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 H₃O₂⁻ 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 ∼0.1 cm⁻¹) which still lead to only moderate computational demands for ML-MCTDH.

如果势能表面（PES）具有乘积和（SOP）或多层算子（MLOp）结构，则使用MCTDH或ML-MCTDH进行的量子分子动力学模拟效果最佳。在这里，我们研究了四种不同的基于POTFIT的方法来表示一般的PES这样的结构，其中包括新颖的随机采样多层Potfit（RS-MLPF）。我们研究了PES代表性的格式和准确性如何影响一个基准的运行时间（ML-）MCTDH计算，H的基态，即计算₃ Ô ₂ ^-离子。我们的结果表明，与SOP格式相比，MLOp格式可更好地缩放（ML-）MCTDH运行时，并具有PES精度。在相当高的PES准确度下，ML-MCTDH计算速度提高了20倍，并且极端的是，RS-MLPF方法产生了极其精确的PES表示（全局均方根误差为〜0.1 cm ^-1），仍然只导致对ML-MCTDH的适度计算需求。