Accuracy of Potfit-based potential representations and its impact on the performance of (ML-)MCTDH

TL;DR

This paper evaluates different Potfit-based methods for representing potential energy surfaces in quantum molecular dynamics, demonstrating how format and accuracy significantly impact the computational efficiency of (ML-)MCTDH simulations.

Contribution

It introduces the novel RS-MLPF method and analyzes how PES representation formats affect (ML-)MCTDH performance, highlighting the advantages of MLOp over SOP.

Findings

MLOp format scales better with PES accuracy than SOP.

ML-MCTDH can be up to 20 times faster with high-accuracy PES.

RS-MLPF achieves highly accurate PES with moderate computational cost.

Abstract

Quantum molecular dynamics simulations with MCTDH or ML-MCTDH perform best if the potential energy surface (PES) has a sum-of-products (SOP) or multi-layer operator (MLOp) structure. Here we investigate four different POTFIT-based methods for representing a general PES as such a structure, among them the novel random-sampling multi-layer Potfit (RS-MLPF). We study how the format and accuracy of the PES representation influences the runtime of a benchmark (ML-)MCTDH calculation, namely the computation of the ground state of the ${\text{H}_3\text{O}_2}^-$ ion. Our results show that compared to the SOP format, the MLOp format leads to a much more favorable scaling of the (ML-)MCTDH runtime with the PES accuracy. At reasonably high PES accuracy, ML-MCTDH calculations thus become up to 20 times faster, and taken to the extreme, the RS-MLPF method yields extremely accurate PES representations (global root-mean-square error of $\sim 0.1\,\text{cm}^{-1}$) which still lead to only moderate computational demands for ML-MCTDH.