Knowledge Bank

Spectroscopic studies of molecules embedded in helium droplets provide a unique opportunity to investigate a superfluid. High-resolution infrared spectra of CO$2$-(He) clusters ranging in size from small' ($N\!\simeq \!1-17$) to intermediate' ($N\sim 60$) have been reported recently by McKellar and co-workers.\ {\bf 92}, 145503 (2004);~ A.R.W.\ McKellar, {\em J.\ Chem.\ Phys.}\ {\bf 128}, 044308 (2008).}~ However, they have not yet been able to extend this range to clusters large enough that the observed vibrational band origins shifts $\Delta \nu 3$ and rotational constants $B0$ and $D0$ approached the nanodroplet limit values.\ {\bf 115}, 10254 (2001);~ R.\ Lehnig and W.\ J{" a}ger, {\em Chem.\ Phys.\ Lett.}\ {\bf 424}, 146 (2006).} This paper describes the use of modeling techniques to explore the domain between intermediate and larger' ($N\!\sim\!10^2-10^3$) clusters, seeking to characterize the onset of nanodroplet behaviour. Path integral Monte Carlo (PIMC) simulations using the worm algorithm can in principle provide reliable quantitative results for ``larger'' clusters approaching the nanodroplet limit. We have recently determined a three-dimensional analytical Morse/Long-Range' potential energy surface for CO$2$-He, which explicitly depends on the $Q3$ asymmetric-stretch vibrational motion of CO$2$, and takes account of change in the average value of $Q1$ when $\nu 3$ is excited. {\bf 10}, 4128 (2008).}$,$\ (2009, in press).} Using this potential, predicted vibrational frequency shifts have been found to be in excellent agreement with experiment across the range $N=1-40$, so it is expected to provides a good description of larger clusters. This paper describes results obtained on using this potential in PIMC simulations to predict the effective rotational constant $B0$ and the $\Delta \nu 3$ band-origin shift for CO$2$ in (He) clusters with $N>102$. The importance of identical-particle exchange effects will be examined by comparing results obtained using both Boltzmann and Bose-Einstein statistics.