some exact treatment.

DOI
10.1163/9789004457638_008

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Idealization presents well known problems for realist views of theories: truth cannot be what we want in our theories if we knowingly introduce falsity into our theoretical treatments. One attractive defence of realism has it that, although idealized models themselves falsely represent their subjects, they stand in for intractable exact treatments in the theoretical deductions from true premises that constitute explanations and predictions. In this paper I will argue that on this proxy view of idealized models, certain relations are to be expected between theory and model, relations that fail to hold between quantum mechanics and its applications in quantum chemistry. What is needed is a view of what makes a molecular model a good one that is independent of its relation to some exact treatment.
Scientific realists often say that there should be belief in the approximate truth of ‘our best scientific theories.’ It is hard to hear the phrase ‘our best scientific theories’ without thinking of quantum mechanics and quantum field theories. But as numerous chapters in this collection make clear, it is unclear that some experts even know how to make sense of being a realist about quantum theories. They provide recipes for calculating incredibly precise predictions for observations, but beyond the recipes, they do not seem to offer a clear-cut or unambiguous picture of what physical reality is like at the fundamental level. After giving an overview of the problems that beset any attempt to believe in the truth or approximate truth of quantum theories, Chapter 2 turns to the question of how to protect scientific realism from the ills of the quantum. The aim is to show that it is possible to quarantine the worst of those ills, freeing us to adopt a robustly realistic attitude toward many other extremely successful areas of contemporary science, such as (parts of) geology, microbiology, and chemistry. The quarantine barrier may be imperfect and permeable in places, but is strong enough (the chapter argues) to help the cause of scientific realism.
The logic of approximation gives a precise mathematical formulation to the notion of approximate truth and to deductions based on it. We study properties of quantum propositions expressed in this logic, in connection to a modal accessibility predicate which induces a metric on the set of states of a mechanical system. We then relate the logic to some quantum logical calculi, and discuss possible applications to probability theory and to the Hilbert space formulation of quantum mechanics. Natural deductions in mathematical logic are concerned with expressions of the form Ft-$ (read: ‘I’ yields @‘), where @ is a formula of a certain formal language L and I is a set of formulae of L . Semantically, the expression Ft@ means: ‘if all formulae in the set F are true then $J is also true’. In this paper we deal with natural deductions applied to the natural sciences, in particular to physics. The problem is that in the context of scientific theories we cannot always speak about (absolute) truth: we have to take into account the uncertainties and errors arising in experiments and
Probably the most dramatic historical challenge to scientific realism concerns Arnold Sommerfeld’s 1916 derivation of the fine structure energy levels of hydrogen. Not only were his predictions good, he derived exactly the same formula that would later drop out of Dirac’s 1928 treatment (something not possible using 1925 Schrödinger–Heisenberg quantum mechanics). And yet the most central elements of Sommerfeld’s theory were not even approximately true: his derivation leans heavily on a classical approach to elliptical orbits, including the necessary adjustments to these orbits demanded by relativity. Even physicists call Sommerfeld’s success a ‘miracle’, which rather makes a joke of the so-called ‘no miracles argument’. However, this can all be turned around. Here I argue that the realist has a story to tell vis-à-vis the discontinuities between the old and the new theory, leading to a realist defence based on sufficient continuity of relevant structure.
This note is intended to address one particular issue in the relative status of Quantum Chemistry in comparison to both Chemistry and Physics. It has been suggested, in the context of the question of the reduction relations between Chemistry and Physics that Quantum Chemistry as a research programme is incapable of furnishing useful guidance to practising chemists. If true, this claim will let us qualify Quantum Chemistry as a degenerating research programme, which, due to its complexity has difficulty to be applied to Chemistry. This claim is shown to be false. The replacement claim I wish to make is that Quantum Chemistry is perfectly capable of furnishing such guidance, but renders the ontological status of many models favored by chemists problematic. Quantum Chemistry, however, validates these models in an instrumental fashion. I will argue that Quantum Chemistry is a progressive research programme.
Quantum chemistry is the use of quantum mechanics to model molecules and their dynamics. In this article we will seek to understand quantum chemical practice via the lens of `de-idealization' based upon a selection of examples together with a more general survey of relevant scientific literature. We will offer some general remarks regarding the problem of modelling molecules and the different approach quantum chemists have developed. We will then consider features of two particular models relating to diatomic molecules and environmental interaction before returning to a more general discussion of the different dimensions of de-idealization relevant to quantum chemistry. Our discussion will support the general claim of continuity between the various families of models in quantum chemistry show and other areas of quantum matter modelling and of the commonness of de-idealization approach under which a model can be modified to be more realistic model in the sense of empirical adequacy without necessarily involving constructing representations that are more veridical.
Abstract Philosophers have claimed that: (a) Born–Oppenheimer approximation methods for solving molecular Schrödinger equations violate the Heisenberg uncertainty relations; therefore, (b) ‘quantum chemistry’ is not fully quantum; and (c) therefore chemistry does not reduce to physics. This paper analyses the reasoning behind Born–Oppenheimer methods and shows that they are internally consistent and fully quantum mechanical, contrary to (a)–(c). Our analysis addresses important issues of mathematical rigour, physical idealization, reduction, and classicality in the quantum theory of molecules, and we propose an agenda for the philosophy of quantum chemistry more grounded in scientific practice.