Excited Electronic States in Total Isotropic Scattering from Molecules

Ultrafast X-ray scattering experiments are routinely analyzed in terms of the isotropic scattering component. Here, we present an analytical method for calculating total isotropic scattering for ground and excited electronic states directly from ab initio two-electron densities. The method is generalized to calculate the isotropic elastic, inelastic, and coherent mixed scattering. The presented computational results focus on the potential for differentiating between electronic states and the decomposition of the total scattering in terms of elastic and inelastic scattering. For the specific example of the umbrella motion in the first excited state of ammonia, we show that the redistribution of electron density along this coordinate leaves a comparably constant fingerprint in the total scattering that is similar in magnitude to the effect of changes in molecular geometry.