  Based on the elementary band representations (EBR), some topologically
trivial materials are classified as unconventional ones (obstructed atomic
limit), where the EBR decomposition of electronic states is not consistent with
the atomic valence-electron band representations. In the work, we identify that
the unconventional nature can also exist in phonon spectra, where the EBR
decomposition of the phonon modes is not consistent with atomic vibration band
representations (ABR). The unconventionality has two types: type I is on an
empty site; type II is on an atom site with non-atomic vibration orbitals. Our
detailed calculations show that black phosphorus (BP) and 1H-MoSe2 have
unconventional both phonon spectra and electronic band structures. The BP has
the type-I unconventional phonon spectrum, while 1H-MoSe2 has the type-II one.
The obstructed phonon modes are obtained for two types of unconventional phonon
spectra.
