Partition functions, molecular, molar

E17.10(b) The contributions of rotational and vibrational modes of motion to the molar Gibbs energy depend on the molecular partition functions... 

Note on the molar properties - in the expressions of the molecular and canonical partition functions, we have based our discussions on a certain number of molecules - a number of particles symbolized by Np, for the component A. 

Molecular weight of species A Avogadro s number Number of particles of species. A Hypothetical number of activated complexes Density of states for the ath degree(s) of freedom of an activated molecule with energy in the specified degree(s) of freedom Momentum flux in x direction Probability density for states of energy e Enthalpy release per mole of reaction Molar partition function for species A Reduced molar partition function for the activated complex... 

BE = bond increment GE = group increment HFE = Hartree-Fock energy MH = molar heat content MM2, MMP2, MM3, MM4 = molecular mechanics programs PFC = partition function contribution POP = population contribution SE = structural features increment TOR = torsional contribution. 

The energy and entropy, which are related in this equation to the molecular partition function, are statistical entities, defined by particles which do not interact except to maintain the equilibrium conditions. To obtain similar relationships for real systems, it is necessary to apply statistical mechanics to the calculation of the thermodynamic entities, which correspond to the molar quantities of particles, or that is N approaches 1 this treatment it is convenient to use the canonical ensemble already discussed and presented in Figure n.l. This ensemble consists of a very large number of systems, N, each containing 1 mol of molecules and separated from the others by diathermic walls, which allow heat conduction but do not allow particles to pass. The set of all the systans is isolated from the outside and has a fixed energy E, which is the energy of the canonical ensemble. 

Table 9.3 Molar thermodynamic functions in terms of the molecular partition...

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