Indices to evaluate the reliability of coarse-grained representations of mixed inter/intramolecular vibrations

We propose some methods for quantifying the reliability of coarse-grained representations of displacement vectors of normal mode vibrations. In the framework of our basic theory, the original displacement vectors are projected onto a lower-dimensional (i.e., a coarse-grained) space. Four types of functions denoted fidelity indices were introduced as measures of the similarity of the original to the restored displacement vectors. These indices were applied to several hydrogen-bonded homodimers, and the behavior of each index was examined. We found that a coarse-grained representation with high reliability resulted in the accurate restoration of properties such as eigenfrequency, modal mass, and modal stiffness.