Quadratic String Method for Locating Instantons in Tunneling Splitting Calculations.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Molecular Dynamics

Background:

• The ring-polymer instanton (RPI) method approximates tunneling splittings in complex molecular systems.
• Finding the minimum action path (MAP) is crucial but computationally intensive in RPI.
• Existing methods like NEB and string methods have improved MAP search efficiency.

Purpose of the Study:

• To develop a novel quadratic string method for efficient instanton localization.
• To reduce the computational cost associated with finding the minimum action path (MAP).
• To enhance the applicability of RPI for high-dimensional molecular systems.

Main Methods:

• Developed a quadratic string method to minimize Euclidean action.
• Propagated paths over a quadratic potential energy surface using updated Hessians.
• Utilized Cartesian coordinates for a general and widely applicable approach.

Main Results:

• The quadratic string method significantly reduces computational effort by taking multiple minimization steps between potential/gradient calls.
• The computational cost of finding the instanton is often lower than determining the minimum energy path (MEP).
• The method effectively exploits the smoothness of potential energy surfaces.

Conclusions:

• The new quadratic string method offers an efficient and general approach for locating instantons in molecular systems.
• This method can be combined with advanced computational techniques for broader applicability.
• It provides a significant advancement in calculating tunneling splittings for complex molecular systems.