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

Automated summary

In this study, the coarse-graining method was applied to analyze intermolecular vibrations in molecular heterodimers assembled by double hydrogen bonding. The analysis provided three parameters relevant to the mechanical nature of molecular assembly, showing a good correlation with the association energies of the dimers. The reordering schemes of intramolecular vibration vectors played a crucial role in constructing the optimal coarse-grained space.