  We present how to compute vibrational eigenstates with tree tensor network
states (TTNSs), the underlying ansatz behind the multilayer multiconfiguration
time-dependent Hartree (ML-MCTDH) method. The eigenstates are computed with an
algorithm that is based on the density matrix renormalization group (DMRG). We
apply this to compute the vibrational spectrum of acetonitrile (CH$_3$CN) to
high accuracy and compare TTNSs with matrix product states (MPSs), the ansatz
behind the DMRG. The presented optimization scheme converges much faster than
ML-MCTDH-based optimization. For this particular system, we found no major
advantage of the more general TTNS over MPS. We highlight that for both TTNS
and MPS, the usage of an adaptive bond dimension significantly reduces the
amount of required parameters. We furthermore propose a procedure to find good
trees.
