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 H 3 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 ∼ 0.1 cm −1 ) which still lead to only moderate computational demands for ML-MCTDH.

The coupling of the hydrated proton to its first solvation shell

“…This algorithm suffers from the curse of dimensionality because ultimately it requires a full representation of the primitive product grid in configuration space. Modifications of Potfit have been developed over the years to partially overcome this difficulty 51 – 53 , making it possible to work with about 9–15 coordinates. This is clearly insufficient to approach a system of the size of the Eigen cation.…”

CH4·F− revisited: full-dimensional ab initio potential energy surface and variational vibrational states

“…Vibrational computations of high(er)-dimensional molecular systems with floppy modes have been challenging due to the dimensionality and poor separability of the problem, and in general, due to the exponential scale-up of exact quantum dynamics methodologies with the number of the coupled vibrational degrees of freedom. Over the past decade, development is observed in several important directions, (a) coordinate representation and the kinetic energy operator [10,11,12,13,14,15,16,17]; (b) contraction techniques [3,4,5,6,7], (c) gridpruning techniques [1,18,19,20,21,22]; (d) collocation [23,24,25]; and (e) PES representation for high-dimensional quantum dynamics [26,27,28]; and (f) highly parallel computation of millions of states [29,30,31]. Methodological progress makes it possible to attenuate the exponential scale-up, including systems with large-amplitude motions [1,21,32].…”

Representation of Diabatic Potential Energy Matrices for Multiconfiguration Time-Dependent Hartree Treatments of High-Dimensional Nonadiabatic Photodissociation Dynamics

“…The kinetic energy operator (KEO) typically fulfils the SOP requirement, while the potential energy operator (PEO) often needs extra effort to conform to the SOP form. Several methods have been developed, among which POTFIT , and its variants − are shown to be quite successful. However, the POTFIT method is based on the Tucker decomposition, in which the scaling is still exponential.…”