Ring-polymer instanton theory for tunneling between asymmetric wells

Area of Science:

• Quantum mechanics
• Chemical physics
• Computational chemistry

Background:

• Instanton theory is a key tool for calculating molecular tunneling splittings.
• The original instanton theory fails for asymmetric double wells due to the absence of specific periodic orbits.

Purpose of the Study:

• To develop a new formulation of instanton theory for asymmetric double wells.
• To accurately calculate tunneling splittings in non-degenerate molecular systems.

Main Methods:

• Developed a novel instanton theory formulation using a projected flux correlation function.
• Validated the new theory against exact quantum-mechanical results in 1D and 2D models.
• Applied the theory to the biomolecule α-fenchol.

Main Results:

• The new instanton theory formulation accurately calculates tunneling splittings in asymmetric systems.
• Achieved high accuracy comparable to the original theory in symmetric cases.
• Demonstrated good agreement with experimental tunneling data for α-fenchol.

Conclusions:

• The projected flux correlation function approach extends instanton theory to asymmetric molecular systems.
• The developed method provides a reliable tool for studying molecular tunneling.
• Clarified the relationship between tunneling splittings and reaction rate constants.