10.1002/anie.201909461
Angewandte Chemie International Edition
RESEARCH ARTICLE
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core electrons and linear combinations of atomic orbitals to
construct the valence states. The generalized gradient
approximation (GGA) of the exchange and correlation functional
was used with the Perdew-Burke-Ernzerhof parameterization
(PBE), a double-ζ polarized (DZP) basis set, a real-space grid
defined with an equivalent energy cut-off of 250 Ry. The
geometry optimization for each structure was performed to the
forces smaller than 10 meV/Ang. The mean-field Hamiltonian
obtained from the converged DFT calculation or a simple tight-
binding Hamiltonian was combined with our Gollum quantum
transport code to calculate the phase-coherent, elastic scattering
properties of the each system consist of left (source) and right
(drain) leads and the scattering region. The transmission
coefficient T (E) for electrons of energy E (passing from the
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source to the drain) was calculated via the relation ꢀ ꢀ
=
=
ꢀꢁꢂꢃꢄ ꢀ (ꢀ)ꢀ!(ꢀ)ꢀ (ꢀ)ꢀ!!(ꢀ) . In this expression, ꢀ
ꢀ
!
!
!,!
!
ꢀ ∑!,! ꢀ − ∑!,!
ꢀ
described the level broadening due to the
coupling between left (L) and right (R) electrodes and the central
scattering region, ∑!,!
ꢀ
were the retarded self-energies
!!
associated with this coupling and ꢀ! = ꢀꢁ − ꢀ − ∑! − ∑!
was the retarded Green’s function, where H was the Hamiltonian
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and
S was overlap matrix. Using obtained transmission
coefficient ( ꢀ E ), the conductance could be calculated by
Landauer formula ( G = G! dE T E (− ∂f/ ∂E) ) where ꢀ! =
2ꢀ!/ℎ
was
the
conductance
quantum,
Fermi-Dirac
!!
ꢀ ꢀ = 1 + ꢀꢁꢂ ((ꢀ − ꢀ!) ꢀ!ꢀ)
was
the
distribution function, T was the temperature and kB = 8.6×10-5
eV/K was Boltzmann’s constant.
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This work was supported by the National Key R&D Program of
China (2017YFA0204902), National Natural Science Foundation
of China (Nos. 21673195, 21703188, 21503179). It was also
supported by EPSRC grants EP/P027156/1, EP/N03337X/1,
EP/N017188/1, the EC H2020 FET Open project 767187
“QuIET”, the EU project Bac-to-Fuel and the Australian
Research Council (DP190100074). S.S. acknowledge the
Leverhulme Trust (Leverhulme Early Career Fellowships no.
ECF-2018-375) for funding. H.S. acknowledges the UKRI Future
Leaders Fellowship no. MR/S015329/1. M. N. and M. K.
gratefully acknowledge support from the Forrest Research
Foundation. The crystallographic structures of N1 and N2 were
determined using facilities and instrumentation provided by the
Centre for Microscopy, Characterisation and Analysis (CMCA),
University of Western Australia.
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Keywords: density functional calculations • destructive quantum
interference • scanning tunnelling microscope break junction •
single-molecule studies
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