Hyperfine Rovibrational States of H_{3}^{+} in a Weak External Magnetic Field

Area of Science:

• Quantum Chemistry
• Molecular Spectroscopy
• Astrochemistry

Background:

• The hydrogen molecule ion (H_{3}^{+}) is a fundamental system in chemistry and physics.
• Understanding its behavior under external fields is crucial for various applications.
• Previous studies have not fully accounted for magnetic couplings in H_{3}^{+}.

Purpose of the Study:

• To compute rovibrational energies, wave functions, and Raman transition moments for H_{3}^{+}.
• To investigate the effects of weak external magnetic fields on H_{3}^{+}.
• To develop a methodology applicable to higher energy states and other molecules.

Main Methods:

• Construction and diagonalization of the rovibrational-hyperfine-Zeeman Hamiltonian matrix.
• Utilizing rovibrational eigenstates and proton spin functions.
• Computational quantum mechanical approach.

Main Results:

• Reported energies, wave functions, and Raman transition moments for low-energy H_{3}^{+} states.
• Detailed analysis of magnetic couplings between proton spins and molecular rotation.
• Demonstrated the influence of weak external magnetic fields.

Conclusions:

• The developed methodology accurately predicts hyperfine-Zeeman effects in H_{3}^{+}.
• This approach can be extended to higher rovibrational states and other closed-shell molecules.
• The findings will facilitate future quantum logic spectroscopy experiments on polyatomic systems.