Machine Learning-Enhanced Structure-Based Gaussian Expansion for Efficient Wavepacket Calculations

The theoretical treatment of molecular wavepackets remains computationally demanding and becomes increasingly impractical for complex systems with a large number of atoms. To tackle this problem, we previously developed the structure-based Gaussian (SBG) expansion method, where space-fixed Gaussian basis functions for the expansion of wavepackets are placed intensively around reaction pathways connecting equilibrium structures and transition states. In this study, we incorporated two machine learning techniques into the SBG expansion, thereby developing a highly efficient and versatile approach for wavepacket calculations: the principal component analysis for systematic construction of the SBG basis set and the Gaussian process regression for interpolation of potential energy surfaces. To demonstrate the performance of this approach, we constructed full-dimensional nuclear wave functions for the umbrella inversion tunneling in H₃O⁺. The improved expansion using 33 SBG bases successfully reproduced the experimental vibrational energies up to overtone excited states with only 19 quantum chemical calculations. We also confirmed the feasibility for larger systems through the applications to intramolecular hydrogen transfer in 9-hydroxyphenalenone and its asymmetrically deuterated species.