Off-diagonal derivative discontinuities in the reduced density matrices of electronic systems
Jerzy Ciosłowski
Abstract
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.