  We present exemplary results of extensive studies of mechanical, electronic
and transport properties of covalent functionalization of graphene monolayers
(GML) with -NH2. We report new results of ab initio studies of covalent
functionalization of GML with -NH2 groups up to 12.5% concentration. Our
studies are performed in the framework of the density functional theory (DFT)
and non-equilibrium Green's function (NEGF). We discuss the stability
(adsorption energy), elastic moduli, electronic structure, band gaps, and
effective electron masses as a function of the density of the adsorbed
molecules. We also show the conductance and I(V) characteristic of these
systems. Generally, the stability of the functionalized graphene layers
decreases with the growing concentration of attachments and we determine the
critical density of the molecules that can be chemisorbed on the surface of
GLs. Because of local deformations of GLs and sp3 rehybridization of the bonds
induced by fragments, elastic moduli decrease with increasing number of groups.
Simultaneously, we observe that the functionalizing molecules stretch the
graphenes lattice, the effect being more pronounced for higher concentration of
adsorbed molecules. We find out that the GLs functionalization leads in many
cases to the opening of the graphene band gap (up to 0.5302 eV for 12.5%
concentration) and can be therefore utilized in graphene devices. The new HOMO
and LUMO originate mostly from the impurity bands induced by the
functionalization and they exhibit parabolic dispersion with electron effective
masses comparable to ones in silicon or gallium nitride.
