QUANTUM-MECHANICS OF SMALL NE, AR, KR, AND XE CLUSTERS

We compute energy levels and wave functions of Ne, Ar, Kr, and Xe trimers, modeled by pairwise Lennard-Jones potentials, using the discrete variable representation (DVR) and the successive diagonalization-truncation method. For the Ne and Ar trimers, we find that almost all of the energy levels lie above the energy required classically to achieve a collinear configuration. For the Kr and Xe trimers, we are able to determine a number of energy levels both below the classical transition energy as well as above it. Energy level statistics for these heavier clusters reveal behavior that correlates well with classical chaotic behavior that has previously been observed above the transition energy. The eigenfunctions of these clusters show a wide variety of behavior ranging from very regular behavior for low lying eigenstates to a combination of regular and irregular behavior at energies above the transition energy. These results, along with quantum Monte Carlo calculations of the ground states for a variety of small clusters, lead to the construction of a local mode model for the eigenstates of these clusters. This simple model reproduces quite well many of the calculated energy levels. From the findings here, a simple picture emerges for quantum mechanical clusters of Ne, Ar, Kr, and Xe that correlates very strongly to classical models of these systems.