Performing vibrational analysis of large QM/MM systems is impractical due to the computational cost of calculating the full Hessian, mainly the computationally expensive derivatives with respect to the positions of the nuclei in the QM subsystem. One way to reduce the computational cost is the partial Hessian vibrational analysis (PHVA) approximation. Using PHVA within QM/MM usually implies that only geometrical derivatives with respect to QM nuclei are included, i.e., only the QM-QM block of the Hessian matrix is calculated, disregarding the MM-MM, QM-MM, and MM-QM blocks. The outcome is a system with mobile QM atoms surrounded by immobile MM atoms. Here, we will refer to this approach as QM/MM-PHVA. Other more advanced partial Hessian approaches have been proposed, such as the mobile block Hessian (MBH) and the vibrational subsystem analysis (VSA) approaches. In this work, we only consider the PHVA. Specifically, we will use it with the fragment-based polarizable embedding (PE) model extended recently to enable calculations of analytical Hessians and geometrical property derivatives. The fragment-based PE approach is one of several PE models that implement analytic Hessians using an atomistic polarizable environment. The eigenanalysis of the partial Hessian in the QM/MM-PHVA approach results in 3N normal modes and corresponding frequencies (where N is the number of atoms in the QM subsystem). A minimum of six normal modes (assuming a nonlinear molecule) correspond to vibrations that can be characterized as full or partial pseudo-translational and pseudorotational modes because they resemble translations and rotations of the QM subsystem in a vacuum. These modes would involve atoms in both the QM and MM subsystems in the full Hessian vibrational analysis, but because the MM atoms are immobile by design, it is only the QM atoms that are collectively vibrating inside a cage defined by the MM atoms.