Z. Phys. B 98, 421 428 (1995) ZEITSCHRIFT FORPHYSIK B 9 Springer-Verlag 1995 Static and dynamical distortions of helium clusters M.A. McMahon, R.N. Barnett, K.B. Whaley Department of Chemistry,Universityof California, Berkeley,CA 94720, USA Abstract. We examine the effects of impurities ('doping') and rotational excitation on the structural and energetic properties of helium clusters. Quantum Monte Carlo (QMC) techniques are used to study ground and rotation- ally excited states of pure and doped clusters. We use exponentially correlated wave functions and treat the molecular impurities as rigid. Whereas pure HeN show essentially monotonic decay of density from a central maximum value, addition of impurities induces local or- dering of He to an extent dependent on the impurity-He binding. Rotational excitation of HeN gives rise to ex- tremely large centrifugal distortions. The location of im- purities also appears to change upon rotational excitation. The implications of these distortions on impurity spectra are discussed for SF6HeN, and compared to recent experi- mental results. PACS: 36.40. +d; 33.70.Jg; 67.40.Yv I. Introduction Isolated clusters of pure helium-4 are extremely weakly bound and are unique among van der Waals clusters in being liquid-like under all conditions of formation. This is a consequence of the small binding energies and associated high degree of delocalization. Theoretical cal- culations of ground state, non-rotating, HeN show the structures to be dominated by zero point effects, with very weak traces of hard core packing constraints [1]. A quite different situation arises when an impurity species is ad- ded to HeN. Depending on the binding of the foreign species, it may be localized or delocalized. If localized it may cause considerable rearrangement of the helium den- sity distribution around it. Rotational excitations of the cluster may also be expected to cause significant distortion of the helium density distribution because these weakly bound systems are very susceptible to centrifugal forces. In this paper we describe the results of quantum Monte Carlo calculations for a number of molecular im- purities in HeN, i.e., Hz, Da, Cl2, and SF6, and for rotation- ally excited HeN and doped XHeN. Of particular interest are the changes in cluster structure upon addition of an impurity, rotational excitation, or both. The calculations are done at the variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) levels. For XHeN we find two general trends: (i) localization and centralization of the impurity increases as the strength of the binding to helium increases, (ii) for a given dopant, delocalization of the impurity increases as the cluster size increases. We show that rotational excitation causes large centrifugal distortion and yields oblate shaped clusters which evolve to toroidal shapes as the angular momentum increases. Results for doped clusters with relatively small angular momenta indicate that the effect of rotation on the impu- rity is greater than on the surrounding He atoms. For high angular momenta the structural distortion becomes severe and our preliminary calculations have revealed that differ- ent circulation patterns, including the line vortex state, can be found with careful design of the rotational wave function form. We then discuss how these distorted structures are relevant to the spectroscopy of the impurity molecule. The cluster-induced shift of the v3 vibration for SF6HeN is analyzed in detail for the non-rotating, L = 0, ground state cluster, and comparison is made with recent experi- mental results [2]. We find that the sign and magnitude of the shift is well reproduced by the instantaneous dipole- induced dipole model which was successfully used for analysis of shifts for SF6 in argon clusters [3]. In the L = 0 state we find that the symmetry of the He distribution about the SF6 precludes any splitting of the v3 absorption within this model [4]. However, the size-dependent delocalization of the SF6 suggests that the surrounding finite helium distribution provides a confining potential, and we propose that quantized vibrations of the SF6 against this confinement potential give rise to satellite peaks about the central v3 absorption. Estimates of these satellite positions are given and com- pared with experimental absorption peak splittings, as well as with alternative possibilities for the origin of a split absorption.