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Theoretical Chemistry Group Heidelberg

Multi-Configurarion time-dependent Hartree

MCTDH stands for Multi Configuration Time Dependent Hartree. MCTDH is a general algorithm to solve the time-dependent Schrödinger equation for multidimensional dynamical systems consisting of distinguishable particles. It was first published by H.-D. Meyer, U. Manthe, and L.S. Cederbaum in Chem.Phys.Lett. 165, 73 (1990). MCTDH can determine the quantal motion of the nuclei of a molecular system evolving on one or several coupled electronic potential energy surfaces. MCTDH by its very nature is an approximate method. However, as it is variational, it can be made as accurate as any competing method, but its numerical efficiency deteriorates with growing accuracy.

MCTDH is designed for treating multi-dimensional problems, in particular problems that are difficult or even impossible to attack in a conventional way. There is no or only little gain when treating systems with less than three degrees of freedom by MCTDH. However, for convenience − not for numerical speed − we have used the MCTDH package even for one-dimensional problems. The traditional MCTDH algorithm will in general be best suited for systems with 4 to 12 degrees of freedom. With the Multi-Layer generalization, however, much larger systems can be treated (see Wang and Thoss 2003 or Manthe 2008 or Vendrell and Meyer 2011 ).

MCTDH Documentation

MCTDH HTML Documentation

How to get

The MCTDH program package is distributed on request to interested researchers. If you want to work with MCTDH, please send an e-mail to


"High Dimensional Quantum Dynamics" (HDQD-2024), Hamburg, July 16-19, organized by Peter Schmelcher.


  1. M. H. Beck, A. Jäckle, G. A. Worth and H.-D. Meyer.
    The multiconfiguration time-dependent Hartree method: A highly efficient algorithm for propagating wavepackets.
    Physics Reports 324 (2000), 1.
    Download from publisher

  2. H.-D. Meyer and G. A. Worth
    Quantum molecular dynamics: Propagating wavepackets and density operators using the Multi-configuration time-dependent Hartree (MCTDH) method.
    Theor. Chem. Acc. 109 (2003), 251.
    Download from publisher

  3. G. A. Worth, H.-D. Meyer, H. Köppel, L.S. Cederbaum, and I. Burghardt
    Using the MCTDH wavepacket propagation method to describe multimode nonadiabatic dynamics.
    Int. Rev. in Phys. Chem. 27 (2008), 569
    Download from publisher

  4. Joel M. Bowman, Tucker Carrington Jr., and Hans-Dieter Meyer
    Variational Quantum Approaches for Computing Vibrational Energies of Polyatomic Molecules
    Mol.Phys. 106 (200), 2145-2182
    Download from publisher

  5. H.-D. Meyer
    Studying molecular quantum dynamics with the multiconfiguration time-dependent Hartree method.
    Wiley Interdisciplinary Reviews: Computational Molecular Science 2 (2012) 351.
    Download from publisher


"Applications of Quantum Dynamics in Chemistry"
Fabien Gatti, Benjamin Lasorne, Hans-Dieter Meyer and André Nauts (Sep. 2017)  in the series "Lectures Notes in Chemistry" (Springer).

"Multidimensional Quantum Dynamics: MCTDH Theory and Applications"
Editors: H.-D. Meyer, F. Gatti, and G. A. Worth, editors (Apr. 2009)

MCTDH Literature

A comprehensive list of MCTDH publications can be found at the List of MCTDH Publications or in a bibtex file

Literature Downloads

  1. Lecture Notes: Introduction to MCTDH.
  2. Numerical Methods: DVRs, Integrators (notes 2011).
  3. MCTDH Review, preprint version, published in: Physics Reports 324 (2000), 1.
  4. A List of corrections for the review. (The download version above is already corrected)
  5. Feature Article. Quantum molecular dynamics (Preprint version).
  6. IRPC-review (preprint version). Using the MCTDH wavepacket propagation method...
  7. Studying molecular quantum dynamics with MCTDH. Review preprint version.


Prof. Dr. H.-D. Meyer    Web Page
- Universität Heidelberg -
Im Neuenheimer Feld 229
69120 Heidelberg
e-mail: hans-dieter.meyer[at]
Phone: +49 6221/54-5210