  The multi-layer multi-configuration time-dependent Hartree method (ML-MCTDH)
is a highly efficient scheme for studying the dynamics of high-dimensional
quantum systems. Its use is greatly facilitated if the Hamiltonian of the
system possesses a particular structure through which the multi-dimensional
matrix elements can be computed efficiently. In the field of quantum molecular
dynamics, the effective interaction between the atoms is often described by
potential energy surfaces (PES), and it is necessary to fit such PES into the
desired structure. For high-dimensional systems, the current approaches for
this fitting process either lead to fits that are too large to be practical, or
their accuracy is difficult to predict and control.
  This article introduces multi-layer Potfit (MLPF), a novel fitting scheme
that results in a PES representation in the hierarchical tensor (HT) format.
The scheme is based on the hierarchical singular value decomposition, which can
yield a near-optimal fit and give strict bounds for the obtained accuracy.
Here, a recursive scheme for using the HT-format PES within ML-MCTDH is
derived, and theoretical estimates as well as a computational example show that
the use of MLPF can reduce the numerical effort for ML-MCTDH by orders of
magnitude, compared to the traditionally used Potfit representation of the PES.
Moreover, it is shown that MLPF is especially beneficial for high-accuracy PES
representations, and it turns out that MLPF leads to computational savings
already for comparatively small systems with just four modes.
