Electronic current density expanded in natural orbitals

Quantum electronic currents can be determined directly from off-diagonals of the one electron reduced density matrix. Behaviour of the density matrix in a natural orbital expansion is well understood, whereas very little is known about the current density expressed in any orbital basis. Given the relationship of the current to the density matrix, it seems plausible that improved approximations to the reduced density matrix should lead to better descriptions for the current density. To examine how improved approximations to the reduced density matrix are related to the current density, an upper limit to the error resulting from truncating a natural orbital expansion of the current is found and related to the density matrix and kinetic energy expressed in the same basis. As a consequence, it is confirmed that quantum transport formulations leading to an accurate one-electron reduced density matrix will deliver controllable and well-behaved approximations for quantum electronic currents.