A matrix completion algorithm for efficient calculation of quantum and variational effects in chemical reactions.

Area of Science:

• Computational Chemistry
• Chemical Physics
• Theoretical Chemistry

Background:

• Calculating quantum and variational effects in chemical reactions typically requires computationally expensive full nuclear Hessians.
• Variational Transition State Theory with Multidimensional Tunneling (VTST-MT) relies on accurate vibrational frequencies for rate coefficient calculations.

Purpose of the Study:

• To evaluate matrix completion methods as a cost-effective alternative to full nuclear Hessians for quantum and variational effects in chemical reactions.
• To assess the performance of the harmonic variety-based matrix completion (HVMC) algorithm for recovering vibrational frequencies essential for VTST-MT calculations.

Main Methods:

• The study utilizes the harmonic variety-based matrix completion (HVMC) algorithm, which exploits the low-rank nature of potential energy expansions.
• HVMC recovers vibrational frequencies from a limited set of nuclear Hessian eigenvalues.
• The algorithm's performance is tested on four S_N2 reactions and five hydrogen transfer reactions, including those with strongly coupled vibrational modes.

Main Results:

• HVMC accurately captures key observables for VTST-MT, including zero-point energies, vibrational free energies, and tunneling corrections.
• The method successfully determines adiabatic ground state and free energy barriers and their positions along the reaction coordinate.
• For hydrogen transfer reactions, accurate recovery of VTST-MT observables requires less than 35% of the total eigenvalue information, demonstrating significant computational savings.

Conclusions:

• Matrix completion methods, specifically HVMC, provide a robust and computationally efficient alternative to full nuclear Hessians for calculating quantum and variational effects in chemical reactions.
• HVMC's ability to accurately determine vibrational frequencies and reaction barriers from sparse data makes it a valuable tool for chemical kinetics and reaction path analysis.
• The findings suggest that HVMC can significantly reduce the computational cost associated with accurate chemical reaction rate predictions.