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Multilayer multiconfiguration time-dependent Hartree method: Implementation and applications to a Henon–Heiles Hamiltonian and to pyrazine

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10.1063/1.3535541

### Abstract

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.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 *et al.* [J. Chem. Phys.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 min. When pushing the method toward convergence, results of similar quality than the best available MCTDH benchmark, which is based on a wavepacket with time-dependent coefficients, are obtained with a much more compact wavefunction consisting of only coefficients and requiring a shorter computation time.

© 2011 American Institute of Physics

Received 17 November 2010
Accepted 17 December 2010
Published online 28 January 2011

Acknowledgments: Financial support by the Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledged.

Article outline:

I. INTRODUCTION

II. MULTILAYER MCTDH

A. *Ansatz* and general concept

B. ML-MCTDH equations of motion and recursive implementation

C. Separable part of the Hamiltonian across layers

III. RESULTS AND DISCUSSION

A. Henon–Heiles

1. 6D simulations

2. 18D simulations

3. 1458D simulations

B. Pyrazine

IV. SUMMARY AND CONCLUSION

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2011-01-28

2014-04-20

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