Hybrid density-functional theory calculations of near-edge x-ray absorption fine-structure spectra: Applications on benzonitrile in gas phase

Abstract

The experimental $\mathrm{N}(1s)$ near-edge x-ray-absorption fine-structure spectrum of the benzonitrile molecule in the gas phase shows well separated double peaks with different vibrational profiles. Hybrid density-functional theory calculations reveal that such a separation is a result of the conjugation effect on the nitrogen $2p$ orbitals and the double spectral peaks can be assigned as the $\mathrm{N}(1s)\ensuremath{-}\ensuremath{\pi}*$ out-of-plane and in-plane resonances. The vibrational profiles have been analyzed using a combined transition state theory and linear coupling model. Each profile consists of two different vibrational progressions corresponding to stretching modes and a broad continuum of bending excited states. The use of transition state theory allows identifying the dynamics of the N $1s$ core excitation. It is found that upon core excitations the $\mathrm{C}\mathrm{N}$ bond of the benzonitrile molecule can go from initial linear to final bent structures through different paths. The calculated spectrum is in excellent agreement with experiment.