The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets

A review is given on the multiconfiguration time-dependent Hartree (MCTDH) method, which is an algorithm for propagating wavepackets. The formal derivation, numerical implementation, and performance of the method are detailed. As demonstrated by example applications, MCTDH may perform very efficiently, especially when there are many (typically four to twelve, say) degrees of freedom. The largest system treated with MCTDH to date is the pyrazine molecule, where all 24 (!) vibrational modes were accounted for. The particular representation of the MCTDH wavefunction requires special techniques for generating an initial wavepacket and for analysing the propagated wavefunction. These techniques are discussed. The full efficiency of the MCTDH method is only realised if the Hamiltonian can be written as a sum of products of one-dimensional operators. The kinetic energy operator and many model potential functions already have this required structure. For other potential functions, we describe an efficient algorithm for determining optimal fits of product form. An alternative to the product representation, the correlation discrete variable representation (CDVR) method, is also briefly discussed.