Configurational entropy anharmonic contribution

Figure 15. (a) Temperature dependence of the Gibbs free energy for ice Ih (solid line) and ice Ic (dotted line) at atmospheric pressure, where contributions from the configurational entropy and anharmonic vibrations are omitted, (b) Temperature dependence of the energy which is defined as the sum of the interaction energy at its minimum structure and the vibrational energy for ice Ih (solid line) and ice Ic (dotted line). 

The question arises whether these series of Q branches could be interpreted on a slightly anharmonic potential function rather than on a cosine function type of pseudo-rotation. For a low barrier ( 7.5 kJ mol ) the contribution to the entropy at 298 K of a hindered pseudo-rotator differs from that of a harmonic oscillator of the same frequency by 6 J K mol , which is certainly measurable. But for a high barrier ( 14.6 kJ mol ) the difference between the entropy contributions is 0.6 J K mol at 298 K and only 1.2 JK mol at 398 K. Therefore only for a low barrier can the two possibilities be distinguished by thermodynamic measurements. For Y-butyrolactone and ethylene carbonate the barriers are calculated to be 46 kJ mol and 75 kJ mol , respectively, which would negate the effect of pseudo-rotation at reasonable temperatures. Thus, in molecules with a sufficiently high barrier the motion can be treated as an ordinary vibration in which the puckering oscillates about a stable configuration. 

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