Improved on-the-fly MCTDH simulations with many-body-potential tensor decomposition and projection diabatisation.

We have recently demonstrated how potential energy surface (PES) interpolation methods, such as kernel ridge regression (KRR), can be combined with accurate wave function time-propagation methods, specifically the multi-configuration time-dependent Hartree (MCTDH) method, to generate a new "on-the-fly" MCTDH scheme (DD-MCTDH) that does not require the pre-fitting of the PES, which is normally required by MCTDH. Specifically, we have shown how our DD-MCTDH strategy can be used to model non adiabatic dynamics in a 4-mode/2-state model of pyrazine, with ab initio electronic structure calculations performed directly during propagation, requiring around 100 h of computer wall-time. In this Article, we show how the efficiency and accuracy of DD-MCTDH can be dramatically improved further still by (i) using systematic tensor decompositions of the KRR PES, and (ii) using a novel scheme for diabatization within the framework of configuration interaction (CI) methods which only requires local adiabatic electronic states, rather than non-adiabatic coupling matrix elements. The result of these improvements is that our latest version of DD-MCTDH can perform a 12-mode/2-state simulation of pyrazine, with PES evaluations at CAS level, in just 29-90 h on a standard desktop computer; this work therefore represents an enormous step towards direct quantum dynamics with MCTDH.