The structural and elastic properties of orthorhombic black phosphorus have been investigated using first-principles calculations based on density functional theory. The structural parameters have been calculated using the local density approximation
(LDA), the generalized gradient approximation (GGA), and with several dispersion corrections to include van der Waals interactions. It is found that the dispersion corrections improve the lattice parameters over LDA and GGA in comparison with experimental results. The calculations reproduce well the experimental trends under pressure and show that van der Waals interactions are most important for the crystallographic b-axis, in the sense that they have the largest effect on the bonding between the phosphorus layers. The elastic constants are calculated and are found to be in good agreement with experimental values. The calculated C$_{22}$ elastic constant is significantly larger than the C$_{11}$ and C$_{33}$ parameters, implying that black phosphorus is stiffer against strain along the a-axis than along the b- and c-axes. From the calculated elastic constants,the mechanical properties such as bulk modulus, shear modulus, Youngs modulus and Poissons ratio are obtained. The calculated Raman active optical phonon frequencies and their pressure variations are in excellent agreement with available experimental results.
We propose a new class of materials, which can be viewed as graphene derivatives involving Group IA or Group VIIA elements, forming what we refer to as graphXene. We show that in several cases large band gaps can be found to open up, whereas in other
cases a semimetallic behavior is found. Formation energies indicate that under ambient conditions, sp$^3$ and mixed sp$^2$/sp$^3$ systems will form. The results presented allow us to propose that by careful tuning of the relative concentration of the adsorbed atoms, it should be possible to tune the band gap of graphXene to take any value between 0 and 6.4 eV.
Using the GW approximation, we study the electronic structure of the recently synthesized hydrogenated graphene, named graphane. For both conformations, the minimum band gap is found to be direct at the $Gamma$ point, and it has a value of 5.4 eV in
the stable chair conformation, where H atoms attach C atoms alternatively on opposite sides of the two dimensional carbon network. In the meta-stable boat conformation the energy gap is 4.9 eV. Then, using a supercell approach, the electronic structure of graphane was modified by introducing either an hydroxyl group or an H vacancy. In this last case, an impurity state appears at about 2 eV above the valence band maximum.
