Destructive quantum interference in electron transport: A reconciliation of the molecular orbital and the atomic orbital perspective

Abstract

Destructive quantum interference (DQI) in single molecule electronics is a purely quantum mechanical effect and entirely defined by inherent properties of the molecule in the junction such as its structure and symmetry. This definition of DQI by molecular properties alone suggests its relation to other more general concepts in chemistry as well as the possibility of deriving simple models for its understanding and molecular device design. Recently, two such models have gained wide spread attention, where one was a graphical scheme based on visually inspecting the connectivity of carbon sites in conjugated π systems in an atomic orbital (AO) basis and the other one put the emphasis on the amplitudes and signs of the frontier molecular orbitals (MOs). There have been discussions on the range of applicability for these schemes, but ultimately conclusions from topological molecular Hamiltonians should not depend on whether they are drawn from an AO or a MO representation, as long as all the orbitals are taken into account. In this article we clarify the relation between both models in terms of the zeroth order Green's function and compare their predictions for a variety of systems. From this comparison we conclude that for a correct description of DQI from a MO perspective it is necessary to include the contributions from all MOs rather than just those from the frontier orbitals. The cases where DQI effects can be successfully predicted within a frontier orbital approximation we show to be limited to alternant even-membered hydrocarbons, as a a direct consequence of the Coulson-Rushbrooke pairing theorem in quantum chemistry.

Scale-Up of Room-Temperature Constructive Quantum Interference from Single Molecules to Self-Assembled Molecular-Electronic Films

“…molecules exhibit CQI near their gap centres and the conductance ratio arises from the different degrees of constructive QI associated with their different connectivities. 33,34,[48][49][50][51][52][53] When the terminal groups of molecules are changed from thioethers to thioacetates, the transmission coefficients for molecules 3 and 4 show the same trend as those associated with molecules 1 and 2 (see Table 1).…”

Quantum interference in coherent tunneling through branched molecular junctions containing ferrocene centers

“…Larsson's formula was originally introduced for the definition of the transfer integral in the context of Marcus theory for the description of electron hopping [57][58][59] , but recently it has been shown that it can be also used for approximating T (E) as T (E) ∼ Γ 2 (E) for coherent tunneling 40,60 , where the resulting T(E) can be normalized 60 and qualitatively reproduces the curves obtained from NEGF-TB 17 . Equation 1 has the additional advantage that a simple mathematical condition can be defined for the energetic positions of DQI induced zeros in T(E), because at the same energies the effective coupling Γ(E) = γ 1 /(E −ε 1 )+ γ 2 /(E−ε 2 )+γ 3 /(E−ε 3 ) with γ i = α i β i for the three MOs resulting from the simple model in Fig.…”

“…Our definition of DQI is that the transmission through a system with more than one MO around E F is lower than the sum of the individual contributions of these MOs to T(E) 40 . The exact energetic position of the Fermi energy within the HOMO-LUMO gap, which is also affected by the underestimation of this gap in our calculations due to the PBE parametrization of the XC functional, will have a crucial impact on the quantitative conductance but qualitatively DQI will always result in a significant conductance lowering for the structures where it occurs regardless of the details of the Fermi level alignment 17 .…”

Characterizing destructive quantum interference in electron transport

“…With this observation, many guidelines have been developed for predicting molecules and moleculeelectrode configurations that exhibit DQI [19][20][21][22][23][24][25][26][27], including some graphical approaches [28][29][30]. However, these guidelines tend to focus only on the existence of DQI, and are most applicable to alternant hydrocarbons…”