Role of the virtual orbitals and HOMO-LUMO gap in mean-field approximations to the conductance of molecular junctions

Abstract

We investigate the role of virtual orbitals on the molecular conductance at the static mean-field level of approximation in the nonequilibrium Green's functions (NEGFs) formalism, within a model system with wide-band leads. We use a projector operator formalism to define corrections to the molecular Hamiltonian that solely act on its virtual-orbital subspace, leaving ground-state properties invariant. In its most trivial limit, these corrections reduce to the scissor operator. More generally, we also propose a parameterless correction aimed toward improved fundamental energy gap estimates in the context of local self-energy approximations. We demonstrate how within any mean-field description dramatical differences in conductance values can be generated with the application of the scissor operators. For our model system, we show how the dramatical difference in conductance values obtained from the restricted Hartree--Fock and Hartree--Fermi--Amaldi approximations can be related to the different HOMO-LUMO gaps of each method and to a lesser extent differences in the molecular orbitals. Finally, we comment on the impact of different coupling-strength regimes and illustrate how the ${E}_{g}$-related differences in the two mean-field descriptions gradually lose their impact on the conductance with increasing molecular coupling to the leads. Our analysis points out some implications of the pragmatic use of the Kohn--Sham (KS) potentials in the NEGF-KS theory, and how to modify the scheme toward better physical consistency so that the resulting Hamiltonian is more physical and the position of the transmission resonances is improved.