Adaptive integration grids in instanton theory improve the numerical accuracy at low temperature

Area of Science:

• Quantum chemistry
• Computational physics
• Chemical reaction dynamics

Background:

• The instanton method accurately calculates tunneling rates at low temperatures.
• Computational cost increases significantly at lower temperatures due to increased discretization points, often concentrated in small configuration space regions.

Purpose of the Study:

• To develop a more efficient instanton method by optimizing path discretization.
• To reduce the computational burden for calculating tunneling rates, especially at low temperatures.

Main Methods:

• A flexible, temperature-adapted discretization of the instanton path.
• Uniform distribution of discretization points (images) along the path.
• Modified Newton-Raphson optimizer with successive Hessian updates.

Main Results:

• Reduced the number of required discretization images by approximately 50%.
• Achieved converged reaction rates with computational costs reduced by over an order of magnitude.
• Demonstrated method's success on analytic potentials and density functional theory (DFT) calculations.

Conclusions:

• The proposed flexible discretization significantly enhances the efficiency of the instanton method.
• This advancement enables more feasible calculations of tunneling rates at low temperatures.
• The method offers substantial computational savings for quantum chemical and physical simulations.