Quantum solvation dynamics of HCN in a helium-4 droplet

Ultracold nanodroplets of helium-4, containing several thousands of He atoms, offer considerable promise as microscopic cryogenic chambers. Potential applications include the creation of tailor-made chemical or biomolecular complexes and studies of superfluidity in nanoscale systems. Recent experiments have succeeded in interrogating droplets of quantum solvent which consist of as few as 1-20 helium-4 atoms and which contain a single solute molecule. This allows the transition from a floppy, but essentially molecular, complex to a dissolved molecule to be followed and, surprisingly, the transition is found to occur quite rapidly, in some cases for as few as N = 7-20 solvent atoms. For example, in experiments on helium-4 droplets seeded with CO molecules [Tang and McKellar, J. Chem. Phys. 119, 754 (2003)], two series of transitions are observed which correlate with the a-type (Delta K = 0) and b-type (Delta K = +/-1) lines of the binary complex, CO-He (K is the quantum number associated with the projection of the total angular momentum onto the vector connecting the atom and the molecular center of mass). The a-type series, which evolves from the end-over-end rotational motion of the CO-He binary complex, saturates to the nanodroplet limit for as few as 10-15 helium-4 atoms, i.e., the effective moment of inertia of the molecule converges to its asymptotic (solvated) value quite rapidly. In contrast, the b-type series, which evolves from the free-molecule rotational mode, disappears altogether for N approximately 7 atoms. Similar behavior is observed in recent computational studies of HCN(4He)N droplets [Paolini et al., J. Chem. Phys. 123, 114306 (2005)]. In this article the quantum solvation of HCN in small helium-4 droplets is studied using a new fixed-node diffusion Monte Carlo (DMC) procedure. In this approach a Born-Oppenheimer-type separation of radial and angular motions is introduced as a means of computing nodal surfaces of the many-body wave functions which are required in the fixed-node DMC method. Excited rotational energies are calculated for HCN(4He)N droplets with N = 1-20: the adiabatic node approach also allows concrete physical mechanisms to be proposed for the predicted disappearance of the b-type series as well as the rapid convergence of the a-type series to the nanodroplet limit with increasing N. The behavior of the a-type series is traced directly to the mechanics of angular momentum coupling-and decoupling-between identical bosons and the molecular rotor. For very small values of N there exists significant angular momentum coupling between the molecule and the helium atoms: at N approximately 10 solvation appears to be complete as evidenced by significant decoupling of the molecule and solvent angular momenta. The vanishing of the b-type series is predicted to be a result of increasing He-He repulsion as the number of solvent atoms increases.