For electronic structure: UV visible spectroscopy, VB-XPS spectroscopy.

For crystal structure: XRD

For Surface Structure: BET surface area measurement, HR-TEM and FE-SEM studies.

Density Functional Theory, ;-)

electronic structure: photoelectron spectroscopy with hard X-rays

crystal structure: XRD, raman spectroscopy

surface structure: AFM, SEM

U can choose TEM for atomic structure of TiO2 and SEM for surface structure and for crystal structure XRD .... But you can go with DFT also ... It will give you electronic structure information for it .

I agree with sourav sorcar answer.

Shape structure - to use SEM and TEM

Crystal Structure - XRD and Raman

But in electronic structure means where ever to perturbed the system using electromagnetic radiation to generate the exciton and their behaviors.

Hope the attached article helps you.

Article Synthesis and characterization of solar photoactive TiO2 nan...