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Synthese Library/Synthese library

Models and Idealizations in Quantum Chemistry: The Case of the Born-Oppenheimer Approximation

Hernán Lucas Accorinti, Juan Camilo Martínez González

Published Jan 1, 2022• 1 citation
Publisher
DOI
10.1007/978-3-030-98373-4_5

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•Sep 30, 2022•3 citations
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.
In this article, we demonstrate the first-principles computation of quantum chemistry through symbolic computation, using computational algebraic geometry. We have developed a Python program that generates symbolic formulas of one- and two-electron integrals. The approximations of those integrals by multivariate polynomials yield the set of equations required by quantum chemistry. We solve these equations in hybrid ways where numeric and symbolic computations are intertwined. We discuss the possibility of the extension of our scheme to treat the models beyond the Born-Oppenheimer approximation.