Ab initio theory of X-ray emission spectral of liquid water

X-ray emission spectral (XES) has recently been established as a powerful experimental tool in detecting the local H-bond network of liquid water. In the current work, we have developed an {\it ab initio} scheme for calculating the XES spectra of water. Based on the equilibrium trajectories generated by {\it ab initio} molecular dynamics, we perform additional atomic dynamics in the presence of a core-hole within the time scale corresponding to the experimental core-hole lifetime. The XES spectra is then determined by computing the transition matrix based on many body perturbation theory within the GW approximation. It is found that both the core-hole dynamics and the ensemble average of the local chemical environment, due to fluctuations of the H-bond network, are crucial in obtaining a physically meaningful XES spectra of liquid water.