Toward Efficient Direct Dynamics Studies of Chemical Reactions: A Novel Matrix Completion Algorithm

Area of Science:

• Computational chemistry
• Theoretical chemistry
• Chemical kinetics

Background:

• Calculating reaction rate coefficients is computationally intensive.
• Variational transition state theory with multidimensional tunneling (VTST-MT) requires significant computational resources.
• Eigenvalue prediction of quantum mechanical Hessians is crucial for understanding reaction dynamics.

Purpose of the Study:

• To develop a novel algorithm, polynomial variety-based matrix completion (PVMC), to reduce computational effort in reaction rate coefficient calculations.
• To enable efficient recovery of eigenvalues of quantum mechanical Hessians using limited data.
• To enhance compatibility with quantum chemistry workflows.

Main Methods:

• Developed a PVMC algorithm incorporating a polynomial constraint in the objective function.
• Leveraged underlying eigenvalue properties and matrix completion principles.
• Enabled sampling of matrix columns, unlike traditional element-wise sampling methods.

Main Results:

• PVMC accurately recovers eigenvalues of quantum mechanical Hessians.
• The algorithm requires a significantly smaller sample of information compared to conventional methods.
• Demonstrated accurate prediction of quantum and variational effects for diverse reaction types (e.g., S₂, hydrogen atom transfer, catalysis, enzyme chemistry).

Conclusions:

• PVMC offers a computationally efficient approach for reaction rate coefficient calculations.
• The method requires an average of only six to seven Hessian calculations for accurate predictions.
• PVMC is a promising tool for advancing theoretical chemical studies and quantum chemistry applications.