Toward Robust Three-State Diabatization: A Systematic Benchmark of O(3) Transformation Parameterizations

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.