Second harmonic generation (SHG) has emerged as one of the most powerful techniques used to selectively monitor surface dynamics and reactions for all types of interfaces as well as for imaging non-centrosymmetric structures, although the molecular origin of the SHG signal is still poorly understood. Here, we present a breakthrough approach to predict and interpret the SHG signal at the atomic level, which is freed from the hyperpolarisability concept and self-consistently considers the non-locality and the coupling with the environment. The direct ab initio method developed here shows that a bulk quadrupole contribution significantly overwhelms the interface dipole term in the purely interfacial induced second-order polarisation for water/air interfaces. The obtained simulated SHG responses are in unprecedented agreement with the experimental signal. This work not only paves the road for the prediction of SHG response from more complex interfaces of all types, but also suggests new insights in the interpretation of the SHG signal at a molecular level. In particular, it highlights the modest influence of the molecular orientation and the high significance of the bulk quadrupole contribution, which does not depend on the interface, in the total experimental response.