Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2507.12223

What are we talking about when we discuss the Born-Oppenheimer approximation?

Olímpia Lombardi, Sebastián Fortín, Juan Camilo Martínez González, Hernán Lucas Accorinti

Published Jul 16, 2025• 1 citation
arXivHTMLPDF

Abstract

Nick Huggett, James Ladyman, and Karim Thebault (HLT) have presented a comprehensive article examining the Born-Oppenheimer Approximation (BOA). Their central objective is to challenge our position on the matter-namely, that the BOA incorporates a classical assumption incompatible with the Heisenberg Uncertainty Principle. In contrast, HLT contend that the BOA involves no such classical assumption and, as a result, supports the view that chemistry can be reduced to physics. The purpose of this paper is to offer a critical analysis of the HLT article and to clarify why we consider their arguments unpersuasive.

DOI
10.48550/arxiv.2507.12223

Related papers

On the Quantum Theory of Molecules: Rigour, Idealization, and Uncertainty

Nick Huggett, James Ladyman, Karim P. Y. Thébault

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.

arXiv:2411.01942•Philosophy of Science•Apr 22, 2026•2 citations

The Born–Oppenheimer approximation: A toy version

Gautam Gangopadhyay, Binayak Dutta-Roy

The Born–Oppenheimer approximation, which is central to the physics and chemistry of molecules and solids, is illustrated by a one-dimensional toy model that is easily solved.

American Journal of Physics•Feb 12, 2004•7 citations

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

Hernán Lucas Accorinti, Juan Camilo Martínez González

Synthese Library/Synthese library•Jan 1, 2022•1 citation

The moving Born–Oppenheimer approximation

Bernardo Barrera, Daniel P. Arovas, Anushya Chandran +1 more

We develop a mixed quantum-classical framework, dubbed the moving Born-Oppenheimer approximation (MBOA), to describe the dynamics of slow degrees of freedom (DOFs) coupled to fast ones. As in the Born-Oppenheimer approximation (BOA), the fast degrees of freedom adiabatically follow a state that depends on the slow ones. Unlike the BOA, this state depends on both the positions and the momenta of the slow DOFs. We study several model systems: a spin-1/2 particle and a spinful molecule moving in a spatially inhomogeneous magnetic field, and a gas of fast particles coupled to a piston. The MBOA reveals rich dynamics for the slow degree of freedom, including reflection, dynamical trapping, and mass renormalization. It also significantly modifies the state of the fast DOFs. For example, the spins in the molecule are entangled and squeezed, while the gas of fast particles develops gradients that are synchronized with the motion of the piston for a long time. The MBOA can be used to describe both classical and quantum systems and has potential applications in quantum chemistry, correlated materials, atomic physics, molecular dynamics, and quantum sensing.

arXiv:2502.17557•Proceedings of the National Academy of Sciences•Feb 13, 2026•4 citations

Publisher’s Note: Born-Oppenheimer approximation for open quantum systems within the quantum trajectory approach [Phys. Rev. A81, 052113 (2010)]

X. L. Huang, S. L. Wu, L. C. Wang +1 more

Physical Review A•Jun 8, 2010•2 citations

On the Autonomous Existence of Chemical Entities

Olímpia Lombardi, Martín Labarca

According to a traditional assumption, in principle chemistry could be derived from physics because chemical entities are nothing else than very complex physical entities. This assumption counts against the autonomy of chemistry as a scientific discipline or, at least, supports its secondary position with respect to physics. In this paper we review the arguments used for and against the idea that chemistry is nothing else than a branch of physics. In particular, we consider the status of chemical entities in the light of the discussions around the supposed visualization of orbitals. On this basis, we defend the autonomous existence of the chemical world. Keywords: Molecular chemistry, Quantum mechanics, Reduction, Orbitals, Wavefunction, Semiclassical-electrons, Born-Oppenheimer approximation, Autonomous Existence, medieval alchemy, Dirac's words, phenomenological science, macroscopic phenomena, multicomponent systems, billiard-ball, secondary science, illuminating metaphor, Existence of Orbitals, SchrOdinger equation, contextuality of quantum mechanics, hypothetical superposition, quasi-classical WKB, unacceptable self-contradiction

Current Physical Chemistry•Jan 1, 2011•11 citations
Nick Huggett, James Ladyman, and Karim Thebault (HLT) have presented a comprehensive article examining the Born-Oppenheimer Approximation (BOA). Their central objective is to challenge our position on the matter-namely, that the BOA incorporates a classical assumption incompatible with the Heisenberg Uncertainty Principle. In contrast, HLT contend that the BOA involves no such classical assumption and, as a result, supports the view that chemistry can be reduced to physics. The purpose of this paper is to offer a critical analysis of the HLT article and to clarify why we consider their arguments unpersuasive.
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.
We develop a mixed quantum-classical framework, dubbed the moving Born-Oppenheimer approximation (MBOA), to describe the dynamics of slow degrees of freedom (DOFs) coupled to fast ones. As in the Born-Oppenheimer approximation (BOA), the fast degrees of freedom adiabatically follow a state that depends on the slow ones. Unlike the BOA, this state depends on both the positions and the momenta of the slow DOFs. We study several model systems: a spin-1/2 particle and a spinful molecule moving in a spatially inhomogeneous magnetic field, and a gas of fast particles coupled to a piston. The MBOA reveals rich dynamics for the slow degree of freedom, including reflection, dynamical trapping, and mass renormalization. It also significantly modifies the state of the fast DOFs. For example, the spins in the molecule are entangled and squeezed, while the gas of fast particles develops gradients that are synchronized with the motion of the piston for a long time. The MBOA can be used to describe both classical and quantum systems and has potential applications in quantum chemistry, correlated materials, atomic physics, molecular dynamics, and quantum sensing.
According to a traditional assumption, in principle chemistry could be derived from physics because chemical entities are nothing else than very complex physical entities. This assumption counts against the autonomy of chemistry as a scientific discipline or, at least, supports its secondary position with respect to physics. In this paper we review the arguments used for and against the idea that chemistry is nothing else than a branch of physics. In particular, we consider the status of chemical entities in the light of the discussions around the supposed visualization of orbitals. On this basis, we defend the autonomous existence of the chemical world. Keywords: Molecular chemistry, Quantum mechanics, Reduction, Orbitals, Wavefunction, Semiclassical-electrons, Born-Oppenheimer approximation, Autonomous Existence, medieval alchemy, Dirac's words, phenomenological science, macroscopic phenomena, multicomponent systems, billiard-ball, secondary science, illuminating metaphor, Existence of Orbitals, SchrOdinger equation, contextuality of quantum mechanics, hypothetical superposition, quasi-classical WKB, unacceptable self-contradiction