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Peer-reviewedCC BY 4.0The Journal of Chemical Physics

On the connection between the exact factorization and the Born–Huang representation of the molecular wavefunction

  • Peter Schürger
  • Yorick Lassmann
  • Federica Agostini
  • Basile F E Curchod
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Abstract

In these Notes we present a new perspective on the exact-factorization expression of a molecular wavefunction, which does not rely of the probabilistic interpretation of the molecular wavefunction as a joint probability amplitude. Instead, we demonstrate a close relation with the traditional Born-Huang representation, as the exact factorization emerges as the representation in the basis the of eigenvectors of the density matrix at nuclear position R. In doing so, the partial normalization condition and gauge freedom arise naturally from the formalism. In a second part, we derive the equation of motion in the here introduced exact factorization basis.

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Cite

BibTeXRIS
BibTeX
@article{schurger2026connection,
  title = {{On the connection between the exact factorization and the Born–Huang representation of the molecular wavefunction}},
  author = {Peter Schürger and Yorick Lassmann and Federica Agostini and Basile F E Curchod},
  journal = {The Journal of Chemical Physics},
  year = {2026},
  month = sep,
  doi = {10.1063/5.0254090},
  url = {https://hal.science/hal-05737504v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - On the connection between the exact factorization and the Born–Huang representation of the molecular wavefunction
AU  - Peter Schürger
AU  - Yorick Lassmann
AU  - Federica Agostini
AU  - Basile F E Curchod
PY  - 2026
DA  - 2026/09/03
JO  - The Journal of Chemical Physics
DO  - 10.1063/5.0254090
UR  - https://hal.science/hal-05737504v1
AB  - In these Notes we present a new perspective on the exact-factorization expression of a molecular wavefunction, which does not rely of the probabilistic interpretation of the molecular wavefunction as a joint probability amplitude. Instead, we demonstrate a close relation with the traditional Born-Huang representation, as the exact factorization emerges as the representation in the basis the of eigenvectors of the density matrix at nuclear position R. In doing so, the partial normalization condition and gauge freedom arise naturally from the formalism. In a second part, we derive the equation of motion in the here introduced exact factorization basis.
SN  - 0021-9606
SN  - 1089-7690
ER  -