Although most of the simulation tools developed for bulk systems can directly be applied to simulations of the interfaces, surfaces and free-standing 2D materials, the modifications of the methods are necessary for the optimization of the calculations, as detailed below. Besides, in many cases the reduced dimensionality requires the choice of the meaningful parameters, which are different from the 'bulk' values, and which may heavily affect the simulation results. Here are several examples:

1. In electronic structure calculations of the surfaces and 2D materials [1-4] using the plane-wave simulation codes, a vacuum region is introduced to separate periodic images of the system. If local and semi-local exchange and correlation functionals are used, the results (e.g. fundamental band gap) are quickly converged with regard to vacuum area (distance between the images of the system in the transverse direction). However, this is not the case [5] when non-local techniques like the GW approximation are used, and the results require extrapolation to infinite separation between the images.

2. Another prominent example is calculation of charged defect formation energies in 2D systems by introducing compensation background charge [6,7]. In this case, the energies depend on the separation between the images of the defects due to the intrinsically long-ranged nature of Coulombic interaction , and the results should also be extrapolated to the dilute limit. For bulk materials, there are well established schemes how the extrapolation should be carried out [8-9]. However, it can easily be shown [10] that these approaches do not work in 2D systems, as the system is not isotropic, so that the optimum relationship between the system sizes in lateral and transverse directions should be established. A straightforward extrapolation of the vacuum layer thickness to infinity will give rise to qualitatively wrong results, as the compensating charge will be too “thin” near the layer, giving rise to dramatic overestimation of the Coulombic repulsion between the point charges within the infinite plane where the material is confined.

3. Thermal transport in low-dimensional systems is also heavily affected by the reduced dimensionality [11-13]. Spatial confinement of acoustic phonons in nanostructures substantially changes their energy spectra and density of states in comparison with bulk materials, leading to a reduction of the phonon group velocities. Modifications of the phonon properties and enhancement of the phonon-boundary scattering gives rise to lower values of the lattice thermal conductivity in nanostructures as compared with their bulk counterparts. The necessity to account for phonon scattering at boundaries and reduced dimensionality calls for modifications of the existing simulation methods to optimize the simulations.

4. Finally, accurate simulations of scanning tunneling microscopy and atom force microscopy images with account for tip-surface interaction have always been a challenging and important task [14]. It is well known, that even the qualitative picture can be wrong if tip-induced efefcts are neglected.