Our ab initio calculations reveal a rather flat sheet of relaxed borophene with a z corrugation of only 0.43 Å, consistent with prior theoretically investigated structures on Cu(111) with smaller unit cells13,27. The average B–B bond length is 1.72 Å, with a spread of < 0.2 Å, and we found that the sheet on Cu(111) is under anisotro-pic, ~4% on average, tensile strain compared to the correspond-ing structure relaxed in vacuum. More details on other borophene structures we investigated are given in Supplementary Section 4. We investigated the film–substrate interaction, a relevant parameter for prospective sheet transfer and device fabrication (Fig. 5). The cal-culations show that our borophene structure in Fig. 4 is electron doped via charge transfer with no significant covalent bonding. The value of η = 1/5 can be understood if one takes into account that the self-doping mechanism3,28 in conjunction with the electron transfer from Cu to B is expected to increase η above η ≈ 1/9 (the maximum stability for isolated sheets). Our experimental findings are generally in agreement with the predicted behaviour of 2D boron on Cu(111) surfaces13,27 and confirm the predictive power and capabilities of ab initio calculations to guide future choices of material substrates for the structural and electronic engineering of 2D sheets of borophene.