It appears to be generally true that molecules in liquid He have
effective rotational constants, B, smaller than their gas phase
values. Table II summarizes the situation for a range of
molecules. Molecules with large rotational constants have only modest reduction
in B, while heavier molecules have much larger fractional reductions.
A theory based upon a `normal fluid' density that
rotates rigidly with the molecule has been proposed [7].
A microscopic definition of this `normal fluid', based upon
path integral Monte-Carlo calculations, has recently been
proposed and found to reproduce the observed rotational
constant for SF 
[30].
We have recently [31] made
calculations based upon a hydrodynamic model that, given the low
temperature of the droplets, treats the He as 100% superfluid.
TABLE II. Measured rotational constants of molecules in 
He droplets.
This
implies that the molecules do not `drag' any He atoms around with them
as they rotate since the He flow field must be `irrotational'. We
further assume that the He density (which we calculate using Density
Functional Theory [32]) adiabatically follows the rotation
of the molecule. To date, we have only been able to treat cases where
the He-solute interaction is (or can be approximated as) cylindrically
symmetric, as this reduces the numerical solution required to two
dimensions. From the assumptions stated above, we are able to derive
a partial second-order differential equation for the `velocity
potential' that determines the He flow field from which we extract the
hydrodynamic moment of inertia 
.
Table III contains a comparison of the
calculated hydrodynamic moment of inertia with the incremental moment
( 
)
calculated from the comparison of the observed rotational constants
in the gas phase with those in the He droplets. Except for the lightest
rotors, the agreement is excellent, especially considering the
uncertainties in the density of the He solvation structure around the
molecules. For the very lightest rotors, it may well be that the
assumption of `adiabatic following' is breaking
down [33].
In summary, the field of helium droplet isolation spectroscopy has evolved very rapidly from esoteric experimentation to a useful technique in chemical dynamics. Novel unstable species are being prepared and the behavior of the guest molecules in this cold but frictionless medium is starting to be understood. We can confidently look forward to several years full of exciting further developments.
Acknowledgement: This work was supported by the U.S. National Science Foundation (CHE-97-03604). Klaas Nauta and Dr. Roger Miller are acknowledged for sharing their work prior to publication and for many helpful discussions.
TABLE III. Moments of inertia for the molecules studied in this
work.
Units are u 
; experimental values are computed from the spectroscopically measured
rotational constants, via the conversion factor 505.38
GHz 
u .
