Multilayer multi-configuration time-dependent Hartree method: implementation and applications to a Henon-Heiles Hamiltonian and to pyrazine

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method is discussed and a fully general implementation for any number of layers based on the recursive ML-MCTDH algorithm given by Manthe [J. Chem. Phys. {\bf 128}, 164116 (2008)] is presented. The method is applied first to a generalized Henon-Heiles (HH) Hamiltonian. For 6D HH the overhead of ML-MCTDH makes the method slower than MCTDH, but for 18D HH ML-MCTDH starts to be competitive. We report as well 1458D simulations of the HH Hamiltonian using a seven layer scheme. The photoabsorption spectrum of pyrazine computed with the 24D Hamiltonian of Raab {\em et. al.} [J. Chem. Phys. {\bf 110}, 936 (1999)] provides a realistic molecular test case for the method. Quick and small ML-MCTDH calculations needing a fraction of the time and resources of reference MCTDH calculations provide already spectra with all the correct features. Accepting slightly larger deviations, the calculation can be accelerated to take only 7 minutes. When pushing the method towards convergence, results of similar quality than the best available MCTDH benchmark, which is based on a wavepacket with $4.6\times 10^7$ time-dependent coefficients, are obtained with a much more compact wavefunction consisting of only $4.5\times 10^5$ coefficients and requiring a shorter computation time.