Subject: partition sums: answers

From: [email-masked] (Johannes Richardi)
Date: Tue, 1 Aug 95 10:36:09 +0100

Hello,

Some time ago, I sent the following question to you:

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A friend of mine who is working in an experimental field 
has an interesting question:

How can you calculate partition function of complex molecules using 
only spectroscopic data ?
Any hints to literature or comments concerning this subject are welcomed.
I will post the summary of the responces if there would be any.

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I received just one answer:

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Hi, I hope this discussion will help you.
A good reference for this is D.A. MacQuarrie's Statistical Mechanics
text. Here is the usual recipe for estimating partition functions
of molecules near room temperature from spectroscopic data.

It is possible to estimate the partition function for a complex
molecule if one knows the moments of inertia (the 3 principle
moments, that is) and the vibrational frequencies (although
transition frequencies may alternatively be used). If we assume
the separation of vibrations from rotations, transform out the
center of mass, and that only one electronic state is thermally
accessible, the partition function within the Born-Oppenheimer
approximation would then be approximated by the formula

Q = Q(vib)*Q(rot)*Q(trans)*Q(elec)

Q(vib) is the partition function for a many-dimensional quantum
harmonic oscillator, and is given by a simple formula. Q(rot) is
the partition function for rotation. Usually (but not necessarily)
one assumes that the rotational partition function is given by the
classical approximation to rigid molecular rotations (if you know
something about the rotational spectrum this can be relaxed). 
Q(elec) is a factor on the order of unity which is basically the
degeneracy of the electronic state.

Note that the above recipe assumes that the molecule is not 
conformationally flexible (no internal rotation or isomerization allowed)
and neglects vibration-rotation coupling and vibrational mode-mode 
coupling (no Fermi resonances allowed). If you use transition 
frequencies in the calculation of Q(vib) you are implicitly taking
some of the anharmonicity into account, which helps. 

If you need more detailed references on this subject, 
just let me know.

best wishes,
robert topper

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I like to add that although it seems a trivial question the
calculation of partition sums of complex molecules is really
hard work.
Thus, the german industry pays up to 30000 Dollars 
(30 kDollars) for one partition sum.
If anybody has an easy way to solve this problem he might have
the chance to end as a second Bill Gates.

Johannes Richardi 

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