Application of a Lumped-Inertia Technique to Vibrational Analysis of the Torsional-Twisting Modes of Low Molecular Weight Polyphenylenes and Polyethynylphenylenes

The vibrational dynamics of nanosystem components are likely to play a critical role in both nanomechanical and nanoelectronic systems. We demonstrate that vibrational analysis with a lumped-inertia technique can efficiently and reliably anticipate certain vibrational properties without the need for performing costly comprehensive full normal-mode computations. Three classes of linear oligomers with potential for application in nanoelectronics are investigated with this technique. The torsional-twisting frequencies from the lumped-inertia model accurately reproduce the frequencies computed with full normal-mode analysis based on electronic structure calculations. The lumped-inertia model reveals the importance of long-range coupling in torsional-twisting dynamics and affords a partitioning of the effect of phenyl ring substituents on the torsional vibrational frequencies between inertial and electronic structure contributions.