We study the relative ability of several models of x-ray absorption spectra to capture the Franck–Condon structure apparent from an experiment on gaseous nitrogen. In doing so, we adopt the Born–Oppenheimer approximation and a constrained density functional theory method for computing the energies of the x-ray-excited molecule. Starting from an otherwise classical model for the spectrum, we systematically introduce more realistic physics, first by substituting the quantum mechanical nuclear radial density in the bond separation R for the classical radial density, then by adding the effect of zero-point energy and other level shifts, and finally by including explicit rovibrational quantization of both the ground and excited states. The quantization is determined exactly, using a discrete variable representation (DVR). We show that the near-edge x-ray absorption fine structure (NEXAFS) spectrum can be predicted semiquantitatively within this framework. We also address the possibility of non-trivial temperature dependence in the spectrum. By using constrained density functional theory in combination with more accurate potentials, we demonstrate that it is possible to improve the predicted spectrum. Ultimately, we establish the predictive limits of our method with respect to vibrational fine structure in NEXAFS spectra.
S. Fatehi et al., J. Chem. Phys. 132, 094302 (2010)