On the length-scale of single-molecule junctions, quantum electron transport is dominated by coherent tunneling through the π-system. While qualitative features can already be captured at a relatively simple and abstract level of Hückel molecular orbital (MO) theory, specific features require taking into account the chemical complexity of the underlying molecular structure — e.g., within ab-initio computational approaches. Moreover, under certain conditions (e.g., resonant tunneling, open-shell configurations, ...), effective single-particle theories may fail to capture relevant elastic and non-elastic electronic scattering mechanisms, thus requiring more sophisticated many-body simulations.

Within the linear combination of atomic orbitals (LCAO) formalism, the accuracy of density functional theory (DFT) is limited (also) by the quality of the basis set, which is to some extent redundant and hence poses a problem of physical interpretation. A possible solution relies on the introduction of local orbitals (LOs) that inherit the information of the atomic chemical environment and provide a natural interpretation of chemical and physical properties [1]. 
A projection onto a suitable subset of a few LOs allows for a significant reduction of computational resources for, e.g., transport and electronic structure calculations, without sacrificing the numerical accuracy. 

Numerical efficiency and accuracy are demonstrated through a series of benchmarks for both molecular junctions (e.g., Au-BDA-Au, polyacetylene bridges) and periodic monolayers (e.g., graphene, h-BN, MoS2) exhibiting different physical and chemical properties [1].

The LOs provide a natural alternative to Wannier functions to downfold the Kohn-Sham Hamiltonian to a suitable correlated subspace to perform many-body simulations. Within this computational framework, it is shown that in organic radicals, the Coulomb repulsion among electrons in partially occupied molecular orbitals results in a giant electronic scattering rate which induces the splitting of the low-lying transport resonance [2]. Such a mechanism is argued to apply to a broad family of radicals and can explain the poor conductance reported in transport experiments.

[1] Gandus et al., J. Chem. Phys.. 153, 194103 (2020)
[2] Gandus et al., arXiv:2301.00282 (2023)

Highlights:

• LOs featured in GPAW 23.6.0 and future versions — see [patchnotes] and [documentation]
  
  

Related readings:

• A similar approach was introduced to disentangle transport contributions of the σ and π systems:
  Borges & Solomon, J. Chem. Phys. 144, 194111 (2016)

• A review for ab-initio + many-body quantum transport simulations
  Jacob, J. Phys.: Condens. Matter 27, 245606 (2015)

It is interesting to consider how scattering processes are included in prominent theoretical transport methodologies. Introducing a phenomenological static scattering rate (Γ), insightful numerical and analytical calculations reveal a clear hierarchy of transport approaches for carriers with finite lifetimes. 
This is demonstrated for archetypal trans-polyacetylene molecular wires within the Su–Schrieffer–Heeger model in the topologically trivial configuration [3]. As a function of wire length (N) within the Landauer-Büttiker ballistic transport formalism, the conductance decays exponentially with N and is independent of Γ, even including vertex corrections. Instead, within the Kubo linear-response formalism, the electron conductance exhibits a hyperbolic scaling with N and converges to the Landauer exponential one as Γ decreases. The electron scattering controls the crossover between a high-temperature activated regime and a low-temperature conductance plateau. In the limit of infinitely long-lived quasi-particles, the Kubo conductivity — to the leading order 1/Γ — reduces to the Boltzmann expression, and the response is activated down to zero temperature.   
Such an analysis guides the choice of transport methodology for model and ab-initio transport simulations in semiconducting molecular wires. 

[3] Valli & Tomczak, J. Comput. Electron. 22, 1363–1376 (2023) 

Related readings:

• The existence of edge states in the topological configuration can drastically modify the scenario:
  Li, Nuckolls, Venkataraman, J. Phys. Chem. Lett. 14, 5141–5147 (2023)

Organic frameworks (e.g., porphyrins or phthalocyanine) with a transition-metal atom core manifest a phenomenon known as spin crossovers (SCO) in which the molecule can switch between a low-spin (LS) and a high-spin (HS) state. The SCO arises from the interplay between the π-ligand field of the organic framework and the Coulomb interaction at the transition-metal atom (e.g., Mn, Fe, Co, Ni, or Cu) which can be tuned by external stimuli (e.g., strain, electric and magnetic fields, a light pulse), thus realizing molecular spin switches. 
The fingerprint of the SCO can be identified in the electronic transport properties of a FeP single-molecule junction as a function, e.g., of mechanical uniaxial strain [4]. In the S=1 LS state, Fe is in the 2+ oxidation state (i.e., with 6 electrons in the Fe-3d shell) one of the 3d orbitals from the eg-manifold (e.g., dx2-y2) is far from the Fermi energy and empty, due to the strong ligand field splitting. Uniaxial strain results in a softening of the Fe-N bonds, and a corresponding reduction of the ligand field. Eventually, it becomes favorable to promote an electron to the dx2-y2 orbital, thus realizing an S=2 HS state. The redistribution of the electron charge within the Fe-3d shell results in an abrupt change of the electron transmission due to nearly-resonant transport channel through the partially-filled dx2-y2 orbital close to the Fermi energy [4]. 

[4] Bhandary et al., Nanoscale Adv.  3, 4990–4995 (2021)

It is well established that, in the coherent electron transport regime, π-conjugated single-molecule junctions bridging metallic electrodes display quantum interference (QI) effects, which appear in the electronic transmission function. Typically, a Fano shape (with e.g., q>0) identifies the resonant scattering between a discrete state (resonance) and a continuum (background) while an antiresonance (q=0) is the hallmark of destructive QI. The latter is particularly interesting for its dramatic effects on the electronic transmission, which changes a few orders of magnitude over a narrow energy range. 

In graphene nanostructures, due to the sublattice imbalance realized at zigzag edges, the Coulomb interaction makes the π system unstable towards magnetism [1]. Remarkably, the simultaneous presence of a spin-ordered pattern and of destructive QI induces spin-resolved antiresonances, which selectively suppress electronic transport in each spin channel at different energies. This mechanism is at the heart of QI assisted spin-filtering effect [2]. 

Electrostatic control of the current spin polarization can be achieved by inducing a spatial charge modulation that can couple to external electric fields. This scenario could be realized in practice, e.g., by deposition of graphene on a suitable substrate, such as h-BN, which generates a different chemical environment for each sublattice [2,3].  

This represents a specific realization of a generic mechanism that applies also to other degrees of freedom besides spins, e.g., the valley index [3].

[1] Valli et al., Phys. Rev. B 94, 245146 (2016)
[2] Valli et al., Nano Lett. 18, 2158–2164 (2018)
[3] Valli et al., Phys. Rev. B 100, 075118 (2019)

Cross-reference:

For additional material related to spin phenomena in graphene nanostructures see also the discussion at this [link]

Related readings:

• Press release: "Graphene flakes for future transistors"  [link]

• The spin-selective splitting of the QI node can be exploited to drive a spin current with a temperature gradient:
  Phùng et al., Phys. Rev. B 102, 035160 (2020)

It has been shown that QI features survive in the presence of electron-electron scattering [1,2,3], and are also resilient against electron-phonon scattering and disorder [4].

Remarkably, the transmission function exhibits a universal behavior: T(ω) ∝ ω² that can be completely ascribed to the presence of a nearby QI antiresonance, and it results in a non-linear I-V characteristic: I ∝ V³ [4]. Hence, it suggests that the dramatic effects of QI are not limited to the conductance but extend away from the Fermi energy within the HOMO-LUMO gap, and the fingerprint of QI can be identified in the electric response (e.g., the I-V characteristic) even when the suppression of the conductance is weak. 

[4] Valli et al., Carbon 214, 118358 (2023)

 Related readings:

• Press release: "Perfection is futile" [link]

• AI-generated summary (but proofread by a human) experiment [science cast]

The QI properties are strongly connected with the topological structure of the molecular bridge. In the case of the organometallic compound phenyl-lithium (PhLi) where a meta-benzene molecular junction bonds with a Li atom. The transport properties depend on the strength and the topology of the phenyl-Li bond, i.e., whether Li forms a π bond (e.g., with the Li atom in the hollow position) or a σ- bond with an sp3-hybridized C atom (effectively removing it from the π system).

[5] Valli, in preparation

Related readings:

• Sadlej-Sosnowskaa, Phys. Chem. Chem. Phys. 17, 23716 (2015)