Calculating the physical properties of isotopes

I am trying to determine the theoretical physical properties (namely melting and boiling temperatures) of isotopic substances. Harold Urey used Debye thermodynamics (which is quite dense) in his [1946 paper](http://pubs.rsc.org/en/content/articlepdf/1947/jr/jr9470000562) to calculate the physical properties of isotopic substances. Most of the equations appear to be for exchange rates of the isotopes within a given system. I would like to know which equations are available to determine isotope effects on physical properties of isotopologues and the assumptions that go with them.





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> The [Debye frequency](https://en.wikipedia.org/wiki/Debye_frequency) of a crystal is a theoretical maximum frequency of vibration for the atoms that make up the crystal. 
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It seems safe to assume melting will be occurring at the Debye frequency. 


It is quite possible that the authors of your paper used the [Lindemann model](https://en.wikipedia.org/wiki/Melting_point#Predicting_the_melting_point_of_substances_.28Lindemann.27s_criterion.29), which was published in 1910, in conjunction with Debye frequency, which is unique to each topoisomer, to predict the melting point using the following equation of Lindemann: 


$$ T\_m = \cfrac{4\pi^2 m \nu^2 c^2 a^2}{k\_B} $$


$$m = \mathrm{atomic\ mass}$$ $$ v = \mathrm{frequency} $$ $$ k\_B=\mathrm{Boltzmann\ constant}$$ $$T=\mathrm{temperature}\ \left(^\circ \mathrm K\right)$$ $$c = \mathrm{Lindemann\ constant}$$ $$a = \mathrm{atomic\ spacing}$$


Different diastereomers have different resonant frequencies which can be found through either Debye calculations or [IR and Raman spectroscopy](http://www.spectra-analysis.com/documents/AppNote025IRAppliedToIsomers.pdf).


Substituting in the Debye expression for frequency (I copied this from Wikipedia; I didn't actually derive it myself) gives:


$$ T\_m = \cfrac{2\pi m (\theta^2\_D k\_B)c^2 a^2}{\hbar^2} $$


Where $\theta^2\_D$ is the [Debye temperature](https://en.wikipedia.org/wiki/Debye_temperature) and $\hbar$ is Planck's constant. 


Another way of doing it is by using a hard sphere model in combination with Debye/Lindemann ([PDF link](http://web.gps.caltech.edu/~mbrown/classes/ge131/notes/djs06.pdf)). 


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