The eigenfunctions of electronic Hamiltonians determine the stable structures and dynamics of molecules through the local distributions of their densities. In this paper an a priori upper bound for such local distributions of the densities is given. The bound means that concentration of electrons is prohibited due to the repulsion between the electrons. A relation between one-electron and two-electron densities resulting from the antisymmetry of the eigenfunctions plays a crucial role in the proof.
"Upper bounds of local electronic densities in molecules." Hokkaido Math. J. 52 (3) 495 - 516, October 2023. https://doi.org/10.14492/hokmj/2021-577