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
- Publication
- May 21, 2025
Abstract:
In this Note, we propose a new perspective on the foundations of the exact factorization (EF) representation of the molecular wavefunction,1,2 strengthening its connection to the more traditional Born–Huang (BH) representation, which invokes an expansion of the molecular wavefunction in terms of a basis of electronic states.3,4 In particular, we demonstrate that EF is the representation of the molecular wavefunction in terms of eigenstates of the density operator. From this viewpoint, we show that the U(1) gauge freedom in the definition of the electronic and nuclear amplitudes as well as the partial (electronic) normalization condition arise naturally when diagonalizing the density operator. To conclude, we comment on the equations of motion within this formalism.
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DOI:
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J. Chem. Phys. 2025, 162, 196101