Enthalpy statistical thermodynamics formula

Statistical thermodynamics provides exact formulas for the calculation of the fundamental quantities of heat capacities, enthalpies and entropies, provided that certain assumptions are valid. Among these assumptions are ... 

ZPE and thermal and entropic corrections at the appropriate experimental temperatures can be calculated using the frequencies in conjimction with the standard textbook formulas for the statistical thermodynamics of an ideal gas under the harmonic oscillator/rigid rotor approximation. Equations (4) and (5) relates the rate constant and equilibrium constant with the Gibbs free energy, which can be described in terms of the enthalpy (H) and the entropy (S) in the following equation ... 

A higher quality approximation method for radicals was proposed by Forgeteg and Berces (1967). This method uses the spectroscopic assignment of the parent molecule, from which the vibrations relevant to the atom missing in the radical are deleted. Other vibrations may then be adjusted according to known ratios between bond lengths or force constants in the molecule and the radical. Thereafter the ordinary statistical mechanics formulas can be used to calculate the thermodynamic properties. Benson s additivity method or other estimates can be used to obtain the enthalpy of formation. 

In these formulas the letter X stands for the average copolymer composition, while of denotes the dispersion of the SCD quantitatively characterizing its width. The second of these statistical characteristics is extremely significant for the thermodynamics of the melt of a heteropolymer specimen, being in a simple way AHmix = RT jof connected with the specific enthalpy of mixing Affmix per mole of monomeric units. Here T is the absolute temperature, R represents the gas constant, whereas / denotes the Flory /-parameter whose values are available from the literature for many pairs of monomeric units (see, for example, [7]). 

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