Fluctuations vibrational entropy

From a thermodynamic perspective, Stillinger and Weber demonstrated that the total entropy of the liquid can similarly be divided into two additive terms, a configurational and a vibrational contribution.5,6 The configurational part Sc measures the number of structurally distinct basins of attraction on the PEL that the configuration point accesses at a given temperature, whereas the vibrational contribution Svib characterizes the number of states associated with intra-basin fluctuations. Thus, the AG relationship, when viewed from the PEL perspective, suggests that it is the thermodynamic availability of basins on the landscape that dominates the rate of liquid-state diffusive processes. 

The free energy of the system also includes entropic contributions arising from the internal fluctuations, which are expected to be different for the separate species and for the liganded complex. These can be estimated from normal-mode analyses by standard techniques,136,164 or by quasi-harmonic calculations that introduce approximate corrections for anharmonic effects 140,141 such approaches have been described in Chapt. IV.F. From the vibrational frequencies, the harmonic contribution to the thermodynamic properties can be calculated by using the multimode harmonic oscillator partition function and its derivatives. The expressions for the Helmholtz free energy, A, the energy, E, the heat capacity at constant volume, C , and the entropy are (without the zero-point correction)164... 

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