Reducing the complexity of sum-of-products potential energy surfaces for efficient MCTDH calculations

The efficiency of the multi-configuration time-dependent Hartree (MCTDH) method depends critically on the availability of a compact sum-of-products (SOP) representation of the potential energy surface (PES). For medium- and high-dimensional molecular systems, conventional SOP representations often contain thousands of product terms, leading to long compilation times, high memory consumption, and prohibitive computational cost. In this work, we introduce a physically motivated factorization procedure that transforms an existing SOP PES into a substantially more compact form without altering the underlying potential. The method is applied to three molecular complexes of increasing dimensionality, reducing the number of SOP terms by 73.8%, 51.7%, and 90.6% for PO⁺-H₂, H₂O-HCN, and H₂O-H₂O, respectively. These reductions translate into substantially lower memory requirements and shorter compilation and propagation times. In every case, vibrational energy levels computed with the factorized PES are in excellent agreement with those obtained from the original SOP representation, demonstrating that the factorization preserves the accuracy of quantum-dynamics calculations while markedly improving computational efficiency. The proposed strategy provides a general and efficient framework for extending MCTDH calculations to increasingly complex molecular systems.