We propose several quantum mechanical models to describe electronic field emission from first principles. These models allow to correlate quantitatively the electronic emission current to the electrode surface details at the atomic scale. They all rely on electronic potential energie surfaces obtained from three dimensional density functional theory calculations. They differ by the various quantum mechanical methods (exact or perturbative, time dependent or time independent) which are used to describe tunneling through the electronic potential energy barrier. Comparison of these models between them and with the standard Fowler-Nordheim one in the context of one dimensional tunneling allows to assess the impact on the accuracy of the computed current of the approximations made in each model. Among these methods, the time dependent perturbative one provides a well balanced trade-off between accuracy and computational cost.