Dimensional marginalization and other approximations in quantum chemistry

S. FORTIN

Lille

Conferencia; 26th Conference of the International Society for the Philosophy of Chemistry; 2022

Lille University

Due to the peculiarities of Quantum Mechanics, the creators of the theory were forced to leave aside the traditional physical space and adopt Hilbert space. This space is where the wave function “lives” and differs from the traditional space in several ways. It is a vector space instead of a scalar space, it is a complex space instead of a real space, and it is a multidimensional space instead of a three dimen sional space. These mathematical characteristics allow us to account for phenom ena such as superposition, interference, the uncertainty principle, etc. However, they pose a challenge to those who are interested in providing an acceptable inter pretation of the theory and an understandable ontology, and occupy much of the time of philosophers of physics. However, this issue does not appear in philoso phy of chemistry. However, many of these problems are not very frequent in the literature on the philosophy of quantum chemistry. In this presentation, we will reflect on how quantum chemists proceed to elim inate the inconveniences of Hilbert space. We will pay special attention to two issues that concern obtaining the orbitals. The first is the process of dimensional marginalization, whereby the 3N dimensions of the wave function become the usual 3 dimensions. And the second is the process of “superposition freeze” by which welldefined orbitals are obtained and the possibility of a superposition is excluded. In the first case, the bibliography presents marginalization as a mere ap proximation and in the second case it is simply swept under the rug. We will study both processes in the light of the problem of the reduction of chemistry to physics. We will point out that these processes represent conceptual leaps that go beyond a simple approximation and have profound consequences in the understanding of the relationship between physics and chemistry. Especially on the ontological plane.