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Optimized curvilinear coordinates in vibration correlation methods: Quasi-degenerate perturbation theory.

Andrey Yachmenev1, Guntram Rauhut1

  • 1Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany.

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Researchers developed new curvilinear molecular vibrational coordinates using normalizing flows. These optimized coordinates significantly improve vibrational energy calculations for molecules like H2CO, enhancing accuracy for various vibrational bands.

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Area of Science:

  • Quantum Chemistry
  • Molecular Spectroscopy
  • Computational Chemistry

Background:

  • Standard valence coordinates can limit accuracy in molecular vibrational energy calculations.
  • Vibrational self-consistent field (VSCF) methods are widely used but can be sensitive to coordinate choices.
  • Correlated calculations often require sophisticated coordinate systems for high precision.

Purpose of the Study:

  • To introduce and validate a novel set of curvilinear molecular vibrational coordinates.
  • To improve the accuracy of vibrational energy calculations within the VSCF framework.
  • To assess the performance of these coordinates for correlated calculations using perturbation theory.

Main Methods:

  • Utilized normalizing flow techniques to construct curvilinear molecular vibrational coordinates.
  • Optimized these coordinates using the vibrational self-consistent field (VSCF) framework.
  • Assessed coordinate quality with second-order quasi-degenerate vibrational perturbation theory (QD-VPT2).

Main Results:

  • Optimized curvilinear coordinates significantly improved vibrational energies for H2CO, trans-HCOOH, and CH3F.
  • Enhancements were observed across fundamental, combination, and overtone vibrational bands.
  • The new coordinates effectively handled states with strong Fermi resonances.

Conclusions:

  • The developed curvilinear coordinates offer substantial improvements over standard valence coordinates.
  • These coordinates reduce vibrational correlation by redistributing Hamiltonian couplings.
  • This approach provides a more accurate foundation for computational molecular spectroscopy.