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Factorized molecular wave functions: Analysis of the nuclear factor.

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This study revisits vibrational perturbations in diatomic molecules, showing that a modified nodeless nuclear factor can accurately represent the adiabatic scheme. This simplifies understanding molecular wave function factorization.

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Area of Science:

  • Quantum Chemistry
  • Molecular Spectroscopy
  • Theoretical Chemistry

Background:

  • Exact factorization of molecular wave functions yields nodeless nuclear factors.
  • Vibrational perturbations in diatomic species are typically analyzed using Born-Oppenheimer approximations.
  • Previous work demonstrated deriving factorized wave function forms from coupled equations.

Purpose of the Study:

  • To re-examine vibrational perturbations in diatomic molecules.
  • To investigate the relationship between factorized and adiabatic schemes for molecular wave functions.
  • To develop a simplified approach for obtaining nodeless nuclear factors.

Main Methods:

  • Artificial increase of interstate coupling to reach the adiabatic regime.
  • Diagonalization of the potential matrix to determine the lowest potential.
  • Comparison of nuclear wave functions from factorized and adiabatic schemes.
  • Rectification of the nodeless function for improved agreement.

Main Results:

  • The adiabatic regime allows reducing the molecular wave function to a single product.
  • The nuclear factor in the adiabatic scheme is governed by the lowest potential.
  • A simple rectification method reconciles the modified nodeless function with the adiabatic scheme's nuclear wave function.

Conclusions:

  • The study provides a method to obtain accurate nodeless nuclear factors for diatomic vibrational perturbations.
  • This approach simplifies the treatment of molecular wave functions under vibrational coupling.
  • The findings offer insights into the factorization of molecular wave functions and the adiabatic approximation.