We suggest a consistent framework for the embedding of reduced-space correlated vibrational wave functions in a potential of the remaining modes and generalize this concept to arbitrary many subspaces. We present an implementation of this framework for vibrational coupled-cluster theory and response treatments. For C=O stretches of small molecules, we show that the embedded treatment accelerates convergence for enlarging subsets. For the water dimer and trimer as well as a water wire in bacteriorhodopsin, we investigate different partitioning schemes for the embedding approach: In the local partitioning of the vibrations, the modes dominated by motions in the same spatial region are correlated, whereas in the energy-based partitioning, modes of similar fundamental frequencies are correlated. In most cases, we obtain better agreement with superset reference results for the local partitioning than for energy-based partitioning. This work represents an important step toward multi-level methodologies in vibrational-structure theory required for its application to sizable (bio-)molecular systems.
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