The core-to-sigma* excited state is repulsive for the bond elongation; on the other hand, the core ionized state and the core-to-pi* state are bound and the core-to-Rydberg states are almost parallel to the potential energy curve of the core ionized state. Thus, the core-electron excitation to the unoccupied sigma* orbital can be mixed with the one-electron Rydberg or continuum orbital, as dependent on the bond distance, and even with the unoccupied pi* orbital in some cases. Within the framework of one-electron picture, we show sigma* orbitals mixed with Rydberg character in the 1s excitation of O2 and CH3F, and Rydberg orbitals mixed with valence character in the 1s excitation of CH4, CO2, and N2O.
