sci.physics.research

SHORT SUMMARY FOR BUSY READERS:

whole-body translation and rotation - classical;
torsions - classical;
covalent stretching and bending - non-classical, assume ground state,
if necessary;
Z = ?

FULL TEXT:

Z = sum exp(-E(i)/kT)

in the classical limit, the number of states per unit phase-space
volume is assumed to be 1/h^(3N), so

Z = integral exp(-E(x,p)/kT) (dx dp)^(3N)

In biophysics, for the purposes of estimating the thermodynamic
properties, this approximation is often applied to complex multi-
atomic molecules. This allows the removal of the momentum from the
equation, since the kinetic energy component can be integrated
analytically.

Z ~ integral exp(-U(x)/kT) dx^(3N)

However, we know that the covalent bonds resist stretching and bending
of the angles between them enough to make the classical treatment
unjustified. One could probably even assume that the molecule is in
the ground state with respect to the bending and stretching degrees of
freedom (*).

On the other hand, the rotation around some covalent bonds is
relatively easy (called "torsional degrees of freedom")

I am wondering if there exist expressions for the partition function
using this assumption? Anything that explicitly contains the momentum
or is otherwise very complex, probably won't be useful.

(*) As far as I know, these molecular spectra lie between 3 and 20
microns, shorter than kT = 50 microns.