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We propose a new algorithm for calculation of vibrational spectra ofmolecules using tensor train decomposition. Under the assumption thateigenfunctions lie on a low-parametric manifold of low-rank tensors we suggestusing well-known iterative methods that utilize matrix inversion (LOBPCG,inverse iteration) and solve corresponding linear systems inexactly along thismanifold. As an application, we accurately compute vibrational spectra (84states) of acetonitrile molecule CH$_3$CN on a laptop in one hour using only$100$ MB of memory to represent all computed eigenfunctions.

Calculating vibrational spectra of molecules using tensor train decomposition