Transforming high-dimensional potential energy surfaces into a canonical polyadic decomposition using Monte Carlo...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• High-dimensional potential energy surfaces (PES) are crucial for molecular dynamics simulations.
• Representing PES in a sum-of-products (SOP) form simplifies calculations but is challenging for high dimensions.
• Existing methods like Tucker decomposition can be computationally expensive.

Purpose of the Study:

• To develop a computationally efficient method for transforming high-dimensional PES into a Canonical Polyadic Decomposition (CPD) form.
• To reduce the numerical cost associated with evaluating PES on discrete grid points.
• To enable the treatment of potential energy surfaces with a large number of degrees of freedom.

Main Methods:

• A modified alternating least squares (ALS) method is employed.
• Monte Carlo integration is used to replace numerically exact integrals.
• This avoids evaluating the potential on all grid points, reducing computational burden.

Main Results:

• The proposed Monte Carlo-based ALS method successfully transforms a 15-dimensional PES of the protonated water dimer (Zundel cation) into SOP form (CPD).
• The method demonstrates significant reduction in numerical cost compared to grid-based evaluations.
• Results are comparable to those obtained using Tucker decomposition in previous work.

Conclusions:

• The Monte Carlo approach offers an efficient and scalable strategy for representing high-dimensional potential energy surfaces in a sum-of-products (Canonical Polyadic Decomposition) format.
• This method significantly lowers computational demands, making complex molecular systems more tractable for theoretical studies.
• The approach is validated by its application to the Zundel cation, showing its practical utility in computational chemistry.