Benchmarking Vibrational Spectra: 5000 Accurate Eigenstates of Acetonitrile Using Tree Tensor Network States

Accurate vibrational spectra are essential for understanding
how
molecules behave, yet their computation remains challenging, and benchmark
data to reliably compare different methods are sparse. Here, we present
high-accuracy eigenstate computations for the six-atom, 12-dimensional
acetonitrile molecule, a prototypical, strongly coupled anharmonic
system. Using a density matrix renormalization group (DMRG) algorithm
with a tree-tensor-network-state (TTNS) ansatz, a refinement using
TTNSs as basis set, and reliable procedures to estimate energy errors,
we compute up to 5,000 vibrational states with error estimates below
0.0007 cm–1. Our analysis reveals that previous
works underestimated the energy error by up to 2 orders of magnitude.
Our data serve as a benchmark for future vibrational spectroscopy
methods, and our new method offers a path toward similarly precise
computations of large, complex molecular systems.