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Entanglement in the Born-Oppenheimer Approximation.

Artur F Izmaylov1,2, Ignacio Franco3

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Electron-nuclear entanglement

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Area of Science:

  • Quantum chemistry
  • Theoretical chemistry
  • Chemical physics

Background:

  • The Born-Oppenheimer (BO) approximation is a cornerstone of molecular quantum mechanics, simplifying calculations by separating electronic and nuclear motion.
  • Nonadiabatic couplings can lead to entanglement between electrons and nuclei, potentially violating the BO approximation.

Purpose of the Study:

  • To investigate the relationship between electron-nuclear entanglement and the validity of the Born-Oppenheimer approximation.
  • To determine if entanglement directly correlates with the accuracy of the BO approximation.

Main Methods:

  • Analysis of electron-nuclear entanglement using a minimal avoided crossing model.
  • Comparison of entanglement in BO states versus exact electron-nuclear states.
  • Evaluation of the deviation of BO states from crude BO states and exact states.

Main Results:

  • The degree of electron-nuclear entanglement is surprisingly uncorrelated with the validity of the BO approximation.
  • BO states do not necessarily reflect the entanglement of exact electron-nuclear eigenstates.
  • Cases were identified where highly entangled BO states were accurate, and less entangled states were inaccurate.

Conclusions:

  • The validity of the BO approximation is not solely determined by the degree of electron-nuclear entanglement.
  • Entanglement measures of BO states differ from those of exact eigenstates.
  • The BO approximation becomes exact only when the system is completely unentangled.