Enthalpy derivation from partition functions

Expressions similar to those given above may be derived easily from partition functions in other ensembles.The choice of ensemble is very important in calculations of hydration entropy, enthalpy, and heat capacity, as discussed below. Many other quantities, including all free energies, are ensemble invariant, with the choice of ensemble affecting only system size dependence. For simplicity, the discussion here is therefore limited to the canonical ensemble except in such cases where a true ensemble dependence exists. 

We can now utilize some of the statistical mechanics relationships derived in Chapter 8 to find expressions for the free energy and the equilibrium constant in term of the molecular partition functions. From the definition of the free energy (Eq. 9.1) the expression for the enthalpy of an ideal gas (Eq. 8.121), and recalling that Ho = Eq (for an ideal gas), we obtain... 

Calculation of Thermodynamic Functions from Molecular Properties The calculation methods for thermodynamic functions (entropy S, heat capacities Cp and Cy, enthalpy H, and therefore Gibbs free energy G) for polyatomic systems from molecular and spectroscopic data with statistical methods through calculation of partition functions and its derivative toward temperature are well established and described in reference books such as Herzberg s Molecular Spectra and Molecular Structure [59] or in the earlier work from Mayer and Mayer [7], who showed, probably for the first time in a comprehensive way, that all basic thermochemical properties can be calculated from the partition function Q and the Avagadro s number N. The calculation details are well described by Irikura [60] and are summarized here. Emphasis will be placed on calculations of internal rotations. 

In the following we shall give enthalpy and heat capacity equations for some typical folding models. For each model the relative partition function is given as well as the enthalpy and the heat capacity functions resulting from the temperature derivatives according to equations 35 and 36. In this... 

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