The properties of a single layer of h-BN on top of a Rh(111) surface are discussed in terms of an ab initio generated force field approach as well as by direct ab initio density-functional theory (DFT) calculations. A single-layer model for the h-BN/Rh(111) nanomesh, in contrast to a previously considered (incomplete) double-layer model of h-BN, can explain the experimental data. The main focus of this work is to compare a force field approach described earlier in (Laskowski et al 2007 Phys. Rev. Lett. 98 106802) with direct ab initio calculations. The calculated geometry of the h-BN layer is very similar to the structure predicted by the force field approach. The ab initio calculated density of states projected on N-p(x,y) of BN corresponding to 'low' and 'high' regions with respect to the Rh surface shows a 1 eV splitting and thus explains the observed σ-band splitting. Moreover, we find good agreement between calculated and experimental scanning tunneling microscope (STM) images of this system.