Spatial symmetry holes in many-electron atoms and molecules

When a many-electron system has a spatial symmetry, it is shown that there exist spatial symmetry holes, which imply that two or more electrons are prohibited from being at certain spatial positions simultaneously. Inversion holes, rotation holes, and reflection holes, which result from inversion, twofold rotation, and reflection symmetries, respectively, are discussed in detail. The electron-electron counterbalance hole reported in literature is a particular case of the inversion hole. The spatial symmetry holes are illustrated for simple atoms and molecules.