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Electrons are believed to avoid one another in space （correlation） due to the Coulomb repulsion and/or the Pauli exclusion principle. It is shown, using examples of two-electron systems, that indeed the mean electron-electron distance increases in case of the ground electronic state as compared to the independent electron model. It is demonstrated however that there exist excited states, often of low energy, in which the electrons, while having a lot of free physical space （with nuclei being absent）, choose to be close to each other in their motion （＂anticorrelation＂）, as if they mutually attracted one another. The source of this effect, quantum- mechanical in nature, is the orthogonality of the eigenfunctions, that forces the electronic wave functions to differ widely, even at the price of short electron-electron distances. There are also excited states with a mixed behaviour, with complex and often intriguing correlation-anticorrelation patterns.