Diatomic molecules, rotations, and path-integral Monte Carlo simulations: N2 and H2 on graphite

Abstract

The rotational motion of homonuclear diatomic molecules confined to two dimensions at finite temperatures is discussed within the framework of path-integral Monte Carlo (PIMC) techniques. For single rotators the symmetry restriction on the total wave function coupling nuclear spin and rotations of these diatomic molecules is carried over to PIMC for fermionic and bosonic diatomic molecules. Three experimentally relevant quantum statistical averages are formulated, and quantum effects due to discrete level spacing and exchange are separated with the help of these averages. The method is applied to single N2 and H2 rotators adsorbed on graphite in the frozen-in crystal field which is due to the commensurate (√3×√3)R30° ‘‘2-in’’ herringbone phase. Contrary to H2, 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 √3-ordered and orientationally disordered phase to the herringbone phase were carried out for complete N2 monolayers without a symmetry restriction on the wave function. Due to dispersive quantum fluctuations, transition temperature and ground-state order parameter are depressed by roughly 10% as compared to classical MC simulations of the same realistic model. In addition, the PIMC results are compared to quasiharmonic and quasiclassical approximations. The quasiharmonic treatment yields the correct order parameter suppression, the quasiclassical simulation the lowering of the transition temperature, but only the full quantum PIMC simulations describe the entire temperature range of interest correctly.