Reaction Path Following with Sparse Interpolation.

Area of Science:

• Computational Chemistry
• Theoretical Chemistry
• Chemical Dynamics

Background:

• Calculating potential energy surfaces for N-atom molecules involves optimizing 3N-6 coordinates, which is computationally intensive.
• Following reaction pathways across all molecular coordinates is infeasible for large molecules due to high dimensionality.

Purpose of the Study:

• To develop a computationally efficient method for simulating molecular reaction pathways.
• To enable the study of reaction dynamics in high-dimensional systems by reducing the number of active coordinates.

Main Methods:

• Implementing a method to isolate 'd' molecular coordinates (d < 3N-6) for reaction path following.
• Utilizing Smolyak's sparse grid interpolation algorithm to approximate d-dimensional potential energy surfaces.
• Comparing the efficiency of sparse grids against dense grids for computational accuracy and resource management.

Main Results:

• Sparse grids significantly improve the storage and computation time to accuracy ratio compared to dense grids.
• The developed technique allows for increased dimensionality 'd' in molecular reaction path simulations.
• Evaluating the interpolant is less computationally expensive than direct energy function evaluation.

Conclusions:

• The proposed method offers a computationally efficient approach for simulating reaction paths on potential energy surfaces.
• This technique is applicable to both ground and excited state potential energy surfaces.
• Demonstrated feasibility through simulation of 2-butene isomerization with varying degrees of freedom.