Idealized quantum chemistry? Approximations and molecular structure

JUAN CAMILO MARTÍNEZ GONZÁLEZ; HERNÁN ACCORINTI

París

Congreso; International Society for the Philosophy of Chemistry annual meeting; 2017

Université Paris Diderot - Laboratoire SPHERE

The different theoretical tools used in scientific practice to explain or represent a target system have a feature without which they would be extremely ineffective. Given the many variables of the system, both models and laws are designed as deliberate simplifications of something inherently complex, with the purpose of supplying some kind of understanding of it. This process of simplification, although essential for mathematical calculations and predictive inferences, is often related to philosophical controversies about the foundations of representation (e.g. Cartwrigth 1983). In fact, idealizations and approximations contribute to the distortion of the target system, either by omitting some property or directly by representing it as having some property that in fact doesn't have (Jones 2005; Chuang Liu 2001; Hartmann 1998). On this basis, the literature on the matter (Frigg 2002; Suárez 2003; Morrison 2005) addresses this problem by asking: how is it possible that these so-called ?misrepresentations? can be considered a source of knowledge?But what turns this subject matter into an extremely relevant one is the fact that models succeed in being representative or explanatory, not in spite of those distorting processes, but thanks to them. It could be said that misrepresentations are representative precisely due to the fact of being false representations. Consequently, the generally accepted idea that the less idealized a model is, the more realistic or better it will be, cannot always be sustained. In fact, introducing too many variables in the description not only may generate inaccurate results, but may directly override the calculation capacity and, therefore, the inferential capacity with respect to the target system. Therefore, not only ?de-idealizing? the model is commonly disadvantageous, but reducing the distance between the model and the system is sometimes impossible.Moreover, if predictive power is an indicative of some kind of realism, then, contrary to classical ideas, the most idealized models are the most realistic since they allow us to perform better predictions. As a consequence, if we want to maintain certain realistic intuitions, the indispensability of the distorting factors inherent to the modeling process invites us to identify and understand how idealizations operate in actual scientific practice.In the so-called Galilean idealizations (McMullin 1985; Weisberg 2013), for pragmatic reasons, certain variables are removed in order to perform calculations. Emblematic cases of this type of idealization are: the treatment of sun and planets as homogeneous masses or as geometric figures such as circles (e.g. McMullin 1985); the assumption of the sun at rest in order to derive Kepler?s laws; or the treatment of gravity as a constant in the model of an inclined plane. Although these idealizations do not provide consistent information regarding the phenomenon, they nevertheless do not lead to contradictions with the theory from which the models are developed. It is precisely for this reason that it is usually expected that the model can be ?de-idealized? by reintroducing the originally removed variables, thus generating more complete models. For instance, if the absolutely frictionless motion of a body is not realistic (friction is pervasive in the real physical world), this idealized situation does not contradict Newtonian mechanics. Our central claim in this work is that, although this type of idealization is appropriate to describe at large extent the dynamics of physics, idealized models in quantum chemistry introduce serious interpretative challenges.The central element in the quantum description of a molecule is the Born-Oppenheimer approximation (BOA) (Born, M. y Oppenheimer, J. 1927), which allows us to decompose the Hamiltonian of a molecule in its electronic and its nuclear part. This strategy is based on treating the atomic nuclei as classical particles at rest and with a definite position. In the resulting Hamiltonian, the structure of the molecule is described by the positions of the nuclei. However, from the point of view of quantum mechanics, the BOA contradicts one of the formal features of the theory, the Heisenberg?s principle of uncertainty, by allowing the nuclei definite values for two observables that do not commute with each other (Hendry 1998, 2010; Woolley y Sutcliffe 1977). Our purpose here is to explain the reasons why the BOA cannot be typified as a Galilean idealization. On the one hand, not only the BOA contradicts the postulates of quantum mechanics, but also it is impossible to ?de-idealize? the model by treating it without approximation. Quantum chemistry is unintelligible without the concept of molecular structure arising from this approximation. In other words, without the BOA, the explanatory capacity of the model completely vanishes. On the other hand, despite its name, the BOA is not an approximation in a literal sense. The usual justification for the clamped nuclei assumption is the idea that the mass of the nuclei is infinitely greater than that of the electrons and, therefore, the nuclei?s relative velocity is approximately zero. But not only this is a classical intuition that does not work in the quantum domain (Wolley 1998), but the difference between zero and approximately zero can give rise to two radically different systems when quantum mechanics is taken into account.