A sample configuration of the system. A random chosen probe molecule is displayed in balls and sticks style, while its cage is represented as a molecule in dark sticks.
The employed reference frames. LF: laboratory frame; MF: molecular frame; CF: cage frame.
Trajectory of a generic probe molecule (dashed line) and its cage (solid line) in the LF. The probe and cage coordinates correspond to and , respectively.
Normalized self-correlation functions (of first- and second-rank Wigner functions) for probe (dashed line) and cage (solid line) orientations referred to LF [see Eq. (1)]. Decay times of the slow-relaxing tails are reported.
Trajectory of the Euler angles defining the transformation [frames (a)–(c)] and time evolution of the sum [frame (d)], for the same probe molecule of Fig. 3.
One-dimensional profiles of the actual cage potential; from frames (a)–(e) all the remaining variables are set equal to zero, while in frame (f) the potential profile is in turn displayed as a function of and by setting and zero all the other variables.
Comparison between (a) the actual cage potential and (b) the approximated one [see Eq. (6) with Eqs. (8)–(10)] versus and around the minimum; the other variables are set and . Values are expressed in units. Frame (c) shows the relative percentage deviations (in absolute value) of (b) with respect to (a).
Equilibrium distributions [frames (a) and (b)] and normalized self-correlation functions [frames (c) and (d)] of the parameters and entering Eq. (8).
Normalized self-correlation functions (solid line) and (dashed line) (See Eqs. (18) and (19), respectively).
Normalized self-correlation functions for the components of position, velocity (referred to the CF), and angular momentum (referred to the MF) of the probe molecule.
Analysis of the system probe cage: equilibrium averages and dynamics. The relaxation times with subscripts and are related to the decay of the “fast” and of the “slow” components of the correlation functions, respectively. Angular momenta have been converted into angular frequencies (referred to rotations about the MF axes) by means of , being and the inertia moments of the molecule.
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