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.
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