Vibrationally resolved near-edge x-ray absorption spectra at the K-edge for a number of small molecules have been computed from anharmonic vibrational configuration interaction calculations of the Franck-Condon factors. The potential energy surfaces for ground and core-excited states were obtained at the core-valence separated CC2, CCSD, CCSDR(3), and CC3 levels of theory, employing the adaptive density-guided approach scheme to select the single points at which to perform the energy calculations. We put forward an initial attempt to include pair-mode coupling terms to describe the potential of polyatomic molecules.