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The Problem of the Changes in Rotational Constants Induced by the Helium Nanodroplet

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 tex2html_wrap_inline4130  [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 tex2html_wrap_inline4118 He droplets.

  table1766

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 tex2html_wrap_inline4250 . Table III contains a comparison of the calculated hydrodynamic moment of inertia with the incremental moment ( tex2html_wrap_inline4252 ) 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 tex2html_wrap_inline4254 ; experimental values are computed from the spectroscopically measured rotational constants, via the conversion factor 505.38 GHz tex2html_wrap_inline4256 u tex2html_wrap_inline4254 .

  table1794


next up previous
Next: References Up: From intermolecular forces to Previous: Rotational and Rovibrational Spectra

m.m.law
Tue Aug 17 18:54:52 BST 1999