  The electronic properties of interfaces can depend on their isotopic
constitution. One known case is that of cyclohexane physisorbed on Rh(111), in
which isotope effects have been measured on the work function change and
desorption energies. These effects can only be captured by calculations
including nuclear quantum effects (NQE). In this paper, this interface is
addressed employing dispersion-inclusive density-functional theory coupled to a
quasi-harmonic (QH) approximation for NQE, as well as to fully anharmonic ab
initio path integral molecular dynamics (PIMD). The QH approximation is able to
capture that deuterated cyclohexane has a smaller adsorption energy and lies
about 0.01 A farther from the Rh(111) surface than its isotopologue, which can
be correlated to the isotope effect in the work function change. An
investigation of the validity of the QH approximation relying on PIMD
simulations, leads to the conclusion that although this interface is highly
impacted by anharmonic quantum fluctuations in the molecular layer and at
bonding sites, these anharmonic contributions play a minor role when analysing
isotope effects at low temperatures. Nevertheless, anharmonic quantum
fluctuations cause an increase in the distance between the molecular layer and
Rh(111), a consequent smaller overall work function change, and intricate
changes in orbital hybridization.
