MCTDH on-the-fly : efficient grid-based quantum dynamics without pre-computed potential energy surfaces

We present significant algorithmic improvements to a recently-proposed direct quantum dynamics method, based upon combining well established grid-based quantum dynamics approaches and expansions of the potential energy operator in terms of a weighted sum of Gaussian functions. Specifically, using a sum of low- dimensional Gaussian functions to represent the potential energy surface (PES), combined with a secondary fitting of the PES using singular value decomposition, we show how standard grid-based quantum dynamics methods can be dramatically accelerated without loss of accuracy. This is demonstrated by on-the-fly sim- ulations (using both standard grid-based methods and MCTDH) of both proton transfer on the electronic ground state of salicylaldimine and the non-adiabatic dynamics of pyrazine