Vibronic fine structure in the nitrogen 1s photoelectron spectra of molecules from Franck-Condon simulations: Azines

Abstract

Vibronic coupling plays a pivotal role in molecular spectroscopy. We present a theoretical study on vibrationally resolved x-ray photoelectron spectra (XPS) of seven azines (${\mathrm{C}}_{x}{\mathrm{H}}_{y}{\mathrm{N}}_{z}$; pyridine, three diazines, two triazines, and one tetrazine) at the nitrogen $1s$ edge, to explore the vibronic coupling effects as influenced by consecutive replacement of the CH group with a N atom. Franck-Condon simulations were performed with the Duschinsky rotation effect included, where the electronic structure was calculated by the density functional theory. Validations on pyrimidine show good agreement with the experiment, weak functional dependence, and weak mode mixing effect. We observed an evident blue shift in binding energies with the increasing number of N atoms in this series, together with molecule-dependent vibronic fine structures. These molecules have either ${\mathrm{C}}_{\text{2v}}$ or ${\mathrm{C}}_{\text{s}}$ molecular symmetry at the optimized core-ionized geometries. Franck-Condon-active vibrational modes were identified to be low frequency (500--1650 ${\mathrm{cm}}^{\ensuremath{-}1}$), totally symmetric (${A}_{1}$ or ${A}^{\ensuremath{'}}$), in-plane ring deformation modes. Core ionization on ${\mathrm{N}}^{*}$ always leads to elongation of the ${\mathrm{N}}^{*}\ensuremath{-}\mathrm{N}$ bond length, accompanied by an increase of the $\ensuremath{\angle}\mathrm{C}\ensuremath{-}{\mathrm{N}}^{*}\ensuremath{-}X$ bond angle ($X=\mathrm{C}$, N). Our study predicts accurate theoretical reference spectra for the azine family and provides useful information on the properties of the core-ionized states as influenced by the structural change of $\mathrm{CH}\ensuremath{\leftrightarrow}\mathrm{N}$ replacement.