Partial partition functions

Specifically, following the rate expression of QTST in Eq. (4-1) and assuming the quantum transmission coefficients the dynamic frequency factors are the same, the kinetic isotope effect between two isopotic reactions L and H is rewritten in terms of the ratio of the partial partition functions at the centroid reactant and transition state... 

Moreover, each kind itself is represented by a whole series of states, and partial partition functions may be defined as follows ... 

If the various degrees of freedom are separable (assumption 1 above), then the partition function can be factored into the product of partial partition functions ... 

Thus, we see the emergence of partial partition functions, which pertain to the different forms of energy ... 

Decomposition of the molecular partition function into partial partition functions... 

Calculating partial partition functions requires that the number of degrees of fteedom for each type of molecule movement is known. 

We can show the partial partition functions related to the different types of energies ... 

We now have to examine the three partial partition functions of vibration Zy... 

If only the spins of the nuclei are altered in a given transition, the translational and vibrational contributions to the partition function are identical. Thus, for tiie reaction ortho-Hz - para-H2, the partial-pressure ratio at equilibrium is given by... 

We note that the calculation of At/ will depend primarily on local information about solute-solvent interactions i.c., the magnitude of A U is of molecular order. An accurate determination of this partition function is therefore possible based on the molecular details of the solution in the vicinity of the solute. The success of the test-particle method can be attributed to this property. A second feature of these relations, apparent in Eq. (4), is the evaluation of solute conformational stability in solution by separately calculating the equilibrium distribution of solute conformations for an isolated molecule and the solvent response to this distribution. This evaluation will likewise depend on primarily local interactions between the solute and solvent. For macromolecular solutes, simple physical approximations involving only partially hydrated solutes might be sufficient. 

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