  In this work the role that charge delocalization plays in the non-linear
optical response of ionic liquids is evaluated. The first hyperpolarizability
for the non-linear process of second harmonic generation (SHG) and second
hyperpolarizability for the non-linear process of electro-optical Kerr-Effect
(EOKE) of a large number of ionic liquid forming ions were estimated by means
of density functional theory calculations. The results point to that both
charge delocalization and molecular geometry are the key features that govern
their hyperpolarizabilities. Our findings show that some of the most commonly
used anions in ionic liquids are expected to present strong non-linear
responses while common cations present a much more limited performance.
However, this limitation can be overcome by a proper tailoring of cations to
present charge delocalization over large molecular regions. The hypothesis of
additivity of hyperpolarizabilities in ionic liquids is tested and exploited to
obtain a map of second and third order non-linear susceptibilities of 1496 ion
combinations. This map is intended to be a guide for future works on the
hyperpolarizability of ILs
