Interference effects on the x-ray emission spectra of liquid water and analysis of an attosecond pump-probe model

We report a detailed investigation of the importance of vibrational direct and interference effects in x-ray emission applied to water. We use the full Kramers–Heisenberg (KH) expression on a 2D grid with the two OH-stretches of a central water molecule as coordinates and solve for the relevant vibrational states, providing direct and interference terms. For two pentamer models, we show close agreement between high-level adiabatic diagrammatic construction and time-dependent density functional theory results, and apply to four larger 32-molecule clusters representing high- (HDL) and low-density liquid (LDL) and two intermediate structures. We find for HDL and LDL an initial split (without dynamics) of 0.6 eV, which is increased to 0.7 eV using the full KH expression, i.e., the observed split is dominated by the initial H-bonding. The importance of direct and interference contributions is different for HDL and LDL structures, where for HDL, the full spectrum is well represented by the direct contribution, while for LDL, the 3a1 is strongly enhanced in the direct spectrum, and the 1b1 has large interference contributions. In a recent attosecond x-ray pump/x-ray probe spectrum, only one 1b1 peak was observed together with a significantly increased intensity in the 3a1 region. We reassign the features due to molecules in asymmetric H-bond situations (1b1 peak) and molecules in tetrahedral H-bonding (3a1 intensity) in this experiment, where only direct terms contribute. To eliminate the need for precomputed potential energy surfaces, we show that a semi-classical approximation to the KH formalism gives excellent agreement, including vibrational fine-structure, with the full KH spectra for the four 32-molecule clusters.