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, Φintra, Φinter, and Φapp, which are relevant to the mechanical nature of the molecular assembly. The Φintra values account for the internal stiffness of molecules, while the Φinter values are true stiffness constants of the intermolecular force and show a good correlation with the association energies of the dimers. The Φapp values are the apparent intermolecular stiffness smaller than Φinter, 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.