EIGENSTATES OF A QUANTUM-MECHANICAL PARTICLE ON A TOPOLOGICALLY DISORDERED SURFACE - H(D) ATOM PHYSISORBED ON AN AMORPHOUS ICE CLUSTER (H2O)115

We examined energy levels and stationary states of a quantum-mechanical particle adsorbed on a rough and disordered surface. The specific system examined consists of an H atom (or a D atom) adsorbed on an amorphous ice cluster (H2O)115. Two kinds of stationary states of the adsorbate particle were obtained: states localized in cavities on the cluster surface, and states occupying corridors of low potential energy present on the cluster surface. Zero-point energy effects were found to be very significant; thus the ordering of ground state energies in the different cavities does not follow at all the ordering of minimum potential energies in the cavities. Significant localization was demonstrated of the calculated eigenstates within small portions of connected energetically accessible regions on the cluster surface. The localization seems to be associated with disorder in the three-dimensional potential energy surface, which includes strongly varying well depth, and sharp turns in potential contours. Phase matching of the adsorbate wave function is not easily achieved in the different parts of the potential well, the result being localization of the eigenstates.