Off-diagonal derivative discontinuities in the reduced density matrices of electronic systems

An explicit expression relating the magnitude of the fifth-order off-diagonal cusp in the real part of the one-electron reduced density matrix to the "on-top" two-electron density is derived in a rigorous manner from the behavior of the underlying electronic wavefunction at the electron-electron coalescence. The implications of the presence of this cusp upon electronic structure calculations of quantum chemistry and solid-state physics, including the limits imposed upon their accuracy, are elucidated. In particular, the power-law decay of the occupation numbers of the natural orbitals is demonstrated for ¹S states of systems composed of arbitrary even numbers of electrons. The practical importance of analogous off-diagonal cusps in many-electron reduced density matrices is briefly discussed.