A reduced dimensionality model of torsional vibrations in star molecules

Highlights: • A reduced dimensionality model is used for torsional vibrations in star molecules. • The model shows proper asymptotic behavior when extrapolated into the nano-regime. • Non-bonded torsional interactions are important to the dynamical behavior. • The model explains the anomalously large apparent inertial moments in these systems. The torsional vibrations of star molecules are studied with a reduced dimensionality model. In this model, the molecule is described by two equivalent sets of lumped inertial cylinders and vibrational frequencies are predicted by solution of the coupled equations of motion. Force constants are determined by including them as free parameters in the model and fitting the computed frequencies to their analogs as determined using full normal coordinate analysis at the HFSCF level of theory. Best agreement between the methods occurs when torsional force constants are included for the first two layers of the molecule. This reveals that non-bonded torsional interactions are important in the vibrational dynamics of these systems. Further insight is afforded by an analysis of why simple harmonic oscillator models are sufficient for modeling some related systems but fail to reproduce the trend in global mode frequencies for saturated aliphatic star molecules. The analysis reveals that the origin of this failure lies in backbone flexibility in these branched polymeric systems.