We report detailed DFT calculations and Monte Carlo simulations on the pure and doped cuprate superconductor HgBa2CuO4+delta. For the pure compound (delta = 0), we have obtained an insulating behavior with strong antiferromagnetic copper spin correlations in the CuO2 plane. The high value of the calculated Neel temperature T-N = 333 K reflects the large in-plane exchange interaction J = -145 meV. The obtained optical properties and critical exponents demonstrate the anisotropic quasi-2D character of this type of materials. As for the doped compound the electronic structure and the transport properties have been investigated for various values of doping. Based on these data, we suggest a prediction of the value of optimum doping for HgBa2CuO4+delta (delta optimal = 0.125). (C) 2017 Published by Elsevier B.V.