DIATOMIC-MOLECULES, ROTATIONS, AND PATH-INTEGRAL MONTE-CARLO SIMULATIONS - N-2 AND H-2 ON GRAPHITE

The rotational motion of homonuclear diatomic molecules confined to tw o dimensions at finite temperatures is discussed within the framework of path-integral Monte Carlo (PIMC) techniques. For single rotators th e symmetry restriction on the total wave function coupling nuclear spi n and rotations of these diatomic molecules is carried over to PIMC fo r fermionic and bosonic diatomic molecules. Three experimentally relev ant quantum statistical averages are formulated, and quantum effects d ue to discrete level spacing and exchange are separated with the help of these averages. The method is applied to single N2 and H-2 rotators adsorbed on graphite in the frozen-in crystal field which is due to t he commensurate ( square-root 3 X square-root 3)R30-degrees ''2-in'' h erringbone phase. Contrary to H-2, exchange effects are negligible for N2 in the relevant temperature range. The resulting sign problem for certain combinations of molecule and averaging procedure is discussed. PIMC simulations of the phase transition from the translationally squ are-root 3-ordered and orientationally disordered phase to the herring bone phase were carried out for complete N2 monolayers without a symme try restriction on the wave function. Due to dispersive quantum fluctu ations, transition temperature and ground-state order parameter are de pressed by roughly 10% as compared to classical MC simulations of the same realistic model. In addition, the PIMC results are compared to qu asiharmonic and quasiclassical approximations. The quasiharmonic treat ment yields the correct order parameter suppression, the quasiclassica l simulation the lowering of the transition temperature, but only the full quantum PIMC simulations describe the entire temperature range of interest correctly.