  A matrix product state formulation of the multiconfiguration time-dependent
Hartree (MPS-MCTDH) theory is presented. The Hilbert space that is spanned by
the direct products of the phonon degree of freedoms, which is linearly
parameterized in the MCTDH ansatz and thus results in an exponential increase
of the computational cost, is parametrized by the MPS form. Equations of motion
based on the Dirac-Frenkel time-dependent variational principle is derived by
using the tangent space projection and the projector-splitting technique for
the MPS, which have been recently developed. The mean-field operators, which
appears in the equation of motion of the MCTDH single particle functions, are
written in terms of the MPS form and efficiently evaluated by a sweep algorithm
that is similar to the DMRG sweep. The efficiency and convergence of the MPS
formulation to the MCTDH are demonstrated by quantum dynamics simulations of
extended excitonic molecular systems.
