Solvent effects and pH dependence of the X-ray absorption spectra of proline from electrostatic embedding quantum mechanics/molecular mechanics and mixed-reference spin-flip time-dependent density-functional theory

X-ray absorption spectroscopy (XAS) can provide element-specific local electronic information during chemical transformations when combined with quantum chemical simulations. In this contribution, we develop an efficient theoretical model for simulating the solvent effects on XAS, based on the combination of electrostatic embedding QM/MM and mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT). As a test case, we compute the C, N, and O K-edge X-ray absorption spectra of different protonation forms of proline. We show that the $1s\rightarrow\pi^*$ transitions experience a small rigid shift with respect to the gas phase due to the canceling effect of the red shift due to structure fluctuations and the blue shift due to electrostatic interaction with water. The $1s\rightarrow\sigma^*$ transitions, on the contrary, are more impacted by the fluctuation of proline structure and the electrostatic interaction with the solvent, which affects the mixing with Rydberg-type orbitals. By reconstructing the pH-dependent spectra, we determine that the N K-edge of proline can potentially be used to distinguish the cationic, anionic, and zwitterionic forms of proline.