Optimizing a coarse-grained space for approximate normal-mode vibrations of molecular heterodimers

We applied the method of coarse-graining the intermolecular vibrations to molecular heterodimers assembled by double hydrogen bonding. This method is based on principal component analysis, by which the original atomic displacement vectors are projected onto a lower-dimensional space spanned by a basis set of translations, librations, and intramolecular vibrations of the constituent molecules. Compared with homodimers, the following points are particularly noted: (1) alignment of the constituent molecules in a non-symmetric atomic arrangement of the whole system and (2) the scheme of reordering the bases to construct an optimal coarse-grained space. We tested three schemes for reordering the intramolecular vibration vectors to determine that the best one is equivalent to size reduction based on the singular value decomposition. The coarse-graining analysis affords three parameters, Φ_intra, Φ_inter, and Φ_app, which are relevant to the mechanical nature of the molecular assembly. The Φ_intra values account for the internal stiffness of molecules, while the Φ_inter values are true stiffness constants of the intermolecular force and show a good correlation with the association energies of the dimers. The Φ_app values are the apparent intermolecular stiffness smaller than Φ_inter, as a result of compensation for neglecting intramolecular vibrations. All these values are consistent with each other under the coupled oscillator model, showing that the present coarse-graining analysis is valid for heterodimers as well as homodimers.