Here, we assess the accuracy of various approaches implemented in Vienna ab initio simulation package code to estimate core-level binding energy shifts (ΔBEs) using a projector augmented wave method to treat core electrons. The performance of the Perdew-Burke-Ernzerhof (PBE) and the Tao-Perdew-Staroverov-Scuseria (TPSS) exchange-correlation density functionals is examined on a dataset of 68 molecules containing B→F atoms in diverse chemical environments, accounting for 185 different 1s core level binding energy shifts, for which both experimental gas-phase X-ray photoemission (XPS) data and accurate all electron ΔBEs are available. Four procedures to calculate core-level shifts are investigated. Janak-Slater transition state approach yields mean absolute errors of 0.37 (0.21) eV at PBE (TPSS) level, similar to highly accurate all electron ΔSCF approaches using same functionals, and close to XPS experimental accuracy of 0.1 eV. The study supports the use of these procedures to assign ΔBEs of molecular moieties on material surfaces of interest in surface science, nanotechnology, and heterogeneous catalysis.