  Time-resolved X-ray scattering patterns from photoexcited molecules in
solution are in many cases anisotropic at the ultrafast time scales accessible
at X-ray Free Electron Lasers (XFELs). This anisotropy arises from the
interaction of a linearly polarized UV-vis pump laser pulse with the sample,
which induces anisotropic structural changes that can be captured by
femtosecond X-ray pulses. In this work we describe a method for quantitative
analysis of the anisotropic scattering signal arising from an ensemble of
molecules and we demonstrate how its use can enhance the structural sensitivity
of the time-resolved X-ray scattering experiment. We apply this method on
time-resolved X-ray scattering patterns measured upon photoexcitation of a
solvated di-platinum complex at an XFEL and explore the key parameters
involved. We show that a combined analysis of the anisotropic and isotropic
difference scattering signals in this experiment allows a more precise
determination of the main photoinduced structural change in the solute, i.e.
the change in Pt-Pt bond length, and yields more information on the excitation
channels than the analysis of the isotropic scattering only. Finally, we
discuss how the anisotropic transient response of the solvent can enable the
determination of key experimental parameters such as the Instrument Response
Function.
