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

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.

(C) 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license. http://creativecommons.org/licenses/by-nc-nd/4.0/