Efficient algorithms for semiclassical instanton calculations based on discretized path integrals.

Area of Science:

• Quantum chemistry
• Computational physics
• Chemical dynamics

Background:

• The path integral instanton method is crucial for calculating tunneling splitting in degenerate two-state systems.
• Current methods often rely on approximations like long imaginary time durations.

Purpose of the Study:

• To develop a novel, analytically tractable formula for tunneling splitting using discretized path integrals.
• To improve computational efficiency and numerical accuracy in tunneling calculations.
• To integrate this method with ab initio electronic structure calculations for accurate potential energy surfaces.

Main Methods:

• Development of a new formula for tunneling splitting based on discretized path integrals.
• Analytical evaluation of the zero-temperature or infinite imaginary time limit.
• Combination with on-the-fly electronic structure calculations (ab initio method).

Main Results:

• The new analytical formula significantly reduces computational cost.
• Improved numerical accuracy was achieved compared to previous methods.
• Successful application to model systems and the ammonia umbrella flip motion.

Conclusions:

• The developed analytical path integral instanton method offers a more efficient and accurate approach to tunneling splitting calculations.
• The ab initio instanton method provides accurate interatomic potentials for complex molecular dynamics.
• This work paves the way for more precise studies of quantum phenomena in chemical systems.