Invariance of molecular charge transport upon changes of extended molecule size and several related issues

Abstract

SummaryAs a sanity test for the theoretical method employed, studies on (steady-state) charge transport through molecular devices usually confine themselves to check whether the method in question satisfies the charge conservation. Another important test of the theory’s correctness is to check that the computed current does not depend on the choice of the central region (also referred to as the “extended molecule”). This work addresses this issue and demonstrates that the relevant transport and transport-related properties are indeed invariant upon changing the size of the extended molecule, when the embedded molecule can be described within a general single-particle picture (namely, a second-quantized Hamiltonian bilinear in the creation and annihilation operators). It is also demonstrates that the invariance of nonequilibrium properties is exhibited by the exact results but not by those computed approximately within ubiquitous wide- and flat-band limits (WBL and FBL, respectively). To exemplify the limitations of the latter, the phenomenon of negative differential resistance (NDR) is considered. It is shown that the exactly computed current may exhibit a substantial NDR, while the NDR effect is absent or drastically suppressed within the WBL and FBL approximations. The analysis done in conjunction with the WBLs and FBLs reveals why general studies on nonequilibrium properties require a more elaborate theoretical than studies on linear response properties (e.g., ohmic conductance and thermopower) at zero temperature. Furthermore, examples are presented that demonstrate that treating parts of electrodes adjacent to the embedded molecule and the remaining semi-infinite electrodes at different levels of theory (which is exactly what most NEGF-DFT approaches do) is a procedure that yields spurious structures in nonlinear ranges of current–voltage curves.

Transient Charge and Energy Flow in the Wide-Band Limit

“…The WBL for charge transport is justified when the bandwidth is large compared to the applied bias. 21−27 An important requirement for the WBL is that it should not induce any spurious, unphysical dynamics. Its only purpose is to allow for an efficient description of dynamics in large scale open quantum systems.…”

“…The WBL assumes that the detailed structure of the density of states in the leads is not important for the description of transport, which substantially simplifies computations. The WBL for charge transport is justified when the bandwidth is large compared to the applied bias [21][22][23][24][25][26][27] .…”

Modified Superexchange Model for Electron Tunneling Across the Terminated Molecular Wire

“…The operators of creation and annihilation of an electron in the single‐electron band state k are denoted through and , respectively. For a molecular wire, we will use the tight‐binding Hamiltonian in the same form as has been used to study distant superexchange transfer of an electron from a donor to an acceptor or from one electrode to another . It is assumed that the transferred electron can leave the twofold filled energy level of the HOMO n , or occupy an empty energy level of the LUMO n , located on the wire unit .…”

“…For a molecular wire, we will use the tight-binding Hamiltonian in the same form as has been used to study distant superexchange transfer of an electron from a donor to an acceptor [51,52] or from one electrode to another. [25,54,58,[67][68][69] It is assumed that the transferred electron can leave the twofold filled energy level of the HOMO n , or occupy an empty energy level of the LUMO n , located on the wire unit n ¼ 0:1; . .…”

Nonequilibrium diagrammatic technique for Hubbard Green functions

“…We note in passing that NEGF-DFT (and NEGF-TDDFT) approaches have also fundamental limitations related to both foundations of (TD)DFT (utilization of Kohn-Sham orbitals as physical objects, non-uniqueness of the excited-state potentials, question of stability, and chaos of the mapping of densities on potentials, etc.) [38,39] and in combination of DFT with NEGF for transport description [40].…”