Identifying the origin for core-level binding-energy shift induced by surface relaxation or nanosolid formation, and quantifying the crystal binding energy in a bulk solid has been a challenge. Here we show that a recent bond order-length-strength correlation mechanism allows us to unify the effects of surface relaxation and nanosolid formation on the core-level binding-energy shift into the atomic-coordination number imperfection. A new and simple method has been developed that enables us to elucidate the intra-atomic trapping energy (the core-level position of an isolated atom) and the crystal binding strength (core-level bulk shift) to the core electrons at the energy levels of Si and a number of metals by matching the predictions to the measurements.
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