Magnetic materials are typically described in terms of the Heisenberg model, which provides an accurate account of thermodynamic properties when combined with first principles calculations. This approach is usually based on an energy mapping between density functional theory and a classical Heisenberg model. However, for two-dimensional systems the the eigenenergies of the Heisenberg model may differ significantly from the classical approximation, which leads to modified expressions for exchange parameters. Here we demonstrate that density functional theory yields local magnetic moments that are in accordance with strongly correlated anti-ferromagnetic eigenstates of the Heisenberg Hamiltonian implying that density functional theory provides a description of these states that conforms with the quantum mechanical eigenstates of the model. We then provide expressions for exchange parameters based on a proper eigenstate mapping to the Heisenberg model and find that they are typically reduced by 5-15 % compared to a classical analysis. Finally, we calculate the corrections to critical temperature for magnetic ordering for a previously predicted set of two-dimensional insulators and find that the inclusion of quantum effects may reduce the predictions of critical temperatures by up to 10 %.