The multiconfiguration time-dependent Hartree (MCTDH) method is an algorithm for propagating multi-dimensional wavepackets or density operators.

This algorithm is introduced and its efficiency is explained. In short, the efficiency originates from using an variationally optimized time-dependent basis set. To achieve the full efficiency, however, the Hamiltonian must be given as a sum of products of one-dimensional operators. A special algorithm was developed to expand a general potential into product form .

The efficiency of MCTDH is best demonstrated through the calculations on the absorption spectrum of pyrazine . There the correlated motion of all the 24 modes evolving on two coupled electronic surfaces is treated with high accuracy. To emphasize the very large gain obtained here we note that the underlying primitive basis consists of $10^{21}$ points, whereas there are only $3.8\times 10^6$ configurations are needed for convergence.

MCTDH has been applied to a wide range of molecular processes, including photodissociation, surface scattering, reactive scattering, isomerization and the computation of vibrational spectra. Further information, a list of references, etc, can be found on the MCTDH web site: \textbf{\texttt{http://www.pci.uni-heidelberg.de/tc/usr/mctdh/ }}\\

To a large part the talk will discuss the MCTDH algorithm as such. As application we will discuss the trans-cis isomerization of HONO.