Understanding
and controlling the electronic structure of nanomaterials
is the key to tailoring their use in a wide range of practical applications.
Despite this need, many important electronic states are invisible
to conventional optical measurements and are typically identified
indirectly based on their inferred impact on luminescence properties.
This is especially common and important in the study of nanomaterial
surfaces and their associated defects. Surface trap states play a
crucial role in photophysical processes yet remain remarkably poorly
understood. Here we demonstrate for the first time that broadband
electronic sum frequency generation (eSFG) microspectroscopy can directly
map the optically bright and dark states of nanoparticles, including
the elusive below gap states. This new approach is applied to model
cadmium selenide (CdSe) quantum dots (QDs), where the energies of
surface trap states have eluded direct optical characterization for
decades. Our eSFG measurements show clear signatures of electronic
transitions both above the band gap, which we assign to previously
reported one- and two-photon transitions associated with the CdSe
core, as well as broad spectral signatures below the band gap that
are attributed to surface states. In addition to the core states,
this analysis reveals two distinct distributions of below gap states,
providing the first direct optical measurement of both shallow and
deep surface states on this system. Finally, chemical modification
of the surfaces via oxidation results in the relative increase in
the signals originating from the surface states. Overall, our eSFG
experiments provide an avenue to directly map the entirety of the
QD core and surface electronic structure, which is expected to open
up opportunities to study how these materials are grown in situ and
how surface states can be controlled to tune functionality.