# Computational Atomistic Modeling in Carbon Flatland and Other 2D Nanomaterials
## 1 Introduction  
The invention of the scanning tunneling microscope (STM) in 1981 [1; 2], winning of the Nobel Prize in Physics by the inventors in 1986, and the invention of the atomic force microscope (AFM) in the same year [3], opened the doors to the _Small World_ described by [PERSON] in his visionary lecture _There's Plenty of Room at the Bottom_[4]. This new ability to see and eventually manipulate individual atoms was soon complemented by other prominent experimental achievements--the discovery of fullerenes in 1985 [5], the development of nanoscale transistors, the structural assignement of carbon nanotubes in 1991 [6]--that definitely established nanosciences as the major research field that we know today. Around the same time, the first quantum-simulation codes were developed based on different flavors of theory such as Hartree-Fock (HF), Density Functional Theory (DFT), Moller-Plesset perturbation (MP2), Configuration Interaction (CI), Coupled Cluster (CC), or multi-reference methods [7; 8; 9; 10; 11], facilitating the theoretical investigation of materials and nanostructures at the atomic scale. A major advantage of these quantum-mechanical modelling methods compared for example to the semi-empirical tight-binding (TB) techniques [12] is their _ab initio_, i.e. parameter-free, character. Nevertheless, the computational cost of _ab initio_ methods remains much higher than the one of TB techniques. In UCLouvain, all these new exciting tools for nanosciences arrived in the nineties. The first AFM and STM were acquired in 1994 [13; 14]. The first DFT and TB simulators were developed and used in the early nineties [15; 16; 17; 18] and the Abinit project was launched officially in 1997 [19].  
The exfoliation of graphene in 2004 [20], and the early measurements of its superlative properties shed light on a new class of nanomaterials--two-dimensional (2D) crystals--that exhibits peculiar properties due to the quantum confinement of their electrons in the _flatland_[21]. Presently, the existence and the stability under ambient conditions of more than a few dozens of different 2D crystals have been reported, including hexagonal boron nitride (_h_-BN), transition metal dichalcogenides (MoS\({}_{2}\), MoSe\({}_{2}\), WS\({}_{2}\), WSe\({}_{2}\), NbSe\({}_{2}\),...), thin oxide layers (TiO\({}_{2}\), MoO\({}_{3}\), WO\({}_{3}\),...), silicene, germanene, phosphorene, borophene, arsenene, stanene, MXenes, and many others.  
In this review article, published in the special issue entitled 'State of the art of nanosciences in Belgium', a small country being sometimes called the _flatland_[22], the predictive power of DFT and TB techniques for various properties of 2D materials is illustrated. Through a selection of monolayered systems, namely graphene, borophene, MXene, and _h_-BN, the potential use of 2D materials in many fields of applications including electronics, electron optics, valleytronics, phononics, and spintronics, will be exposed. The article includes four sections, each investigating a property of a given 2D system using a specific modeling technique. The first section describes the electronic transport properties in polycrystalline graphene using the [PERSON]'s function approach within the Landauer-Buttiker formalism. The second section presents the optical properties of borophene and graphene monolayers including optical Hall effect. The third section introduces the recent and large family of MXenes and in particular their versatile electronic and phononic properties. Last but not least, the genuine use of _h_-BN in innovative magnetic tunnel junctions is discussed in the fourth section. With the present review paper, we wish you an exciting modeling experience in a quite localized region of the still hugely unexplored Flatlands!