The simulation of X-ray absorption spectra including vibronic coupling: application of the QD-DFT/MRCI(2) method

We here demonstrate the accuracy and computational efficiency of the recently introduced QD-DFT/MRCI(2) formalism [Neville et al., J. Chem. Phys., 2024, 160, 234109.] for the direct calculation of quasi-diabatic core-excited electronic states via the simulation of the X-ray absorption spectra for a trio of unsaturated hydrocarbons: ethylene, allene, and butadiene. This is achieved via the construction of vibronic coupling Hamiltonians, including anharmonicity through 6th-order in the one-mode terms, as well as bilinear two-mode coupling terms. The models include all vibronically-coupled core-excited states below the core-ionization potential: 24, 27, and 26 states of the C K-edge for ethylene, allene, and butadiene, respectively. These results, which furnish excellent agreement with recently measured X-ray absorption spectra, demonstrate the effectiveness of the QD-DFT/MRCI(2) method. Further, they highlight the importance of accounting for vibronic coupling in first principles simulation of X-ray absorption spectra. Specifically, we demonstrate that simulations constructed from best estimate vertical excitation energies and oscillator strengths alone generally fail to predict the positions of experimental peak maxima, particularly for transition energies above the band origin.