Comment on "Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction" [J. Chem. Phys. 137, 22A530 (2012)]

TL;DR

This paper critiques a recent molecular wavefunction factorization method by highlighting the missing proof of norm conservation for electronic and nuclear wavefunctions during evolution.

Contribution

It provides a proof that the norms of electronic and nuclear wavefunctions are preserved in the proposed nonlinear equations of motion.

Findings

Confirmed norm conservation in the equations of motion

Clarified a key mathematical property of the wavefunction factorization

Strengthened the theoretical foundation of the method

Abstract

In spite of the relevance of the proposal introduced in the recent work A. Abedi, N. T. Maitra and E. K. U. Gross, J. Chem. Phys. 137, 22A530, 2012, there is an important ingredient which is missing. Namely, the proof that the norms of the electronic and nuclear wavefunctions which are the solutions to the nonlinear equations of motion are preserved by the evolution. To prove the conservation of these norms is precisely the objective of this Comment.