  Tunnelling Two-Level Systems (TLS) dominate the physics of glasses at low
temperatures. Yet TLS are extremely rare and it is extremely difficult to
directly observe them $\it{in \, silico}$. It is thus crucial to develop simple
structural predictors that can provide markers for determining if a TLS is
present in a given glass region. It has been speculated that Quasi-Localized
vibrational Modes (QLM) are closely related to TLS, and that one can extract
information about TLS from QLM. In this work we address this possibility. In
particular, we investigate the degree to which a linear or non-linear
vibrational mode analysis can predict the location of TLS independently found
by energy landscape exploration. We find that even though there is a notable
spatial correlation between QLM and TLS, in general TLS are strongly non-linear
and their global properties cannot be predicted by a simple normal mode
analysis.
