Why local and non-local terms are essential for second harmonic generation simulation?

Second Harmonic Generation (SHG) today represents one of the most powerful techniques to selectively probe all types of interfaces. However, the origin of the SHG signal at a molecular level is still debated since the local dipole contribution, which is strongly correlated to the molecular orientation can be counterbalanced by non-local quadrupole contributions. Here, we propose a method to simulate the SHG signal of a model water/air interface from the molecular response of each contribution. This method includes both local and non-local terms, which are represented, respectively, by the dependency of the polarisability and hyperpolarisability upon the chemical environment of the molecule and by the bulk quadrupole response. The importance of both terms for the sound simulation of the SHG signals and their interpretation is assessed. We demonstrate that the sole dipole term is unable to simulate a SHG signal, even if the dependency of the hyperpolarisability on the local environment is considered. The inclusion of the bulk quadrupole contribution, which largely dominates the dipole contribution, is essential to predict the SHG response, although the accuracy of the prediction is increased when the dependency upon the local environment is considered.