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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Direct adiabatic-to-diabatic (ATD) transformations are crucial for studying multi-state systems.
  • Extending ATD to three-state systems is less explored than two-state systems.
  • The valence bond wave function-based automatic diabatization (VBADA) approach provides a framework for constructing diabatic states.

Purpose of the Study:

  • To investigate various O(3) group unitary transformations for creating three-state diabatic representations.
  • To evaluate the performance of different transformations in the diabatization process.
  • To identify stable and accurate methods for generating diabatic states in complex chemical systems.

Main Methods:

  • Utilized the VBADA approach for automatic diabatization.
  • Applied various O(3) group unitary transformations: Householder, composite Givens, Euler angles, Tait-Bryan angles, quaternions, and Rodrigues' rotation formula.
  • Tested transformations using the dissociation of lithium hydride and the H + HCl reaction.

Main Results:

  • A performance hierarchy was observed among the O(3) parametrizations.
  • Householder reflections and composite Givens rotations exhibited numerical instability.
  • Euler/Tait-Bryan angles showed gimbal-lock singularities.
  • Rodrigues' rotation formula and quaternion-based parametrizations yielded smooth, stable diabatic states with localized chemical character.

Conclusions:

  • Rodrigues' rotation formula and quaternion-based methods are superior for constructing stable three-state diabatic representations.
  • These methods avoid numerical instabilities and singularities encountered with other transformations.
  • The findings offer improved computational tools for theoretical chemistry research.