The electrochemical interface is fundamental to understand electrochemical reactions either for electrocatalysis applications (fuel cells), corrosion, electroplating or for electrochemical energy storage such as Li-ion batteries. Nevertheless, it is extremely complex to model not only because of the occurring electrochemical effects but also because of the complexity of the electrode-solvent interface. Classical models fairly well reproduce the behavior of such an interface by introducing more or less complex description of the electric double layer (Helmholtz plane, diffuse layer etc.), but are oblivious of the quantum phenomena occurring at the interface. Ab initio approaches can describe this quantum behavior with good accuracy, nevertheless most of these approaches are not accounting the full complexity of the electrochemical interface as it would necessitate including the surface electrical electrochemical potential, the solvent (at least hundreds/thousands of molecules) and electrolyte (with their interaction with the solvent and the surface) in their structural and time-dependent dimension leading to too costly calculations. We will present a mixed implicit/explicit solvent approach (exemplified by a Li/Ethylene carbonate (EC) interface) that allows recovering the proper electrochemical properties such as surface capacitance at a limited cost. We will highlight the effect of the model parameters on the quality of the calculation. We will discuss how implicit/explicit model should be used in order to recover the potential stability for Li-electrodes in carbonate solvents and how the electrode growth or consumption are linked with the local chemical/electrochemical parameters. We will also focus on the interface electrification and how part of the electrode charge can partially delocalized on the closest solvent layer. This effect has a strong impact on surface electrochemical reactivity and can be investigated by mean of the Fukui function descriptor. Finally, the impact of the electrochemical dimension on the reactivity can also be rationalized by including the solvent approach and can gives quantitative insights into an interface electrochemical reactivity.