Semiclassical initial value calculations of the collinear helium atom

Area of Science:

• Quantum mechanics
• Atomic physics
• Computational chemistry

Background:

• Accurate calculation of atomic energy states is crucial for understanding chemical reactions and molecular properties.
• Semiclassical methods offer a computationally efficient alternative to purely quantum mechanical approaches for complex systems.
• The helium atom, despite its simplicity, presents challenges due to electron-electron interactions and potential for chaotic dynamics.

Purpose of the Study:

• To apply semiclassical calculations using the Herman-Kluk (HK) method to determine energy eigenvalues of bound and resonance states of the collinear helium atom.
• To investigate the performance of the HK method in both chaotic (eZe) and nearly integrable (Zee) electronic configurations.
• To compare the results with established quantum mechanical calculations, specifically the complex rotation method.

Main Methods:

• Utilized the Herman-Kluk (HK) initial value treatment for semiclassical calculations.
• Employed regularization techniques to handle singularities in classical electron-nucleus collisions.
• Calculated energy eigenvalues for bound and resonance states in collinear helium atom models.
• Compared results with energies obtained from the complex rotation method.

Main Results:

• Semiclassical calculations using the HK method yielded accurate energy eigenvalues for bound states.
• The method also provided good agreement for resonance states of the collinear helium atom.
• Effective treatment of both chaotic (eZe) and nearly integrable (Zee) configurations was demonstrated.
• Results showed very good agreement with energies calculated by the complex rotation method.

Conclusions:

• The Herman-Kluk semiclassical method is a reliable tool for calculating energy eigenvalues of bound and resonance states in the collinear helium atom.
• The HK method performs well across different classical dynamics regimes, including chaotic and integrable systems.
• This approach offers a viable and accurate alternative to traditional quantum mechanical methods for such atomic systems.