Subject: mixing entropies for a molecule with multiple minima

From: Patrick Bultinck <[email-masked]>
Date: Wed, 02 Aug 2000 11:25:22 +0200

Dear,

I would like to calculate thermodynamical parameters (Delta-H°, Delta-S° 
and Delta-G°) for an ensemble of conformations of a molecule. DH° etc. can 
easily be calculated for each conformation by calculating the hessian. DG° 
is also easily calculated of course. Using Boltzmann's law, one can 
calculate the mole fractions of each conformation you would have for one 
mole of the molecule. DH° is easily calculated for the ensemble using the 
individual mole fractions and DH° values for each conformation. DS° also in 
first approximation, but... should DS° not be augmented with a mixing 
entropy term because you are mixing different conformations, which you all 
treat separately as ideal gases ? I think you would need to add a term 
DS°(mix)=sum(x_i*ln(x_i)), where x_i is the mole fraction for conformation 
i. Since you treat them as ideal gases, nothing changes in DH° for the 
ensemble (they do not interact). Using the mixing-corrected DS°, a new DG° 
can be calculated.

So I am using the following steps to calculate DG° for an ensemble of 
conformations of the same molecule :
- Calculate DH°, DS° and DG° for each conformation separately
- Correct where necessary for chiral degeneracy of each conformation, and 
obtain (for some conformations) chiral corrected values (not every ab 
initio program does this on the fly).
- Calculate Boltzmann determined occupations for all conformations.
- Calculate DH° for the ensemble of conformations, as well as DS° from 
individual DH° and DS° values of all conformations
- Correct DS° with a mixing term, accounting for the fact that each 
conformation is an ideal gas, and that mixing ideal gases brings about a 
mixing entropy.
- Calculate a new DG° value from DH° and the corrected DS° value.

In my opinion, only then can I calculate the DG° value in a reaction : 
metal + ligand -> complex.

I would very much appreciate your opinions on this. I am not ignorant in 
thermodynamics, but I would like to have more experienced people to comment 
on my way to calculate DG° for an ensemble of conformations of the same 
molecule. Especially for the fact that Boltzmann is used to calculate mole 
fractions for each conformation, based on individual values for each 
conformation, and that then later on, a term is added to DS° which can only 
be calculated for an ensemble (but to calculate S_mix, you need the mole 
fractions first)...

Thanks,

Patrick Bultinck
Ghent University
Belgium